diff --git a/toolchain/check/testdata/alias/no_prelude/alias_of_alias.carbon b/toolchain/check/testdata/alias/no_prelude/alias_of_alias.carbon
index 7a1df001bf91..29e92c854ace 100644
--- a/toolchain/check/testdata/alias/no_prelude/alias_of_alias.carbon
+++ b/toolchain/check/testdata/alias/no_prelude/alias_of_alias.carbon
@@ -46,6 +46,7 @@ let d: c = {};
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/alias/no_prelude/export_name.carbon b/toolchain/check/testdata/alias/no_prelude/export_name.carbon
index 2d94efaf6cb1..5e40b73ede28 100644
--- a/toolchain/check/testdata/alias/no_prelude/export_name.carbon
+++ b/toolchain/check/testdata/alias/no_prelude/export_name.carbon
@@ -91,12 +91,15 @@ var d: D* = &c;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- export.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -117,12 +120,15 @@ var d: D* = &c;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- export_orig.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -143,6 +149,7 @@ var d: D* = &c;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- use_export.carbon
@@ -150,6 +157,7 @@ var d: D* = &c;
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -172,6 +180,7 @@ var d: D* = &c;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -216,6 +225,7 @@ var d: D* = &c;
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT:   %.4: type = ptr_type %C [template]
 // CHECK:STDOUT: }
@@ -246,6 +256,7 @@ var d: D* = &c;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/alias/no_prelude/fail_aliased_name_in_diag.carbon b/toolchain/check/testdata/alias/no_prelude/fail_aliased_name_in_diag.carbon
index 30cb57538135..7b3ce9c9ddef 100644
--- a/toolchain/check/testdata/alias/no_prelude/fail_aliased_name_in_diag.carbon
+++ b/toolchain/check/testdata/alias/no_prelude/fail_aliased_name_in_diag.carbon
@@ -52,6 +52,7 @@ let c_var: c = d;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -59,6 +60,7 @@ let c_var: c = d;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/alias/no_prelude/fail_modifiers.carbon b/toolchain/check/testdata/alias/no_prelude/fail_modifiers.carbon
index 8dfcc2101c50..e19ad43b6f30 100644
--- a/toolchain/check/testdata/alias/no_prelude/fail_modifiers.carbon
+++ b/toolchain/check/testdata/alias/no_prelude/fail_modifiers.carbon
@@ -77,5 +77,6 @@ extern alias C = Class;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Class
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/alias/no_prelude/fail_name_conflict.carbon b/toolchain/check/testdata/alias/no_prelude/fail_name_conflict.carbon
index e8a5270ee375..2f9ad7adb6e2 100644
--- a/toolchain/check/testdata/alias/no_prelude/fail_name_conflict.carbon
+++ b/toolchain/check/testdata/alias/no_prelude/fail_name_conflict.carbon
@@ -62,6 +62,7 @@ alias b = C;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/alias/no_prelude/import.carbon b/toolchain/check/testdata/alias/no_prelude/import.carbon
index 225bdb34df19..706acb2e8f4c 100644
--- a/toolchain/check/testdata/alias/no_prelude/import.carbon
+++ b/toolchain/check/testdata/alias/no_prelude/import.carbon
@@ -95,12 +95,15 @@ var c: () = a_alias_alias;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- class2.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %.3: type = ptr_type %C [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -131,12 +134,15 @@ var c: () = a_alias_alias;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- class3.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %.3: type = ptr_type %C [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -162,6 +168,7 @@ var c: () = a_alias_alias;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- var1.carbon
diff --git a/toolchain/check/testdata/alias/no_prelude/import_access.carbon b/toolchain/check/testdata/alias/no_prelude/import_access.carbon
index bd885ef95a77..fcac795c57ea 100644
--- a/toolchain/check/testdata/alias/no_prelude/import_access.carbon
+++ b/toolchain/check/testdata/alias/no_prelude/import_access.carbon
@@ -75,6 +75,7 @@ var inst: Test.A = {};
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- def.impl.carbon
@@ -82,6 +83,7 @@ var inst: Test.A = {};
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -107,6 +109,7 @@ var inst: Test.A = {};
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/alias/no_prelude/import_order.carbon b/toolchain/check/testdata/alias/no_prelude/import_order.carbon
index 902225cd7b3f..0d985b67074a 100644
--- a/toolchain/check/testdata/alias/no_prelude/import_order.carbon
+++ b/toolchain/check/testdata/alias/no_prelude/import_order.carbon
@@ -68,6 +68,7 @@ var a_val: a = {.v = b_val.v};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .v = %.loc4_16
+// CHECK:STDOUT:   complete_type_witness = %.loc4_22
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- b.carbon
@@ -76,6 +77,7 @@ var a_val: a = {.v = b_val.v};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.v: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT:   %.4: type = unbound_element_type %C, %empty_tuple.type [template]
@@ -122,6 +124,7 @@ var a_val: a = {.v = b_val.v};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.6
 // CHECK:STDOUT:   .v = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/alias/no_prelude/in_namespace.carbon b/toolchain/check/testdata/alias/no_prelude/in_namespace.carbon
index 8f48bbf3bd98..94a6009d1c01 100644
--- a/toolchain/check/testdata/alias/no_prelude/in_namespace.carbon
+++ b/toolchain/check/testdata/alias/no_prelude/in_namespace.carbon
@@ -68,6 +68,7 @@ fn F() -> NS.a {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .v = %.loc11_16
+// CHECK:STDOUT:   complete_type_witness = %.loc11_22
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %return: %C {
diff --git a/toolchain/check/testdata/as/adapter_conversion.carbon b/toolchain/check/testdata/as/adapter_conversion.carbon
index 4cf6b947dedb..9561654e841f 100644
--- a/toolchain/check/testdata/as/adapter_conversion.carbon
+++ b/toolchain/check/testdata/as/adapter_conversion.carbon
@@ -197,6 +197,7 @@ var b: B = {.x = 1} as B;
 // CHECK:STDOUT:   .x = %.loc5_8
 // CHECK:STDOUT:   .y = %.loc6_8
 // CHECK:STDOUT:   .Make = %Make.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -206,6 +207,7 @@ var b: B = {.x = 1} as B;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Make() -> %return: %A {
@@ -333,6 +335,7 @@ var b: B = {.x = 1} as B;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -407,6 +410,7 @@ var b: B = {.x = 1} as B;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc4_21
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -416,6 +420,7 @@ var b: B = {.x = 1} as B;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -425,6 +430,7 @@ var b: B = {.x = 1} as B;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -434,6 +440,7 @@ var b: B = {.x = 1} as B;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -518,6 +525,7 @@ var b: B = {.x = 1} as B;
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .x = %.loc5_8
 // CHECK:STDOUT:   .y = %.loc6_8
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -527,6 +535,7 @@ var b: B = {.x = 1} as B;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -639,6 +648,7 @@ var b: B = {.x = 1} as B;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .x = %.loc5_8
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -648,6 +658,7 @@ var b: B = {.x = 1} as B;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/as/identity.carbon b/toolchain/check/testdata/as/identity.carbon
index 72570b893bd9..445c754ad6a0 100644
--- a/toolchain/check/testdata/as/identity.carbon
+++ b/toolchain/check/testdata/as/identity.carbon
@@ -96,6 +96,7 @@ fn Initializing() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%X
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Value(%n.param_patt: %X) {
diff --git a/toolchain/check/testdata/as/no_prelude/tuple.carbon b/toolchain/check/testdata/as/no_prelude/tuple.carbon
index faf01c5eb85f..80f4559dc246 100644
--- a/toolchain/check/testdata/as/no_prelude/tuple.carbon
+++ b/toolchain/check/testdata/as/no_prelude/tuple.carbon
@@ -65,6 +65,7 @@ fn Var() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%X
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Make() -> %X;
diff --git a/toolchain/check/testdata/as/overloaded.carbon b/toolchain/check/testdata/as/overloaded.carbon
index a81667943740..5cb5330ce522 100644
--- a/toolchain/check/testdata/as/overloaded.carbon
+++ b/toolchain/check/testdata/as/overloaded.carbon
@@ -158,6 +158,7 @@ let n: i32 = ((4 as i32) as X) as i32;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%X
 // CHECK:STDOUT:   .n = %.loc12_8
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Convert.2[%self.param_patt: %i32]() -> %return: %X {
diff --git a/toolchain/check/testdata/builtins/float/eq.carbon b/toolchain/check/testdata/builtins/float/eq.carbon
index ccc10b2e8a28..4a3b022ebb2b 100644
--- a/toolchain/check/testdata/builtins/float/eq.carbon
+++ b/toolchain/check/testdata/builtins/float/eq.carbon
@@ -150,6 +150,7 @@ fn WrongResult(a: f64, b: f64) -> f64 = "float.eq";
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%True
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @False {
@@ -157,6 +158,7 @@ fn WrongResult(a: f64, b: f64) -> f64 = "float.eq";
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%False
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Eq(%a.param_patt: f64, %b.param_patt: f64) -> bool = "float.eq";
diff --git a/toolchain/check/testdata/builtins/float/greater.carbon b/toolchain/check/testdata/builtins/float/greater.carbon
index ada27a1a1a45..92aa05638ffb 100644
--- a/toolchain/check/testdata/builtins/float/greater.carbon
+++ b/toolchain/check/testdata/builtins/float/greater.carbon
@@ -169,6 +169,7 @@ fn RuntimeCall(a: f64, b: f64) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%True
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @False {
@@ -176,6 +177,7 @@ fn RuntimeCall(a: f64, b: f64) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%False
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Greater(%a.param_patt: f64, %b.param_patt: f64) -> bool = "float.greater";
diff --git a/toolchain/check/testdata/builtins/float/greater_eq.carbon b/toolchain/check/testdata/builtins/float/greater_eq.carbon
index e244b86c4ff7..4678f30a58bc 100644
--- a/toolchain/check/testdata/builtins/float/greater_eq.carbon
+++ b/toolchain/check/testdata/builtins/float/greater_eq.carbon
@@ -169,6 +169,7 @@ fn RuntimeCall(a: f64, b: f64) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%True
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @False {
@@ -176,6 +177,7 @@ fn RuntimeCall(a: f64, b: f64) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%False
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @GreaterEq(%a.param_patt: f64, %b.param_patt: f64) -> bool = "float.greater_eq";
diff --git a/toolchain/check/testdata/builtins/float/less.carbon b/toolchain/check/testdata/builtins/float/less.carbon
index d5923b778dad..1d80430a6cc9 100644
--- a/toolchain/check/testdata/builtins/float/less.carbon
+++ b/toolchain/check/testdata/builtins/float/less.carbon
@@ -169,6 +169,7 @@ fn RuntimeCall(a: f64, b: f64) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%True
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @False {
@@ -176,6 +177,7 @@ fn RuntimeCall(a: f64, b: f64) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%False
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Less(%a.param_patt: f64, %b.param_patt: f64) -> bool = "float.less";
diff --git a/toolchain/check/testdata/builtins/float/less_eq.carbon b/toolchain/check/testdata/builtins/float/less_eq.carbon
index d769d01a4d69..c7b4e898a68c 100644
--- a/toolchain/check/testdata/builtins/float/less_eq.carbon
+++ b/toolchain/check/testdata/builtins/float/less_eq.carbon
@@ -169,6 +169,7 @@ fn RuntimeCall(a: f64, b: f64) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%True
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @False {
@@ -176,6 +177,7 @@ fn RuntimeCall(a: f64, b: f64) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%False
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @LessEq(%a.param_patt: f64, %b.param_patt: f64) -> bool = "float.less_eq";
diff --git a/toolchain/check/testdata/builtins/float/neq.carbon b/toolchain/check/testdata/builtins/float/neq.carbon
index e82dd10ccbae..39c1e787d8e9 100644
--- a/toolchain/check/testdata/builtins/float/neq.carbon
+++ b/toolchain/check/testdata/builtins/float/neq.carbon
@@ -150,6 +150,7 @@ fn WrongResult(a: f64, b: f64) -> f64 = "float.neq";
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%True
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @False {
@@ -157,6 +158,7 @@ fn WrongResult(a: f64, b: f64) -> f64 = "float.neq";
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%False
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Neq(%a.param_patt: f64, %b.param_patt: f64) -> bool = "float.neq";
diff --git a/toolchain/check/testdata/builtins/int/eq.carbon b/toolchain/check/testdata/builtins/int/eq.carbon
index b5329d02f83a..9970cfb841c6 100644
--- a/toolchain/check/testdata/builtins/int/eq.carbon
+++ b/toolchain/check/testdata/builtins/int/eq.carbon
@@ -162,6 +162,7 @@ fn WrongResult(a: i32, b: i32) -> i32 = "int.eq";
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%True
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @False {
@@ -169,6 +170,7 @@ fn WrongResult(a: i32, b: i32) -> i32 = "int.eq";
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%False
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Eq(%a.param_patt: %i32, %b.param_patt: %i32) -> bool = "int.eq";
diff --git a/toolchain/check/testdata/builtins/int/greater.carbon b/toolchain/check/testdata/builtins/int/greater.carbon
index 5b9aabcdd3a4..2c8d9aac79c1 100644
--- a/toolchain/check/testdata/builtins/int/greater.carbon
+++ b/toolchain/check/testdata/builtins/int/greater.carbon
@@ -184,6 +184,7 @@ fn RuntimeCall(a: i32, b: i32) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%True
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @False {
@@ -191,6 +192,7 @@ fn RuntimeCall(a: i32, b: i32) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%False
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Greater(%a.param_patt: %i32, %b.param_patt: %i32) -> bool = "int.greater";
diff --git a/toolchain/check/testdata/builtins/int/greater_eq.carbon b/toolchain/check/testdata/builtins/int/greater_eq.carbon
index ef19d8210de6..a58b22ba47d7 100644
--- a/toolchain/check/testdata/builtins/int/greater_eq.carbon
+++ b/toolchain/check/testdata/builtins/int/greater_eq.carbon
@@ -184,6 +184,7 @@ fn RuntimeCall(a: i32, b: i32) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%True
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @False {
@@ -191,6 +192,7 @@ fn RuntimeCall(a: i32, b: i32) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%False
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @GreaterEq(%a.param_patt: %i32, %b.param_patt: %i32) -> bool = "int.greater_eq";
diff --git a/toolchain/check/testdata/builtins/int/less.carbon b/toolchain/check/testdata/builtins/int/less.carbon
index c190fd080f56..5c6a427345e6 100644
--- a/toolchain/check/testdata/builtins/int/less.carbon
+++ b/toolchain/check/testdata/builtins/int/less.carbon
@@ -184,6 +184,7 @@ fn RuntimeCall(a: i32, b: i32) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%True
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @False {
@@ -191,6 +192,7 @@ fn RuntimeCall(a: i32, b: i32) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%False
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Less(%a.param_patt: %i32, %b.param_patt: %i32) -> bool = "int.less";
diff --git a/toolchain/check/testdata/builtins/int/less_eq.carbon b/toolchain/check/testdata/builtins/int/less_eq.carbon
index 9a4dfe406b01..37fa9ebc9105 100644
--- a/toolchain/check/testdata/builtins/int/less_eq.carbon
+++ b/toolchain/check/testdata/builtins/int/less_eq.carbon
@@ -184,6 +184,7 @@ fn RuntimeCall(a: i32, b: i32) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%True
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @False {
@@ -191,6 +192,7 @@ fn RuntimeCall(a: i32, b: i32) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%False
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @LessEq(%a.param_patt: %i32, %b.param_patt: %i32) -> bool = "int.less_eq";
diff --git a/toolchain/check/testdata/builtins/int/neq.carbon b/toolchain/check/testdata/builtins/int/neq.carbon
index 27e3edb47c9d..98be3f18f8de 100644
--- a/toolchain/check/testdata/builtins/int/neq.carbon
+++ b/toolchain/check/testdata/builtins/int/neq.carbon
@@ -153,6 +153,7 @@ fn RuntimeCall(a: i32, b: i32) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%True
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @False {
@@ -160,6 +161,7 @@ fn RuntimeCall(a: i32, b: i32) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%False
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Neq(%a.param_patt: %i32, %b.param_patt: %i32) -> bool = "int.neq";
diff --git a/toolchain/check/testdata/class/access_modifers.carbon b/toolchain/check/testdata/class/access_modifers.carbon
index 19ebebcc852e..adfa357f3592 100644
--- a/toolchain/check/testdata/class/access_modifers.carbon
+++ b/toolchain/check/testdata/class/access_modifers.carbon
@@ -243,6 +243,7 @@ class A {
 // CHECK:STDOUT:   .SOME_INTERNAL_CONSTANT [private] = %SOME_INTERNAL_CONSTANT
 // CHECK:STDOUT:   .SomeInternalFunction [private] = %SomeInternalFunction.decl
 // CHECK:STDOUT:   .Make = %Make.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @SomeInternalFunction() -> %i32 {
@@ -346,6 +347,7 @@ class A {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .x [protected] = %.loc5_18
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Run() {
@@ -462,6 +464,7 @@ class A {
 // CHECK:STDOUT:   .GetRadius = %GetRadius.decl
 // CHECK:STDOUT:   .SomeInternalFunction [private] = %SomeInternalFunction.decl
 // CHECK:STDOUT:   .Compute = %Compute.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc18
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @GetRadius[%self.param_patt: %Circle]() -> %i32 {
@@ -556,6 +559,7 @@ class A {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .x = %x
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -645,6 +649,7 @@ class A {
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .x [protected] = %x
 // CHECK:STDOUT:   .y [private] = %y
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -696,6 +701,7 @@ class A {
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .F [private] = %F.decl
 // CHECK:STDOUT:   .G [private] = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
diff --git a/toolchain/check/testdata/class/adapt.carbon b/toolchain/check/testdata/class/adapt.carbon
index e4a17e63f5c6..dcaafe825880 100644
--- a/toolchain/check/testdata/class/adapt.carbon
+++ b/toolchain/check/testdata/class/adapt.carbon
@@ -98,6 +98,7 @@ fn F(a: AdaptNotExtend) {
 // CHECK:STDOUT:   .Self = constants.%SomeClass
 // CHECK:STDOUT:   .a = %.loc5_8
 // CHECK:STDOUT:   .b = %.loc6_8
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @SomeClassAdapter {
@@ -107,6 +108,7 @@ fn F(a: AdaptNotExtend) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%SomeClassAdapter
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @StructAdapter {
@@ -124,6 +126,7 @@ fn F(a: AdaptNotExtend) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%StructAdapter
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_not_extend.carbon
@@ -173,6 +176,7 @@ fn F(a: AdaptNotExtend) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Adapted
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @AdaptNotExtend {
@@ -182,6 +186,7 @@ fn F(a: AdaptNotExtend) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%AdaptNotExtend
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.1();
diff --git a/toolchain/check/testdata/class/base.carbon b/toolchain/check/testdata/class/base.carbon
index 2cec975e15ff..9256a6dd5843 100644
--- a/toolchain/check/testdata/class/base.carbon
+++ b/toolchain/check/testdata/class/base.carbon
@@ -147,6 +147,7 @@ class Derived {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Base
 // CHECK:STDOUT:   .b = %.loc4_8
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Derived {
@@ -164,6 +165,7 @@ class Derived {
 // CHECK:STDOUT:   .base = %.loc8
 // CHECK:STDOUT:   .d = %.loc10_8
 // CHECK:STDOUT:   extend %Base.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Make() -> %return: %Derived {
@@ -257,6 +259,7 @@ class Derived {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Base
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Derived {
@@ -271,5 +274,6 @@ class Derived {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Derived
 // CHECK:STDOUT:   .d = %.loc7_8
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/base_field.carbon b/toolchain/check/testdata/class/base_field.carbon
index 9127cf743458..57918c884b53 100644
--- a/toolchain/check/testdata/class/base_field.carbon
+++ b/toolchain/check/testdata/class/base_field.carbon
@@ -108,6 +108,7 @@ fn Access(p: Derived*) -> i32* {
 // CHECK:STDOUT:   .a = %.loc12_8
 // CHECK:STDOUT:   .b = %.loc13_8
 // CHECK:STDOUT:   .c = %.loc14_8
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Derived {
@@ -131,6 +132,7 @@ fn Access(p: Derived*) -> i32* {
 // CHECK:STDOUT:   .d = %.loc20_8
 // CHECK:STDOUT:   .e = %.loc21_8
 // CHECK:STDOUT:   extend %Base.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc22
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Access(%p.param_patt: %.10) -> %.11 {
diff --git a/toolchain/check/testdata/class/base_function_unqualified.carbon b/toolchain/check/testdata/class/base_function_unqualified.carbon
index 440b0e3f0b60..896c458e92a2 100644
--- a/toolchain/check/testdata/class/base_function_unqualified.carbon
+++ b/toolchain/check/testdata/class/base_function_unqualified.carbon
@@ -68,6 +68,7 @@ fn Derived.H() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Base
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Derived {
@@ -83,6 +84,7 @@ fn Derived.H() {
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   .H = %H.decl
 // CHECK:STDOUT:   extend %Base.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc20
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F();
diff --git a/toolchain/check/testdata/class/base_method.carbon b/toolchain/check/testdata/class/base_method.carbon
index f7e1121f7a89..b65ba56e111a 100644
--- a/toolchain/check/testdata/class/base_method.carbon
+++ b/toolchain/check/testdata/class/base_method.carbon
@@ -120,6 +120,7 @@ fn Call(p: Derived*) {
 // CHECK:STDOUT:   .Self = constants.%Base
 // CHECK:STDOUT:   .a = %.loc12_8
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Derived {
@@ -131,6 +132,7 @@ fn Call(p: Derived*) {
 // CHECK:STDOUT:   .Self = constants.%Derived
 // CHECK:STDOUT:   .base = %.loc22
 // CHECK:STDOUT:   extend %Base.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc23
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F[addr %self.param_patt: %.3]() {
diff --git a/toolchain/check/testdata/class/base_method_qualified.carbon b/toolchain/check/testdata/class/base_method_qualified.carbon
index 5e3ce4eb90bf..504ac88410b2 100644
--- a/toolchain/check/testdata/class/base_method_qualified.carbon
+++ b/toolchain/check/testdata/class/base_method_qualified.carbon
@@ -188,6 +188,7 @@ fn PassDerivedToBaseIndirect(p: Derived*) -> i32 {
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   extend %Base.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc23
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Base {
@@ -229,6 +230,7 @@ fn PassDerivedToBaseIndirect(p: Derived*) -> i32 {
 // CHECK:STDOUT:   .Self = constants.%Base
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.1[%self.param_patt: %Base]() -> %i32;
diff --git a/toolchain/check/testdata/class/base_method_shadow.carbon b/toolchain/check/testdata/class/base_method_shadow.carbon
index 8ec252a24214..e497e75d093b 100644
--- a/toolchain/check/testdata/class/base_method_shadow.carbon
+++ b/toolchain/check/testdata/class/base_method_shadow.carbon
@@ -130,6 +130,7 @@ fn Call(a: A*, b: B*, c: C*, d: D*) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -152,6 +153,7 @@ fn Call(a: A*, b: B*, c: C*, d: D*) {
 // CHECK:STDOUT:   .base = %.loc16
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   extend %A.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc18
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -174,6 +176,7 @@ fn Call(a: A*, b: B*, c: C*, d: D*) {
 // CHECK:STDOUT:   .base = %.loc21
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc23
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -185,6 +188,7 @@ fn Call(a: A*, b: B*, c: C*, d: D*) {
 // CHECK:STDOUT:   .Self = constants.%D
 // CHECK:STDOUT:   .base = %.loc26
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc27
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.1[addr %self.param_patt: %.1]();
diff --git a/toolchain/check/testdata/class/basic.carbon b/toolchain/check/testdata/class/basic.carbon
index cff857382f6a..71647b1e024c 100644
--- a/toolchain/check/testdata/class/basic.carbon
+++ b/toolchain/check/testdata/class/basic.carbon
@@ -153,6 +153,7 @@ fn Run() -> i32 {
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   .k = %.loc18_8
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%n.param_patt: %i32) -> %i32 {
diff --git a/toolchain/check/testdata/class/complete_in_member_fn.carbon b/toolchain/check/testdata/class/complete_in_member_fn.carbon
index e2ff6d641475..6bf5c1556402 100644
--- a/toolchain/check/testdata/class/complete_in_member_fn.carbon
+++ b/toolchain/check/testdata/class/complete_in_member_fn.carbon
@@ -74,6 +74,7 @@ class C {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .a = %.loc14_8
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%c.param_patt: %C) -> %i32 {
diff --git a/toolchain/check/testdata/class/compound_field.carbon b/toolchain/check/testdata/class/compound_field.carbon
index 36e4dcd027e9..bca73271f205 100644
--- a/toolchain/check/testdata/class/compound_field.carbon
+++ b/toolchain/check/testdata/class/compound_field.carbon
@@ -179,6 +179,7 @@ fn AccessBaseIndirect(p: Derived*) -> i32* {
 // CHECK:STDOUT:   .a = %.loc12_8
 // CHECK:STDOUT:   .b = %.loc13_8
 // CHECK:STDOUT:   .c = %.loc14_8
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Derived {
@@ -202,6 +203,7 @@ fn AccessBaseIndirect(p: Derived*) -> i32* {
 // CHECK:STDOUT:   .d = %.loc20_8
 // CHECK:STDOUT:   .e = %.loc21_8
 // CHECK:STDOUT:   extend %Base.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc22
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @AccessDerived(%d.param_patt: %Derived) -> %i32 {
diff --git a/toolchain/check/testdata/class/cross_package_import.carbon b/toolchain/check/testdata/class/cross_package_import.carbon
index 8e6e8437c747..db16c087bb98 100644
--- a/toolchain/check/testdata/class/cross_package_import.carbon
+++ b/toolchain/check/testdata/class/cross_package_import.carbon
@@ -128,6 +128,7 @@ var c: Other.C = {};
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- other_extern.carbon
@@ -187,6 +188,7 @@ var c: Other.C = {};
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -220,6 +222,7 @@ var c: Other.C = {};
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -278,6 +281,7 @@ var c: Other.C = {};
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -312,6 +316,7 @@ var c: Other.C = {};
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -328,6 +333,7 @@ var c: Other.C = {};
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -362,6 +368,7 @@ var c: Other.C = {};
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/class/derived_to_base.carbon b/toolchain/check/testdata/class/derived_to_base.carbon
index 3711be528259..2074e58b7a84 100644
--- a/toolchain/check/testdata/class/derived_to_base.carbon
+++ b/toolchain/check/testdata/class/derived_to_base.carbon
@@ -206,6 +206,7 @@ fn ConvertInit() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .a = %.loc12_8
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -223,6 +224,7 @@ fn ConvertInit() {
 // CHECK:STDOUT:   .base = %.loc16
 // CHECK:STDOUT:   .b = %.loc17_8
 // CHECK:STDOUT:   extend %A.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc18
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -240,6 +242,7 @@ fn ConvertInit() {
 // CHECK:STDOUT:   .base = %.loc21
 // CHECK:STDOUT:   .c = %.loc22_8
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc23
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @ConvertCToB(%p.param_patt: %.17) -> %.18 {
diff --git a/toolchain/check/testdata/class/extend_adapt.carbon b/toolchain/check/testdata/class/extend_adapt.carbon
index d43443bfcced..b6cc48631b9b 100644
--- a/toolchain/check/testdata/class/extend_adapt.carbon
+++ b/toolchain/check/testdata/class/extend_adapt.carbon
@@ -206,6 +206,7 @@ fn F(a: IntAdapter) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%SomeClassAdapter
 // CHECK:STDOUT:   extend %SomeClass.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @SomeClass {
@@ -236,6 +237,7 @@ fn F(a: IntAdapter) -> i32 {
 // CHECK:STDOUT:   .b = %.loc8_8
 // CHECK:STDOUT:   .StaticMemberFunction = %StaticMemberFunction.decl
 // CHECK:STDOUT:   .AdapterMethod = %AdapterMethod.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @StaticMemberFunction();
@@ -315,6 +317,7 @@ fn F(a: IntAdapter) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%SomeClass
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @SomeClassAdapter {
@@ -325,6 +328,7 @@ fn F(a: IntAdapter) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%SomeClassAdapter
 // CHECK:STDOUT:   extend %SomeClass.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.1[%self.param_patt: %SomeClass]();
@@ -409,6 +413,7 @@ fn F(a: IntAdapter) -> i32 {
 // CHECK:STDOUT:   .Self = constants.%SomeClass
 // CHECK:STDOUT:   .a = %.loc5_8
 // CHECK:STDOUT:   .b = %.loc6_8
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @SomeClassAdapter {
@@ -419,6 +424,7 @@ fn F(a: IntAdapter) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%SomeClassAdapter
 // CHECK:STDOUT:   extend %SomeClass.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%a.param_patt: %SomeClassAdapter) -> %i32 {
@@ -494,6 +500,7 @@ fn F(a: IntAdapter) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%StructAdapter
 // CHECK:STDOUT:   extend %.loc5_33
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%a.param_patt: %StructAdapter) -> %i32 {
@@ -570,6 +577,7 @@ fn F(a: IntAdapter) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%TupleAdapter
 // CHECK:STDOUT:   extend %.loc5_26.5
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%a.param_patt: %TupleAdapter) -> %i32 {
@@ -661,6 +669,7 @@ fn F(a: IntAdapter) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%IntAdapter
 // CHECK:STDOUT:   extend %.loc7_27.2
+// CHECK:STDOUT:   complete_type_witness = %.loc8
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @MakeInt(%N.param_patt: Core.IntLiteral) -> type = "int.make_type_signed";
diff --git a/toolchain/check/testdata/class/fail_abstract.carbon b/toolchain/check/testdata/class/fail_abstract.carbon
index 758e3570b5d2..33dce70601f8 100644
--- a/toolchain/check/testdata/class/fail_abstract.carbon
+++ b/toolchain/check/testdata/class/fail_abstract.carbon
@@ -220,6 +220,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Abstract
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Contains {
@@ -230,6 +231,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Contains
 // CHECK:STDOUT:   .a = %.loc15
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_abstract_var.carbon
@@ -265,6 +267,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Abstract
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Var() {
@@ -315,6 +318,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Abstract
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%a.param_patt: %Abstract) {
@@ -357,6 +361,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Abstract
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Adapter {
@@ -366,6 +371,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Adapter
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- define_and_call_abstract_param.carbon
@@ -420,6 +426,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Abstract
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Param(%a.param_patt: %Abstract);
@@ -488,6 +495,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Abstract
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Derived {
@@ -505,6 +513,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:   .base = %.loc8
 // CHECK:STDOUT:   .d = %.loc10_8
 // CHECK:STDOUT:   extend %Abstract.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Make() -> %return: %Derived {
@@ -573,6 +582,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Abstract
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Derived {
@@ -590,6 +600,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:   .base = %.loc8
 // CHECK:STDOUT:   .d = %.loc10_8
 // CHECK:STDOUT:   extend %Abstract.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Return(%a.param_patt: %Abstract) -> %return: %Abstract {
@@ -665,6 +676,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Abstract
 // CHECK:STDOUT:   .a = %.loc5_8
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Derived {
@@ -682,6 +694,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:   .base = %.loc9
 // CHECK:STDOUT:   .d = %.loc11_8
 // CHECK:STDOUT:   extend %Abstract.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Access(%d.param_patt: %Derived) -> %i32 {
@@ -726,6 +739,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Abstract
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
@@ -780,6 +794,7 @@ fn CallReturnAbstract() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Abstract
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @ReturnAbstract() -> %Abstract;
diff --git a/toolchain/check/testdata/class/fail_adapt_bad_decl.carbon b/toolchain/check/testdata/class/fail_adapt_bad_decl.carbon
index a7335cdef47b..deb74c245a48 100644
--- a/toolchain/check/testdata/class/fail_adapt_bad_decl.carbon
+++ b/toolchain/check/testdata/class/fail_adapt_bad_decl.carbon
@@ -145,6 +145,7 @@ class C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Bad
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Use(%b.param_patt: %Bad) {
@@ -198,6 +199,7 @@ class C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Bad
 // CHECK:STDOUT:   extend <error>
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Use(%b.param_patt: %Bad) {
@@ -244,6 +246,7 @@ class C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%MultipleAdapts
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @MultipleAdaptsSameType {
@@ -255,6 +258,7 @@ class C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%MultipleAdaptsSameType
+// CHECK:STDOUT:   complete_type_witness = %.loc26
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_bad_scope.carbon
@@ -313,5 +317,6 @@ class C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .I = %I.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc25
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_adapt_bad_type.carbon b/toolchain/check/testdata/class/fail_adapt_bad_type.carbon
index 702fcf9e6a81..3e99441a7a80 100644
--- a/toolchain/check/testdata/class/fail_adapt_bad_type.carbon
+++ b/toolchain/check/testdata/class/fail_adapt_bad_type.carbon
@@ -58,5 +58,6 @@ class AdaptIncomplete {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%AdaptIncomplete
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_adapt_modifiers.carbon b/toolchain/check/testdata/class/fail_adapt_modifiers.carbon
index e65850414416..46863d944b24 100644
--- a/toolchain/check/testdata/class/fail_adapt_modifiers.carbon
+++ b/toolchain/check/testdata/class/fail_adapt_modifiers.carbon
@@ -99,6 +99,7 @@ class C5 {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C1 {
@@ -108,6 +109,7 @@ class C5 {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C1
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C2 {
@@ -117,6 +119,7 @@ class C5 {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C2
+// CHECK:STDOUT:   complete_type_witness = %.loc27
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C3 {
@@ -126,6 +129,7 @@ class C5 {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C3
+// CHECK:STDOUT:   complete_type_witness = %.loc35
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C4 {
@@ -136,6 +140,7 @@ class C5 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C4
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc46
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C5 {
@@ -146,5 +151,6 @@ class C5 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C5
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc56
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_adapt_with_base.carbon b/toolchain/check/testdata/class/fail_adapt_with_base.carbon
index 97ee3a170f05..1989f5053d06 100644
--- a/toolchain/check/testdata/class/fail_adapt_with_base.carbon
+++ b/toolchain/check/testdata/class/fail_adapt_with_base.carbon
@@ -53,6 +53,7 @@ base class AdaptWithVirtual {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Simple
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @AdaptWithVirtual {
@@ -63,6 +64,7 @@ base class AdaptWithVirtual {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%AdaptWithVirtual
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: virtual fn @F();
diff --git a/toolchain/check/testdata/class/fail_adapt_with_subobjects.carbon b/toolchain/check/testdata/class/fail_adapt_with_subobjects.carbon
index 69bf16a7fa90..d775f4d5a68a 100644
--- a/toolchain/check/testdata/class/fail_adapt_with_subobjects.carbon
+++ b/toolchain/check/testdata/class/fail_adapt_with_subobjects.carbon
@@ -112,6 +112,7 @@ class AdaptWithBaseAndFields {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Base
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @AdaptWithBase {
@@ -127,6 +128,7 @@ class AdaptWithBaseAndFields {
 // CHECK:STDOUT:   .Self = constants.%AdaptWithBase
 // CHECK:STDOUT:   .base = %.loc15
 // CHECK:STDOUT:   extend %Base.ref
+// CHECK:STDOUT:   complete_type_witness = <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_adapt_with_fields.carbon
@@ -176,6 +178,7 @@ class AdaptWithBaseAndFields {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%AdaptWithField
 // CHECK:STDOUT:   .n = %.loc13_8
+// CHECK:STDOUT:   complete_type_witness = <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @AdaptWithFields {
@@ -205,6 +208,7 @@ class AdaptWithBaseAndFields {
 // CHECK:STDOUT:   .a = %.loc25_8
 // CHECK:STDOUT:   .b = %.loc26_8
 // CHECK:STDOUT:   .c = %.loc27_8
+// CHECK:STDOUT:   complete_type_witness = <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_adapt_with_base_and_fields.carbon
@@ -246,6 +250,7 @@ class AdaptWithBaseAndFields {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Base
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @AdaptWithBaseAndFields {
@@ -265,5 +270,6 @@ class AdaptWithBaseAndFields {
 // CHECK:STDOUT:   .base = %.loc7
 // CHECK:STDOUT:   .n = %.loc8_8
 // CHECK:STDOUT:   extend %Base.ref
+// CHECK:STDOUT:   complete_type_witness = <error>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_addr_not_self.carbon b/toolchain/check/testdata/class/fail_addr_not_self.carbon
index de1e58a46e84..9ccc3573922b 100644
--- a/toolchain/check/testdata/class/fail_addr_not_self.carbon
+++ b/toolchain/check/testdata/class/fail_addr_not_self.carbon
@@ -77,6 +77,7 @@ class Class {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc22
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%a.loc16_13.2: %.1) {
diff --git a/toolchain/check/testdata/class/fail_addr_self.carbon b/toolchain/check/testdata/class/fail_addr_self.carbon
index 9c19ef671669..f76b6f823531 100644
--- a/toolchain/check/testdata/class/fail_addr_self.carbon
+++ b/toolchain/check/testdata/class/fail_addr_self.carbon
@@ -106,6 +106,7 @@ fn F(c: Class, p: Class*) {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc18
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.1[addr %self.param_patt: %.1]();
diff --git a/toolchain/check/testdata/class/fail_base_bad_type.carbon b/toolchain/check/testdata/class/fail_base_bad_type.carbon
index 56f9a66bedce..36e58b18da32 100644
--- a/toolchain/check/testdata/class/fail_base_bad_type.carbon
+++ b/toolchain/check/testdata/class/fail_base_bad_type.carbon
@@ -235,6 +235,7 @@ fn AccessMemberWithInvalidBaseFinal_NoMember(p: DeriveFromFinal*) -> i32 {
 // CHECK:STDOUT:   .Self = constants.%DeriveFromError
 // CHECK:STDOUT:   .base = %.loc9
 // CHECK:STDOUT:   has_error
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @AccessMemberWithInvalidBaseError(%p.param_patt: %.1) -> %i32 {
@@ -304,6 +305,7 @@ fn AccessMemberWithInvalidBaseFinal_NoMember(p: DeriveFromFinal*) -> i32 {
 // CHECK:STDOUT:   .Self = constants.%DeriveFromNonType
 // CHECK:STDOUT:   .base = %.loc12_18
 // CHECK:STDOUT:   has_error
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @AccessMemberWithInvalidBasNonType(%p.param_patt: %.25) -> %i32 {
@@ -397,6 +399,7 @@ fn AccessMemberWithInvalidBaseFinal_NoMember(p: DeriveFromFinal*) -> i32 {
 // CHECK:STDOUT:   .Self = constants.%DeriveFromi32
 // CHECK:STDOUT:   .base = %.loc7_19
 // CHECK:STDOUT:   has_error
+// CHECK:STDOUT:   complete_type_witness = %.loc8
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @ConvertToBadBasei32(%p.param_patt: %.2) -> %.3 {
@@ -496,6 +499,7 @@ fn AccessMemberWithInvalidBaseFinal_NoMember(p: DeriveFromFinal*) -> i32 {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Base
+// CHECK:STDOUT:   complete_type_witness = %.loc2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @DeriveFromTuple {
@@ -509,6 +513,7 @@ fn AccessMemberWithInvalidBaseFinal_NoMember(p: DeriveFromFinal*) -> i32 {
 // CHECK:STDOUT:   .Self = constants.%DeriveFromTuple
 // CHECK:STDOUT:   .base = %.loc9_23
 // CHECK:STDOUT:   has_error
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @ConvertToBadBaseTuple(%p.param_patt: %.4) -> %.5 {
@@ -620,6 +625,7 @@ fn AccessMemberWithInvalidBaseFinal_NoMember(p: DeriveFromFinal*) -> i32 {
 // CHECK:STDOUT:   .Self = constants.%DeriveFromStruct
 // CHECK:STDOUT:   .base = %.loc9_34
 // CHECK:STDOUT:   has_error
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @ConvertToBadBaseStruct(%p.param_patt: %.4) -> %.3 {
@@ -719,6 +725,7 @@ fn AccessMemberWithInvalidBaseFinal_NoMember(p: DeriveFromFinal*) -> i32 {
 // CHECK:STDOUT:   .Self = constants.%DeriveFromIncomplete
 // CHECK:STDOUT:   .base = %.loc16
 // CHECK:STDOUT:   has_error
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @ConvertToBadBaseIncomplete(%p.param_patt: %.1) -> %.2 {
@@ -843,6 +850,7 @@ fn AccessMemberWithInvalidBaseFinal_NoMember(p: DeriveFromFinal*) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Final
 // CHECK:STDOUT:   .a = %.loc3_8
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @DeriveFromFinal {
@@ -854,6 +862,7 @@ fn AccessMemberWithInvalidBaseFinal_NoMember(p: DeriveFromFinal*) -> i32 {
 // CHECK:STDOUT:   .Self = constants.%DeriveFromFinal
 // CHECK:STDOUT:   .base = %.loc11
 // CHECK:STDOUT:   extend %Final.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @ConvertToBadBaseFinal(%p.param_patt: %.9) -> %.10 {
diff --git a/toolchain/check/testdata/class/fail_base_method_define.carbon b/toolchain/check/testdata/class/fail_base_method_define.carbon
index 3b97ec726706..4c68f3c89b5e 100644
--- a/toolchain/check/testdata/class/fail_base_method_define.carbon
+++ b/toolchain/check/testdata/class/fail_base_method_define.carbon
@@ -81,6 +81,7 @@ fn D.C.F() {}
 // CHECK:STDOUT:   .Self = constants.%B
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .C = %C.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -90,6 +91,7 @@ fn D.C.F() {}
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -102,6 +104,7 @@ fn D.C.F() {}
 // CHECK:STDOUT:   .base = %.loc20
 // CHECK:STDOUT:   .F = file.%F.decl
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc21
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.1();
diff --git a/toolchain/check/testdata/class/fail_base_misplaced.carbon b/toolchain/check/testdata/class/fail_base_misplaced.carbon
index fb89006bfe12..06cd79c7a37f 100644
--- a/toolchain/check/testdata/class/fail_base_misplaced.carbon
+++ b/toolchain/check/testdata/class/fail_base_misplaced.carbon
@@ -42,6 +42,7 @@ fn F() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
diff --git a/toolchain/check/testdata/class/fail_base_modifiers.carbon b/toolchain/check/testdata/class/fail_base_modifiers.carbon
index e653b45f3352..17ce699871f6 100644
--- a/toolchain/check/testdata/class/fail_base_modifiers.carbon
+++ b/toolchain/check/testdata/class/fail_base_modifiers.carbon
@@ -98,6 +98,7 @@ class C4 {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C1 {
@@ -109,6 +110,7 @@ class C4 {
 // CHECK:STDOUT:   .Self = constants.%C1
 // CHECK:STDOUT:   .base = %.loc18
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C2 {
@@ -119,6 +121,7 @@ class C4 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C2
 // CHECK:STDOUT:   .base = %.loc30
+// CHECK:STDOUT:   complete_type_witness = %.loc31
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C3 {
@@ -130,6 +133,7 @@ class C4 {
 // CHECK:STDOUT:   .Self = constants.%C3
 // CHECK:STDOUT:   .base = %.loc41
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc42
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C4 {
@@ -141,5 +145,6 @@ class C4 {
 // CHECK:STDOUT:   .Self = constants.%C4
 // CHECK:STDOUT:   .base = %.loc51
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc52
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_base_no_extend.carbon b/toolchain/check/testdata/class/fail_base_no_extend.carbon
index 97db3fa85502..f3df49c66a09 100644
--- a/toolchain/check/testdata/class/fail_base_no_extend.carbon
+++ b/toolchain/check/testdata/class/fail_base_no_extend.carbon
@@ -52,6 +52,7 @@ class C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -62,5 +63,6 @@ class C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .base = %.loc17
+// CHECK:STDOUT:   complete_type_witness = %.loc18
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_base_repeated.carbon b/toolchain/check/testdata/class/fail_base_repeated.carbon
index cee7d94a53d3..73d7e3a8ef0e 100644
--- a/toolchain/check/testdata/class/fail_base_repeated.carbon
+++ b/toolchain/check/testdata/class/fail_base_repeated.carbon
@@ -77,6 +77,7 @@ class D {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B1
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B2 {
@@ -84,6 +85,7 @@ class D {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B2
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -96,6 +98,7 @@ class D {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .base = %.loc15
 // CHECK:STDOUT:   extend %B1.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc24
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -108,5 +111,6 @@ class D {
 // CHECK:STDOUT:   .Self = constants.%D
 // CHECK:STDOUT:   .base = %.loc28
 // CHECK:STDOUT:   extend %B1.ref.loc28
+// CHECK:STDOUT:   complete_type_witness = %.loc36
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_base_unbound.carbon b/toolchain/check/testdata/class/fail_base_unbound.carbon
index c4d132df86e1..ea0433c8c0db 100644
--- a/toolchain/check/testdata/class/fail_base_unbound.carbon
+++ b/toolchain/check/testdata/class/fail_base_unbound.carbon
@@ -56,6 +56,7 @@ let b: B = C.base;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -67,6 +68,7 @@ let b: B = C.base;
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .base = %.loc14
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/class/fail_compound_type_mismatch.carbon b/toolchain/check/testdata/class/fail_compound_type_mismatch.carbon
index 430b790b740e..ae2f701986e7 100644
--- a/toolchain/check/testdata/class/fail_compound_type_mismatch.carbon
+++ b/toolchain/check/testdata/class/fail_compound_type_mismatch.carbon
@@ -93,6 +93,7 @@ fn AccessBInA(a: A) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .a = %.loc12_8
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -106,6 +107,7 @@ fn AccessBInA(a: A) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
 // CHECK:STDOUT:   .b = %.loc16_8
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @AccessBInA(%a.param_patt: %A) -> %i32 {
diff --git a/toolchain/check/testdata/class/fail_convert_to_invalid.carbon b/toolchain/check/testdata/class/fail_convert_to_invalid.carbon
index f3b7bfd9f577..0e6e19782c78 100644
--- a/toolchain/check/testdata/class/fail_convert_to_invalid.carbon
+++ b/toolchain/check/testdata/class/fail_convert_to_invalid.carbon
@@ -62,6 +62,7 @@ fn Make() -> C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .a = %.loc15
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Make() -> %return: %C {
diff --git a/toolchain/check/testdata/class/fail_derived_to_base.carbon b/toolchain/check/testdata/class/fail_derived_to_base.carbon
index 6d46541e9a09..e36433cec11a 100644
--- a/toolchain/check/testdata/class/fail_derived_to_base.carbon
+++ b/toolchain/check/testdata/class/fail_derived_to_base.carbon
@@ -136,6 +136,7 @@ fn ConvertIncomplete(p: Incomplete*) -> A2* { return p; }
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A1
 // CHECK:STDOUT:   .a = %.loc12_8
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @A2 {
@@ -149,6 +150,7 @@ fn ConvertIncomplete(p: Incomplete*) -> A2* { return p; }
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A2
 // CHECK:STDOUT:   .a = %.loc16_8
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B2 {
@@ -166,6 +168,7 @@ fn ConvertIncomplete(p: Incomplete*) -> A2* { return p; }
 // CHECK:STDOUT:   .base = %.loc20
 // CHECK:STDOUT:   .b = %.loc21_8
 // CHECK:STDOUT:   extend %A2.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc22
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Incomplete;
diff --git a/toolchain/check/testdata/class/fail_extend_cycle.carbon b/toolchain/check/testdata/class/fail_extend_cycle.carbon
index d97d5828c188..aab00e6b3845 100644
--- a/toolchain/check/testdata/class/fail_extend_cycle.carbon
+++ b/toolchain/check/testdata/class/fail_extend_cycle.carbon
@@ -69,6 +69,7 @@ base class A {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -80,6 +81,7 @@ base class A {
 // CHECK:STDOUT:   .Self = constants.%B
 // CHECK:STDOUT:   .base = %.loc16
 // CHECK:STDOUT:   extend %A.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @.1 {
@@ -94,5 +96,6 @@ base class A {
 // CHECK:STDOUT:   .base = %.loc27
 // CHECK:STDOUT:   .c = %.loc31
 // CHECK:STDOUT:   extend %A.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc32
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_field_modifiers.carbon b/toolchain/check/testdata/class/fail_field_modifiers.carbon
index 196bda5f0aee..6e6e01c6f401 100644
--- a/toolchain/check/testdata/class/fail_field_modifiers.carbon
+++ b/toolchain/check/testdata/class/fail_field_modifiers.carbon
@@ -120,5 +120,6 @@ class Class {
 // CHECK:STDOUT:   .k = %.loc23_14
 // CHECK:STDOUT:   .l = %l
 // CHECK:STDOUT:   .m = %m
+// CHECK:STDOUT:   complete_type_witness = %.loc35
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_generic_method.carbon b/toolchain/check/testdata/class/fail_generic_method.carbon
index 064ab0903913..9d569ff2831d 100644
--- a/toolchain/check/testdata/class/fail_generic_method.carbon
+++ b/toolchain/check/testdata/class/fail_generic_method.carbon
@@ -131,6 +131,7 @@ fn Class(N:! i32).F[self: Self](n: T) {}
 // CHECK:STDOUT:     .Self = constants.%Class.2
 // CHECK:STDOUT:     .a = %.loc12_8.1
 // CHECK:STDOUT:     .F = %F.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc14_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_import_misuses.carbon b/toolchain/check/testdata/class/fail_import_misuses.carbon
index f7e16f4bbc8e..c4708bac5f31 100644
--- a/toolchain/check/testdata/class/fail_import_misuses.carbon
+++ b/toolchain/check/testdata/class/fail_import_misuses.carbon
@@ -75,6 +75,7 @@ var a: Incomplete;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Empty
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Incomplete;
@@ -117,6 +118,7 @@ var a: Incomplete;
 // CHECK:STDOUT: class @Empty {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @.1 {
@@ -124,6 +126,7 @@ var a: Incomplete;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%.3
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Incomplete;
diff --git a/toolchain/check/testdata/class/fail_incomplete.carbon b/toolchain/check/testdata/class/fail_incomplete.carbon
index 0f64f98eb2fe..0eecb6bb815b 100644
--- a/toolchain/check/testdata/class/fail_incomplete.carbon
+++ b/toolchain/check/testdata/class/fail_incomplete.carbon
@@ -368,6 +368,7 @@ class C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%IncompleteAddrSelf
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc134
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @.1() {
@@ -485,5 +486,6 @@ class C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .c = %.loc11
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_init.carbon b/toolchain/check/testdata/class/fail_init.carbon
index 893d95d4dfd4..7ad6cebf6eee 100644
--- a/toolchain/check/testdata/class/fail_init.carbon
+++ b/toolchain/check/testdata/class/fail_init.carbon
@@ -95,6 +95,7 @@ fn F() {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .a = %.loc12_8
 // CHECK:STDOUT:   .b = %.loc13_8
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
diff --git a/toolchain/check/testdata/class/fail_init_as_inplace.carbon b/toolchain/check/testdata/class/fail_init_as_inplace.carbon
index c4761d8f20ff..a4d53c9bf194 100644
--- a/toolchain/check/testdata/class/fail_init_as_inplace.carbon
+++ b/toolchain/check/testdata/class/fail_init_as_inplace.carbon
@@ -106,6 +106,7 @@ fn F() {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .a = %.loc12_8
 // CHECK:STDOUT:   .b = %.loc13_8
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @G(%p.param_patt: %.5);
diff --git a/toolchain/check/testdata/class/fail_memaccess_category.carbon b/toolchain/check/testdata/class/fail_memaccess_category.carbon
index 13e1edf51ec1..1333ed8c7bbe 100644
--- a/toolchain/check/testdata/class/fail_memaccess_category.carbon
+++ b/toolchain/check/testdata/class/fail_memaccess_category.carbon
@@ -105,6 +105,7 @@ fn F(s: {.a: A}, b: B) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -115,6 +116,7 @@ fn F(s: {.a: A}, b: B) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
 // CHECK:STDOUT:   .a = %.loc16
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.1[addr %self.param_patt: %.1]();
diff --git a/toolchain/check/testdata/class/fail_member_of_let.carbon b/toolchain/check/testdata/class/fail_member_of_let.carbon
index cb655f6f167e..c24867ff0e5a 100644
--- a/toolchain/check/testdata/class/fail_member_of_let.carbon
+++ b/toolchain/check/testdata/class/fail_member_of_let.carbon
@@ -77,6 +77,7 @@ fn T.F() {}
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %i32;
diff --git a/toolchain/check/testdata/class/fail_method.carbon b/toolchain/check/testdata/class/fail_method.carbon
index cc292cd0a702..997056e2d228 100644
--- a/toolchain/check/testdata/class/fail_method.carbon
+++ b/toolchain/check/testdata/class/fail_method.carbon
@@ -106,6 +106,7 @@ fn F(c: Class) {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .NoSelf = %NoSelf.decl
 // CHECK:STDOUT:   .WithSelf = %WithSelf.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @NoSelf();
diff --git a/toolchain/check/testdata/class/fail_method_modifiers.carbon b/toolchain/check/testdata/class/fail_method_modifiers.carbon
index 26fbeecac6ff..c84a473ba1da 100644
--- a/toolchain/check/testdata/class/fail_method_modifiers.carbon
+++ b/toolchain/check/testdata/class/fail_method_modifiers.carbon
@@ -118,6 +118,7 @@ base class BaseClass {
 // CHECK:STDOUT:   .Self = constants.%FinalClass
 // CHECK:STDOUT:   .Abstract = %Abstract.decl
 // CHECK:STDOUT:   .Virtual = %Virtual.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc30
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @AbstractClass {
@@ -143,6 +144,7 @@ base class BaseClass {
 // CHECK:STDOUT:   .Self = constants.%AbstractClass
 // CHECK:STDOUT:   .Default = %Default.decl
 // CHECK:STDOUT:   .Final = %Final.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc45
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @BaseClass {
@@ -159,6 +161,7 @@ base class BaseClass {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%BaseClass
 // CHECK:STDOUT:   .Abstract = %Abstract.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc56
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Abstract.1[%self.param_patt: %FinalClass]();
diff --git a/toolchain/check/testdata/class/fail_method_redefinition.carbon b/toolchain/check/testdata/class/fail_method_redefinition.carbon
index ee9445e6aba0..3453d8a3ae65 100644
--- a/toolchain/check/testdata/class/fail_method_redefinition.carbon
+++ b/toolchain/check/testdata/class/fail_method_redefinition.carbon
@@ -53,6 +53,7 @@ class Class {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .F = %F.decl.loc12
+// CHECK:STDOUT:   complete_type_witness = %.loc20
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
diff --git a/toolchain/check/testdata/class/fail_modifiers.carbon b/toolchain/check/testdata/class/fail_modifiers.carbon
index 5047d4747167..57839be58d03 100644
--- a/toolchain/check/testdata/class/fail_modifiers.carbon
+++ b/toolchain/check/testdata/class/fail_modifiers.carbon
@@ -165,6 +165,7 @@ fn AbstractWithDefinition.G() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%TwoAbstract
+// CHECK:STDOUT:   complete_type_witness = %.loc48
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Virtual {
@@ -172,6 +173,7 @@ fn AbstractWithDefinition.G() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Virtual
+// CHECK:STDOUT:   complete_type_witness = %.loc65
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @WrongOrder {
@@ -179,6 +181,7 @@ fn AbstractWithDefinition.G() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%WrongOrder
+// CHECK:STDOUT:   complete_type_witness = %.loc74
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @AbstractAndBase {
@@ -186,6 +189,7 @@ fn AbstractWithDefinition.G() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%AbstractAndBase
+// CHECK:STDOUT:   complete_type_witness = %.loc83
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @AbstractWithDefinition {
@@ -197,6 +201,7 @@ fn AbstractWithDefinition.G() {
 // CHECK:STDOUT:   .Self = constants.%AbstractWithDefinition
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc92
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: abstract fn @F() {
diff --git a/toolchain/check/testdata/class/fail_out_of_line_decl.carbon b/toolchain/check/testdata/class/fail_out_of_line_decl.carbon
index 6e57d39ad38d..8f774cdde73a 100644
--- a/toolchain/check/testdata/class/fail_out_of_line_decl.carbon
+++ b/toolchain/check/testdata/class/fail_out_of_line_decl.carbon
@@ -48,6 +48,7 @@ fn C.F() {}
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .F = file.%F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
diff --git a/toolchain/check/testdata/class/fail_redeclaration_scope.carbon b/toolchain/check/testdata/class/fail_redeclaration_scope.carbon
index 697d9fbee88e..35db37c1b63d 100644
--- a/toolchain/check/testdata/class/fail_redeclaration_scope.carbon
+++ b/toolchain/check/testdata/class/fail_redeclaration_scope.carbon
@@ -67,6 +67,7 @@ class Y {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A.1
 // CHECK:STDOUT:   .B = %B.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @X {
@@ -77,6 +78,7 @@ class Y {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%X
 // CHECK:STDOUT:   .A = %A.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @A.2 {
@@ -86,6 +88,7 @@ class Y {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A.2
 // CHECK:STDOUT:   .B = %B.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B.1 {
@@ -93,6 +96,7 @@ class Y {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B.1
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B.2;
@@ -103,6 +107,7 @@ class Y {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Y
+// CHECK:STDOUT:   complete_type_witness = %.loc26
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @.1 {
@@ -110,5 +115,6 @@ class Y {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%.3
+// CHECK:STDOUT:   complete_type_witness = %.loc25
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_redefinition.carbon b/toolchain/check/testdata/class/fail_redefinition.carbon
index d2bf338ef40f..3660b85f05e5 100644
--- a/toolchain/check/testdata/class/fail_redefinition.carbon
+++ b/toolchain/check/testdata/class/fail_redefinition.carbon
@@ -98,6 +98,7 @@ fn Class.I() {}
 // CHECK:STDOUT:   .H = %H.decl
 // CHECK:STDOUT:   .I = %I.decl
 // CHECK:STDOUT:   .G = file.%G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @.1 {
@@ -111,6 +112,7 @@ fn Class.I() {}
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   .H = %H.decl
 // CHECK:STDOUT:   .I = %I.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc28
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
diff --git a/toolchain/check/testdata/class/fail_scope.carbon b/toolchain/check/testdata/class/fail_scope.carbon
index 31c4f50fb6ed..2062f3ca7e83 100644
--- a/toolchain/check/testdata/class/fail_scope.carbon
+++ b/toolchain/check/testdata/class/fail_scope.carbon
@@ -92,6 +92,7 @@ fn G() -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %i32 {
diff --git a/toolchain/check/testdata/class/fail_self.carbon b/toolchain/check/testdata/class/fail_self.carbon
index 89733c29cf51..a49814f5d8cf 100644
--- a/toolchain/check/testdata/class/fail_self.carbon
+++ b/toolchain/check/testdata/class/fail_self.carbon
@@ -140,6 +140,7 @@ fn CallWrongSelf(ws: WrongSelf) {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @WrongSelf {
@@ -156,6 +157,7 @@ fn CallWrongSelf(ws: WrongSelf) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%WrongSelf
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc43
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.1(%self.param_patt: %Class) {
diff --git a/toolchain/check/testdata/class/fail_self_param.carbon b/toolchain/check/testdata/class/fail_self_param.carbon
index b1b321defab1..8e54eadd5415 100644
--- a/toolchain/check/testdata/class/fail_self_param.carbon
+++ b/toolchain/check/testdata/class/fail_self_param.carbon
@@ -66,6 +66,7 @@ var v: C(0);
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:     complete_type_witness = %.loc14
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/fail_self_type_member.carbon b/toolchain/check/testdata/class/fail_self_type_member.carbon
index a80d13f0e075..89e5f1b8e4fc 100644
--- a/toolchain/check/testdata/class/fail_self_type_member.carbon
+++ b/toolchain/check/testdata/class/fail_self_type_member.carbon
@@ -48,6 +48,7 @@ fn F() -> bool {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .b = %.loc12_8
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> bool {
diff --git a/toolchain/check/testdata/class/fail_todo_local_class.carbon b/toolchain/check/testdata/class/fail_todo_local_class.carbon
index f1b7386196c1..9f5d720cd107 100644
--- a/toolchain/check/testdata/class/fail_todo_local_class.carbon
+++ b/toolchain/check/testdata/class/fail_todo_local_class.carbon
@@ -45,6 +45,7 @@ class A {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc27
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
diff --git a/toolchain/check/testdata/class/fail_unbound_field.carbon b/toolchain/check/testdata/class/fail_unbound_field.carbon
index 3922c2ef8cdf..455bce116558 100644
--- a/toolchain/check/testdata/class/fail_unbound_field.carbon
+++ b/toolchain/check/testdata/class/fail_unbound_field.carbon
@@ -95,6 +95,7 @@ fn G() -> i32 {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .field = %.loc12_12
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc20
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %i32 {
diff --git a/toolchain/check/testdata/class/fail_unknown_member.carbon b/toolchain/check/testdata/class/fail_unknown_member.carbon
index 0c58beb20182..71d7a87ebc3e 100644
--- a/toolchain/check/testdata/class/fail_unknown_member.carbon
+++ b/toolchain/check/testdata/class/fail_unknown_member.carbon
@@ -80,6 +80,7 @@ fn G(c: Class) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .n = %.loc12_8
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @G(%c.param_patt: %Class) -> %i32 {
diff --git a/toolchain/check/testdata/class/field_access.carbon b/toolchain/check/testdata/class/field_access.carbon
index 591e3012ca5b..fea6af6a1c0f 100644
--- a/toolchain/check/testdata/class/field_access.carbon
+++ b/toolchain/check/testdata/class/field_access.carbon
@@ -85,6 +85,7 @@ fn Run() {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .j = %.loc12_8
 // CHECK:STDOUT:   .k = %.loc13_8
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Run() {
diff --git a/toolchain/check/testdata/class/field_access_in_value.carbon b/toolchain/check/testdata/class/field_access_in_value.carbon
index e9e162ad13af..0ce1970f7ee0 100644
--- a/toolchain/check/testdata/class/field_access_in_value.carbon
+++ b/toolchain/check/testdata/class/field_access_in_value.carbon
@@ -86,6 +86,7 @@ fn Test() {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .j = %.loc12_8
 // CHECK:STDOUT:   .k = %.loc13_8
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Test() {
diff --git a/toolchain/check/testdata/class/generic/adapt.carbon b/toolchain/check/testdata/class/generic/adapt.carbon
index 354f4a80ee17..d80d670c9793 100644
--- a/toolchain/check/testdata/class/generic/adapt.carbon
+++ b/toolchain/check/testdata/class/generic/adapt.carbon
@@ -204,6 +204,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
 // CHECK:STDOUT:     .x = %.loc5_8.1
+// CHECK:STDOUT:     complete_type_witness = %.loc6_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -219,6 +220,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Adapter
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Access(%a.param_patt: %Adapter) -> %i32 {
@@ -328,6 +330,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT: class @Adapter {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @C(constants.%T: type) {
@@ -344,6 +347,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.4
 // CHECK:STDOUT:     .x = imports.%import_ref.5
+// CHECK:STDOUT:     complete_type_witness = constants.%.3
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -470,6 +474,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
 // CHECK:STDOUT:     .x = %.loc5_8.1
+// CHECK:STDOUT:     complete_type_witness = %.loc6_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -486,6 +491,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Adapter
 // CHECK:STDOUT:   extend %C
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Access(%a.param_patt: %Adapter) -> %i32 {
@@ -583,6 +589,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
 // CHECK:STDOUT:     .x = %.loc8_8.1
+// CHECK:STDOUT:     complete_type_witness = %.loc9_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -599,6 +606,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Adapter
 // CHECK:STDOUT:   extend %C
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @C(constants.%T) {
@@ -690,6 +698,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.6
 // CHECK:STDOUT:   extend imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @C(constants.%T: type) {
@@ -706,6 +715,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.3
 // CHECK:STDOUT:     .x = imports.%import_ref.4
+// CHECK:STDOUT:     complete_type_witness = constants.%.3
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -817,6 +827,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Adapter.2
+// CHECK:STDOUT:     complete_type_witness = %.loc6_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -945,6 +956,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT:   class {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.4
+// CHECK:STDOUT:     complete_type_witness = constants.%.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -959,6 +971,7 @@ fn ImportedConvertLocal(a: Adapter(C)) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .n = %.loc11_8
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @ImportedConvert(%a.param_patt: %Adapter.3) -> %i32 {
diff --git a/toolchain/check/testdata/class/generic/base_is_generic.carbon b/toolchain/check/testdata/class/generic/base_is_generic.carbon
index c6c66ced6c06..e8dcdc8a8255 100644
--- a/toolchain/check/testdata/class/generic/base_is_generic.carbon
+++ b/toolchain/check/testdata/class/generic/base_is_generic.carbon
@@ -177,6 +177,7 @@ fn H() {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Base.2
 // CHECK:STDOUT:     .x = %.loc5_8.1
+// CHECK:STDOUT:     complete_type_witness = %.loc6_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -191,6 +192,7 @@ fn H() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Param
 // CHECK:STDOUT:   .y = %.loc9_8
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Derived {
@@ -204,6 +206,7 @@ fn H() {
 // CHECK:STDOUT:   .Self = constants.%Derived
 // CHECK:STDOUT:   .base = %.loc13
 // CHECK:STDOUT:   extend %Base
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @DoubleFieldAccess(%d.param_patt: %Derived) -> %i32 {
@@ -247,12 +250,16 @@ fn H() {
 // CHECK:STDOUT:   %Param: type = class_type @Param [template]
 // CHECK:STDOUT:   %.1: Core.IntLiteral = int_value 32 [template]
 // CHECK:STDOUT:   %i32: type = int_type signed, %.1 [template]
+// CHECK:STDOUT:   %.2: type = struct_type {.y: %i32} [template]
+// CHECK:STDOUT:   %.3: <witness> = complete_type_witness %.2 [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T, 0 [symbolic]
 // CHECK:STDOUT:   %.4: type = struct_type {.x: %T} [symbolic]
 // CHECK:STDOUT:   %.5: <witness> = complete_type_witness %.4 [symbolic]
 // CHECK:STDOUT:   %Base.2: type = class_type @Base, @Base(%T) [symbolic]
 // CHECK:STDOUT:   %T.patt: type = symbolic_binding_pattern T, 0 [symbolic]
 // CHECK:STDOUT:   %Base.3: type = class_type @Base, @Base(%Param) [template]
+// CHECK:STDOUT:   %.7: type = struct_type {.base: %Base.3} [template]
+// CHECK:STDOUT:   %.8: <witness> = complete_type_witness %.7 [template]
 // CHECK:STDOUT:   %.9: type = unbound_element_type %Base.2, %T [symbolic]
 // CHECK:STDOUT:   %.10: type = unbound_element_type %Base.3, %Param [template]
 // CHECK:STDOUT:   %.11: type = struct_type {.x: %Param} [template]
@@ -317,12 +324,14 @@ fn H() {
 // CHECK:STDOUT:   .Self = imports.%import_ref.10
 // CHECK:STDOUT:   .base = imports.%import_ref.11
 // CHECK:STDOUT:   extend imports.%import_ref.12
+// CHECK:STDOUT:   complete_type_witness = constants.%.8
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Param {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.5
 // CHECK:STDOUT:   .y = imports.%import_ref.6
+// CHECK:STDOUT:   complete_type_witness = constants.%.3
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Base(constants.%T: type) {
@@ -339,6 +348,7 @@ fn H() {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.7
 // CHECK:STDOUT:     .x = imports.%import_ref.8
+// CHECK:STDOUT:     complete_type_witness = constants.%.5
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -435,6 +445,7 @@ fn H() {
 // CHECK:STDOUT:     .Self = constants.%C.2
 // CHECK:STDOUT:     .base = %.loc8
 // CHECK:STDOUT:     has_error
+// CHECK:STDOUT:     complete_type_witness = %.loc9
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -445,6 +456,7 @@ fn H() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%X
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @G() {
@@ -568,6 +580,7 @@ fn H() {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%X.2
 // CHECK:STDOUT:     .G = %G.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc6
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -593,6 +606,7 @@ fn H() {
 // CHECK:STDOUT:     .Self = constants.%C.2
 // CHECK:STDOUT:     .base = %.loc9_20.1
 // CHECK:STDOUT:     extend %X.loc9_17.1
+// CHECK:STDOUT:     complete_type_witness = %.loc10_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -736,6 +750,8 @@ fn H() {
 // CHECK:STDOUT:   %C.type: type = generic_class_type @C [template]
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T, 0 [symbolic]
+// CHECK:STDOUT:   %.2: type = struct_type {} [template]
+// CHECK:STDOUT:   %.3: <witness> = complete_type_witness %.2 [template]
 // CHECK:STDOUT:   %U: type = bind_symbolic_name U, 0 [symbolic]
 // CHECK:STDOUT:   %U.patt: type = symbolic_binding_pattern U, 0 [symbolic]
 // CHECK:STDOUT:   %X.3: type = class_type @X, @X(%T) [symbolic]
@@ -804,6 +820,7 @@ fn H() {
 // CHECK:STDOUT:     .Self = imports.%import_ref.8
 // CHECK:STDOUT:     .base = imports.%import_ref.9
 // CHECK:STDOUT:     extend imports.%import_ref.10
+// CHECK:STDOUT:     complete_type_witness = constants.%.6
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -819,6 +836,7 @@ fn H() {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.5
 // CHECK:STDOUT:     .G = imports.%import_ref.6
+// CHECK:STDOUT:     complete_type_witness = constants.%.3
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic/basic.carbon b/toolchain/check/testdata/class/generic/basic.carbon
index d6a40bab8aea..c0ab9c9ad251 100644
--- a/toolchain/check/testdata/class/generic/basic.carbon
+++ b/toolchain/check/testdata/class/generic/basic.carbon
@@ -129,6 +129,7 @@ class Declaration(T:! type);
 // CHECK:STDOUT:     .GetAddr = %GetAddr.decl
 // CHECK:STDOUT:     .GetValue = %GetValue.decl
 // CHECK:STDOUT:     .k = %.loc21_8.1
+// CHECK:STDOUT:     complete_type_witness = %.loc22_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic/call.carbon b/toolchain/check/testdata/class/generic/call.carbon
index 1085c44fbe97..7b191ae1a8a4 100644
--- a/toolchain/check/testdata/class/generic/call.carbon
+++ b/toolchain/check/testdata/class/generic/call.carbon
@@ -195,6 +195,7 @@ class Outer(T:! type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Class.2
+// CHECK:STDOUT:     complete_type_witness = %.loc4_33
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -295,6 +296,7 @@ class Outer(T:! type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Class.2
+// CHECK:STDOUT:     complete_type_witness = %.loc4_33
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -381,6 +383,7 @@ class Outer(T:! type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Class.2
+// CHECK:STDOUT:     complete_type_witness = %.loc4_33
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -467,6 +470,7 @@ class Outer(T:! type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Class.2
+// CHECK:STDOUT:     complete_type_witness = %.loc4_33
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -561,6 +565,7 @@ class Outer(T:! type) {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Outer.2
 // CHECK:STDOUT:     .Inner = %Inner.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc17
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -630,6 +635,7 @@ class Outer(T:! type) {
 // CHECK:STDOUT:     .B = %B.decl
 // CHECK:STDOUT:     .C = %C.decl
 // CHECK:STDOUT:     .D = %D.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc16
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic/field.carbon b/toolchain/check/testdata/class/generic/field.carbon
index 62e4fcd7cdd6..f20765260158 100644
--- a/toolchain/check/testdata/class/generic/field.carbon
+++ b/toolchain/check/testdata/class/generic/field.carbon
@@ -160,6 +160,7 @@ fn H(U:! type, c: Class(U)) -> U {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Class.2
 // CHECK:STDOUT:     .x = %.loc12_8.1
+// CHECK:STDOUT:     complete_type_witness = %.loc13_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic/import.carbon b/toolchain/check/testdata/class/generic/import.carbon
index f5bfbb69822f..8c76ba79ec44 100644
--- a/toolchain/check/testdata/class/generic/import.carbon
+++ b/toolchain/check/testdata/class/generic/import.carbon
@@ -202,6 +202,7 @@ class Class(U:! type) {
 // CHECK:STDOUT:     .Self = constants.%CompleteClass.2
 // CHECK:STDOUT:     .n = %.loc7_8.1
 // CHECK:STDOUT:     .F = %F.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc9
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -328,6 +329,8 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %CompleteClass.1: %CompleteClass.type = struct_value () [template]
 // CHECK:STDOUT:   %.24: Core.IntLiteral = int_value 32 [template]
 // CHECK:STDOUT:   %i32: type = int_type signed, %.24 [template]
+// CHECK:STDOUT:   %.25: type = struct_type {.n: %i32} [template]
+// CHECK:STDOUT:   %.26: <witness> = complete_type_witness %.25 [template]
 // CHECK:STDOUT:   %CompleteClass.2: type = class_type @CompleteClass, @CompleteClass(%T) [symbolic]
 // CHECK:STDOUT:   %.27: type = unbound_element_type %CompleteClass.2, %i32 [symbolic]
 // CHECK:STDOUT:   %F.type.1: type = fn_type @F.1, @CompleteClass(%T) [symbolic]
@@ -624,6 +627,7 @@ class Class(U:! type) {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Class.2
 // CHECK:STDOUT:     .x = %.loc5_8.1
+// CHECK:STDOUT:     complete_type_witness = %.loc6_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -642,6 +646,7 @@ class Class(U:! type) {
 // CHECK:STDOUT:     .Self = imports.%import_ref.38
 // CHECK:STDOUT:     .n = imports.%import_ref.39
 // CHECK:STDOUT:     .F = imports.%import_ref.40
+// CHECK:STDOUT:     complete_type_witness = constants.%.26
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1093,6 +1098,8 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %UseMethod: %UseMethod.type = struct_value () [template]
 // CHECK:STDOUT:   %CompleteClass.type: type = generic_class_type @CompleteClass [template]
 // CHECK:STDOUT:   %CompleteClass.1: %CompleteClass.type = struct_value () [template]
+// CHECK:STDOUT:   %.2: type = struct_type {.n: %i32} [template]
+// CHECK:STDOUT:   %.3: <witness> = complete_type_witness %.2 [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T, 0 [symbolic]
 // CHECK:STDOUT:   %CompleteClass.2: type = class_type @CompleteClass, @CompleteClass(%T) [symbolic]
 // CHECK:STDOUT:   %T.patt: type = symbolic_binding_pattern T, 0 [symbolic]
@@ -1174,6 +1181,7 @@ class Class(U:! type) {
 // CHECK:STDOUT:     .Self = imports.%import_ref.5
 // CHECK:STDOUT:     .n = imports.%import_ref.6
 // CHECK:STDOUT:     .F = imports.%import_ref.7
+// CHECK:STDOUT:     complete_type_witness = constants.%.3
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1272,6 +1280,8 @@ class Class(U:! type) {
 // CHECK:STDOUT:   %CompleteClass.1: %CompleteClass.type = struct_value () [template]
 // CHECK:STDOUT:   %.1: Core.IntLiteral = int_value 32 [template]
 // CHECK:STDOUT:   %i32: type = int_type signed, %.1 [template]
+// CHECK:STDOUT:   %.2: type = struct_type {.n: %i32} [template]
+// CHECK:STDOUT:   %.3: <witness> = complete_type_witness %.2 [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T, 0 [symbolic]
 // CHECK:STDOUT:   %CompleteClass.2: type = class_type @CompleteClass, @CompleteClass(%T) [symbolic]
 // CHECK:STDOUT:   %T.patt: type = symbolic_binding_pattern T, 0 [symbolic]
@@ -1565,6 +1575,7 @@ class Class(U:! type) {
 // CHECK:STDOUT:     .Self = imports.%import_ref.4
 // CHECK:STDOUT:     .n = imports.%import_ref.5
 // CHECK:STDOUT:     .F = imports.%import_ref.6
+// CHECK:STDOUT:     complete_type_witness = constants.%.3
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -2245,6 +2256,7 @@ class Class(U:! type) {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%.22
 // CHECK:STDOUT:     .x = %.loc16
+// CHECK:STDOUT:     complete_type_witness = %.loc17
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic/init.carbon b/toolchain/check/testdata/class/generic/init.carbon
index f1f0fc0f628c..cd2e2ee3813b 100644
--- a/toolchain/check/testdata/class/generic/init.carbon
+++ b/toolchain/check/testdata/class/generic/init.carbon
@@ -146,6 +146,7 @@ fn InitFromAdaptedSpecific(x: i32) -> i32 {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Class.2
 // CHECK:STDOUT:     .k = %.loc5_8.1
+// CHECK:STDOUT:     complete_type_witness = %.loc6_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -337,6 +338,7 @@ fn InitFromAdaptedSpecific(x: i32) -> i32 {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Adapt.2
+// CHECK:STDOUT:     complete_type_witness = %.loc6_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic/member_access.carbon b/toolchain/check/testdata/class/generic/member_access.carbon
index f4ccfbd5f289..0e3ffe557f9f 100644
--- a/toolchain/check/testdata/class/generic/member_access.carbon
+++ b/toolchain/check/testdata/class/generic/member_access.carbon
@@ -232,6 +232,7 @@ fn StaticMemberFunctionCall(T:! type) -> Class(T) {
 // CHECK:STDOUT:     .x = %.loc3_8.1
 // CHECK:STDOUT:     .Get = %Get.decl
 // CHECK:STDOUT:     .GetAddr = %GetAddr.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc8_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -466,6 +467,7 @@ fn StaticMemberFunctionCall(T:! type) -> Class(T) {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Class.2
 // CHECK:STDOUT:     .Make = %Make.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc6
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic/member_inline.carbon b/toolchain/check/testdata/class/generic/member_inline.carbon
index e8fbe56a72a1..dc44291ae75d 100644
--- a/toolchain/check/testdata/class/generic/member_inline.carbon
+++ b/toolchain/check/testdata/class/generic/member_inline.carbon
@@ -128,6 +128,7 @@ class C(T:! type) {
 // CHECK:STDOUT:     .F = %F.decl
 // CHECK:STDOUT:     .G = %G.decl
 // CHECK:STDOUT:     .n = %.loc13_8.1
+// CHECK:STDOUT:     complete_type_witness = %.loc14_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -253,6 +254,7 @@ class C(T:! type) {
 // CHECK:STDOUT:     .Self = constants.%C.2
 // CHECK:STDOUT:     .F = %F.decl
 // CHECK:STDOUT:     .data = %.loc11_11.1
+// CHECK:STDOUT:     complete_type_witness = %.loc12
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic/member_out_of_line.carbon b/toolchain/check/testdata/class/generic/member_out_of_line.carbon
index 4aae219bcf5c..29d3e78fe9b6 100644
--- a/toolchain/check/testdata/class/generic/member_out_of_line.carbon
+++ b/toolchain/check/testdata/class/generic/member_out_of_line.carbon
@@ -226,6 +226,7 @@ fn Generic(T:! ()).WrongType() {}
 // CHECK:STDOUT:     .F = %F.decl
 // CHECK:STDOUT:     .G = %G.decl
 // CHECK:STDOUT:     .n = %.loc7_8.1
+// CHECK:STDOUT:     complete_type_witness = %.loc8_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -374,6 +375,7 @@ fn Generic(T:! ()).WrongType() {}
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%A.2
 // CHECK:STDOUT:     .B = %B.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc8
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -406,6 +408,7 @@ fn Generic(T:! ()).WrongType() {}
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%B.2
 // CHECK:STDOUT:     .F = %F.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc7
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -505,6 +508,7 @@ fn Generic(T:! ()).WrongType() {}
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%NotGeneric
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F();
@@ -580,6 +584,7 @@ fn Generic(T:! ()).WrongType() {}
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Generic.2
 // CHECK:STDOUT:     .TooFew = %TooFew.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc6
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -666,6 +671,7 @@ fn Generic(T:! ()).WrongType() {}
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Generic.2
 // CHECK:STDOUT:     .TooMany = %TooMany.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc6
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -769,6 +775,7 @@ fn Generic(T:! ()).WrongType() {}
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Generic.2
 // CHECK:STDOUT:     .WrongType = %WrongType.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc6
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic/method_deduce.carbon b/toolchain/check/testdata/class/generic/method_deduce.carbon
index e7ba16ad2069..bd8d94d3bfb2 100644
--- a/toolchain/check/testdata/class/generic/method_deduce.carbon
+++ b/toolchain/check/testdata/class/generic/method_deduce.carbon
@@ -130,6 +130,7 @@ fn CallGenericMethodWithNonDeducedParam(c: Class(A)) -> (A, B) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -137,6 +138,7 @@ fn CallGenericMethodWithNonDeducedParam(c: Class(A)) -> (A, B) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Class(%T.loc14_13.1: type) {
@@ -191,6 +193,7 @@ fn CallGenericMethodWithNonDeducedParam(c: Class(A)) -> (A, B) {
 // CHECK:STDOUT:     .Self = constants.%Class.2
 // CHECK:STDOUT:     .Get = %Get.decl
 // CHECK:STDOUT:     .GetNoDeduce = %GetNoDeduce.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc17
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic/redeclare.carbon b/toolchain/check/testdata/class/generic/redeclare.carbon
index 2378a7fdba67..8c4086e8e61a 100644
--- a/toolchain/check/testdata/class/generic/redeclare.carbon
+++ b/toolchain/check/testdata/class/generic/redeclare.carbon
@@ -138,6 +138,7 @@ class E(U:! type) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Generic.2
+// CHECK:STDOUT:     complete_type_witness = %.loc7
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -195,6 +196,7 @@ class E(U:! type) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%.2
+// CHECK:STDOUT:     complete_type_witness = %.loc12
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -284,6 +286,7 @@ class E(U:! type) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%.3
+// CHECK:STDOUT:     complete_type_witness = %.loc12
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -377,6 +380,7 @@ class E(U:! type) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%.3
+// CHECK:STDOUT:     complete_type_witness = %.loc12_29
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -464,6 +468,7 @@ class E(U:! type) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%.3
+// CHECK:STDOUT:     complete_type_witness = %.loc12_19
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -540,6 +545,7 @@ class E(U:! type) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%.2
+// CHECK:STDOUT:     complete_type_witness = %.loc11
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic/self.carbon b/toolchain/check/testdata/class/generic/self.carbon
index ec9eda1dea13..ba0315cd8e13 100644
--- a/toolchain/check/testdata/class/generic/self.carbon
+++ b/toolchain/check/testdata/class/generic/self.carbon
@@ -102,6 +102,7 @@ class Class(T:! type) {
 // CHECK:STDOUT:     .MakeSelf = %MakeSelf.decl
 // CHECK:STDOUT:     .MakeClass = %MakeClass.decl
 // CHECK:STDOUT:     .F = %F.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc20
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic/stringify.carbon b/toolchain/check/testdata/class/generic/stringify.carbon
index 4c9c90895923..73620b18a818 100644
--- a/toolchain/check/testdata/class/generic/stringify.carbon
+++ b/toolchain/check/testdata/class/generic/stringify.carbon
@@ -89,6 +89,7 @@ var w: Outer({}*).Inner({.a: i32}*) = v;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%NoParams
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @EmptyParams {
@@ -96,6 +97,7 @@ var w: Outer({}*).Inner({.a: i32}*) = v;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%EmptyParams.2
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -204,6 +206,7 @@ var w: Outer({}*).Inner({.a: i32}*) = v;
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Outer.2
 // CHECK:STDOUT:     .Inner = %Inner.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc7
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -218,6 +221,7 @@ var w: Outer({}*).Inner({.a: i32}*) = v;
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Inner.2
+// CHECK:STDOUT:     complete_type_witness = %.loc6
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/generic_method.carbon b/toolchain/check/testdata/class/generic_method.carbon
index 4309eb6dcb68..06f52de23160 100644
--- a/toolchain/check/testdata/class/generic_method.carbon
+++ b/toolchain/check/testdata/class/generic_method.carbon
@@ -103,6 +103,7 @@ fn Class(T:! type).F[self: Self](n: T) {}
 // CHECK:STDOUT:     .Self = constants.%Class.2
 // CHECK:STDOUT:     .a = %.loc12_8.1
 // CHECK:STDOUT:     .F = %F.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc14_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/import.carbon b/toolchain/check/testdata/class/import.carbon
index 22f9b7c7a062..9ef671c928cf 100644
--- a/toolchain/check/testdata/class/import.carbon
+++ b/toolchain/check/testdata/class/import.carbon
@@ -101,6 +101,7 @@ fn Run() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Empty
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Field {
@@ -114,6 +115,7 @@ fn Run() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Field
 // CHECK:STDOUT:   .x = %.loc8_8
+// CHECK:STDOUT:   complete_type_witness = %.loc9
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @ForwardDeclared {
@@ -141,6 +143,7 @@ fn Run() {
 // CHECK:STDOUT:   .Self = constants.%ForwardDeclared
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Incomplete;
@@ -157,10 +160,13 @@ fn Run() {
 // CHECK:STDOUT:   %Run: %Run.type = struct_value () [template]
 // CHECK:STDOUT:   %Empty: type = class_type @Empty [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct.1: %Empty = struct_value () [template]
 // CHECK:STDOUT:   %Field: type = class_type @Field [template]
 // CHECK:STDOUT:   %.4: Core.IntLiteral = int_value 32 [template]
 // CHECK:STDOUT:   %i32: type = int_type signed, %.4 [template]
+// CHECK:STDOUT:   %.5: type = struct_type {.x: %i32} [template]
+// CHECK:STDOUT:   %.6: <witness> = complete_type_witness %.5 [template]
 // CHECK:STDOUT:   %.8: Core.IntLiteral = int_value 1 [template]
 // CHECK:STDOUT:   %.9: type = struct_type {.x: Core.IntLiteral} [template]
 // CHECK:STDOUT:   %Convert.type.2: type = fn_type @Convert.1, @ImplicitAs(%i32) [template]
@@ -225,12 +231,14 @@ fn Run() {
 // CHECK:STDOUT: class @Empty {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Field {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.6
 // CHECK:STDOUT:   .x = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @ForwardDeclared.1 {
@@ -238,6 +246,7 @@ fn Run() {
 // CHECK:STDOUT:   .Self = imports.%import_ref.44
 // CHECK:STDOUT:   .F = imports.%import_ref.45
 // CHECK:STDOUT:   .G = imports.%import_ref.46
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @ForwardDeclared.2 {
@@ -245,6 +254,7 @@ fn Run() {
 // CHECK:STDOUT:   .Self = imports.%import_ref.47
 // CHECK:STDOUT:   .F = imports.%import_ref.48
 // CHECK:STDOUT:   .G = imports.%import_ref.49
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Incomplete;
diff --git a/toolchain/check/testdata/class/import_base.carbon b/toolchain/check/testdata/class/import_base.carbon
index 5ba74cf39fdc..529889ce0236 100644
--- a/toolchain/check/testdata/class/import_base.carbon
+++ b/toolchain/check/testdata/class/import_base.carbon
@@ -111,6 +111,7 @@ fn Run() {
 // CHECK:STDOUT:   .Unused = %Unused.decl
 // CHECK:STDOUT:   .x = %.loc8_8
 // CHECK:STDOUT:   .unused = %.loc9_13
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Child {
@@ -122,6 +123,7 @@ fn Run() {
 // CHECK:STDOUT:   .Self = constants.%Child
 // CHECK:STDOUT:   .base = %.loc13
 // CHECK:STDOUT:   extend %Base.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F[%self.param_patt: %Base]();
@@ -138,6 +140,10 @@ fn Run() {
 // CHECK:STDOUT:   %Base: type = class_type @Base [template]
 // CHECK:STDOUT:   %.1: Core.IntLiteral = int_value 32 [template]
 // CHECK:STDOUT:   %i32: type = int_type signed, %.1 [template]
+// CHECK:STDOUT:   %.2: type = struct_type {.x: %i32, .unused: %i32} [template]
+// CHECK:STDOUT:   %.3: <witness> = complete_type_witness %.2 [template]
+// CHECK:STDOUT:   %.5: type = struct_type {.base: %Base} [template]
+// CHECK:STDOUT:   %.6: <witness> = complete_type_witness %.5 [template]
 // CHECK:STDOUT:   %.10: Core.IntLiteral = int_value 0 [template]
 // CHECK:STDOUT:   %.11: Core.IntLiteral = int_value 1 [template]
 // CHECK:STDOUT:   %.12: type = struct_type {.x: Core.IntLiteral, .unused: Core.IntLiteral} [template]
@@ -198,6 +204,7 @@ fn Run() {
 // CHECK:STDOUT:   .Self = imports.%import_ref.9
 // CHECK:STDOUT:   .base = imports.%import_ref.10
 // CHECK:STDOUT:   extend imports.%import_ref.11
+// CHECK:STDOUT:   complete_type_witness = constants.%.6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Base {
@@ -207,6 +214,7 @@ fn Run() {
 // CHECK:STDOUT:   .Unused = imports.%import_ref.5
 // CHECK:STDOUT:   .x = imports.%import_ref.6
 // CHECK:STDOUT:   .unused = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.3
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Run() {
diff --git a/toolchain/check/testdata/class/import_forward_decl.carbon b/toolchain/check/testdata/class/import_forward_decl.carbon
index 674265353828..916a3f2345cf 100644
--- a/toolchain/check/testdata/class/import_forward_decl.carbon
+++ b/toolchain/check/testdata/class/import_forward_decl.carbon
@@ -76,5 +76,6 @@ class ForwardDecl {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%ForwardDecl
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/import_indirect.carbon b/toolchain/check/testdata/class/import_indirect.carbon
index 413c07a0ce5e..303495593bc9 100644
--- a/toolchain/check/testdata/class/import_indirect.carbon
+++ b/toolchain/check/testdata/class/import_indirect.carbon
@@ -129,6 +129,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- b.carbon
@@ -136,6 +137,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT:   %.4: type = ptr_type %C [template]
 // CHECK:STDOUT: }
@@ -173,6 +175,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -192,6 +195,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT:   %.4: type = ptr_type %C [template]
 // CHECK:STDOUT: }
@@ -229,6 +233,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -248,6 +253,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT:   %.4: type = ptr_type %C [template]
 // CHECK:STDOUT: }
@@ -288,6 +294,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -307,6 +314,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT:   %.4: type = ptr_type %C [template]
 // CHECK:STDOUT: }
@@ -347,6 +355,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -366,6 +375,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT:   %.4: type = ptr_type %C [template]
 // CHECK:STDOUT: }
@@ -410,6 +420,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -429,6 +440,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT:   %.4: type = ptr_type %C [template]
 // CHECK:STDOUT: }
@@ -473,6 +485,7 @@ var ptr: E* = &val;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/class/import_member_cycle.carbon b/toolchain/check/testdata/class/import_member_cycle.carbon
index ce65c44e6214..c8551d18b6bb 100644
--- a/toolchain/check/testdata/class/import_member_cycle.carbon
+++ b/toolchain/check/testdata/class/import_member_cycle.carbon
@@ -61,6 +61,7 @@ fn Run() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Cycle
 // CHECK:STDOUT:   .a = %.loc5_8
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- b.carbon
@@ -70,6 +71,8 @@ fn Run() {
 // CHECK:STDOUT:   %Run: %Run.type = struct_value () [template]
 // CHECK:STDOUT:   %Cycle: type = class_type @Cycle [template]
 // CHECK:STDOUT:   %.1: type = ptr_type %Cycle [template]
+// CHECK:STDOUT:   %.2: type = struct_type {.a: %.1} [template]
+// CHECK:STDOUT:   %.3: <witness> = complete_type_witness %.2 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -97,6 +100,7 @@ fn Run() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .a = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.3
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Run() {
diff --git a/toolchain/check/testdata/class/import_struct_cyle.carbon b/toolchain/check/testdata/class/import_struct_cyle.carbon
index 8646c65beffc..18628916efd4 100644
--- a/toolchain/check/testdata/class/import_struct_cyle.carbon
+++ b/toolchain/check/testdata/class/import_struct_cyle.carbon
@@ -75,6 +75,7 @@ fn Run() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Cycle
 // CHECK:STDOUT:   .c = %.loc10_8
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- b.carbon
@@ -85,6 +86,8 @@ fn Run() {
 // CHECK:STDOUT:   %Cycle: type = class_type @Cycle [template]
 // CHECK:STDOUT:   %.1: type = ptr_type %Cycle [template]
 // CHECK:STDOUT:   %.2: type = struct_type {.b: %.1} [template]
+// CHECK:STDOUT:   %.3: type = struct_type {.c: %.2} [template]
+// CHECK:STDOUT:   %.4: <witness> = complete_type_witness %.3 [template]
 // CHECK:STDOUT:   %.6: type = unbound_element_type %Cycle, %.2 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -115,6 +118,7 @@ fn Run() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
 // CHECK:STDOUT:   .c = imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Run() {
diff --git a/toolchain/check/testdata/class/inheritance_access.carbon b/toolchain/check/testdata/class/inheritance_access.carbon
index 2e9e291bbe07..4520149cafee 100644
--- a/toolchain/check/testdata/class/inheritance_access.carbon
+++ b/toolchain/check/testdata/class/inheritance_access.carbon
@@ -283,6 +283,7 @@ class B {
 // CHECK:STDOUT:   .Self = constants.%Shape
 // CHECK:STDOUT:   .x [protected] = %.loc5_18
 // CHECK:STDOUT:   .y [protected] = %.loc6_18
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Circle {
@@ -317,6 +318,7 @@ class B {
 // CHECK:STDOUT:   .base = %.loc10
 // CHECK:STDOUT:   .GetPosition = %GetPosition.decl
 // CHECK:STDOUT:   extend %Shape.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @GetPosition[%self.param_patt: %Circle]() -> %return: %tuple.type.2 {
@@ -399,6 +401,7 @@ class B {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -422,6 +425,7 @@ class B {
 // CHECK:STDOUT:   .base = %.loc9
 // CHECK:STDOUT:   .F [private] = %F.decl
 // CHECK:STDOUT:   extend %A.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -448,6 +452,7 @@ class B {
 // CHECK:STDOUT:   .base = %.loc14
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.1();
@@ -546,6 +551,7 @@ class B {
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .SOME_CONSTANT [protected] = %SOME_CONSTANT
 // CHECK:STDOUT:   .SomeProtectedFunction [protected] = %SomeProtectedFunction.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc9
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -581,6 +587,7 @@ class B {
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   .H = %H.decl
 // CHECK:STDOUT:   extend %A.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc21
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @SomeProtectedFunction() -> %i32 {
@@ -661,6 +668,7 @@ class B {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Shape
 // CHECK:STDOUT:   .y [private] = %.loc5_16
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Square {
@@ -689,6 +697,7 @@ class B {
 // CHECK:STDOUT:   .base = %.loc9
 // CHECK:STDOUT:   .GetPosition = %GetPosition.decl
 // CHECK:STDOUT:   extend %Shape.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc21
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @GetPosition[%self.param_patt: %Square]() -> %i32 {
@@ -736,6 +745,7 @@ class B {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .F [private] = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
@@ -789,6 +799,7 @@ class B {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .F [protected] = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
@@ -845,6 +856,7 @@ class B {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
 // CHECK:STDOUT:   .F [private] = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -858,6 +870,7 @@ class B {
 // CHECK:STDOUT:   .base = %.loc9
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc18
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
@@ -914,6 +927,7 @@ class B {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
 // CHECK:STDOUT:   .F [protected] = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -927,6 +941,7 @@ class B {
 // CHECK:STDOUT:   .base = %.loc9
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   extend %B.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
@@ -1024,6 +1039,7 @@ class B {
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .SOME_PROTECTED_CONSTANT [protected] = %SOME_PROTECTED_CONSTANT
 // CHECK:STDOUT:   .SOME_PRIVATE_CONSTANT [private] = %SOME_PRIVATE_CONSTANT
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Internal {
@@ -1044,6 +1060,7 @@ class B {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Internal
 // CHECK:STDOUT:   .INTERNAL_CONSTANT [protected] = %INTERNAL_CONSTANT
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -1083,6 +1100,7 @@ class B {
 // CHECK:STDOUT:   .internal [private] = %.loc14
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   .SomeFunc = %SomeFunc.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc46
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @G() -> %i32 {
@@ -1153,6 +1171,7 @@ class B {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .x [private] = %.loc5_16
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -1173,6 +1192,7 @@ class B {
 // CHECK:STDOUT:   .base = %.loc9
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   extend %A.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F[%self.param_patt: %B]() {
@@ -1232,6 +1252,7 @@ class B {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
 // CHECK:STDOUT:   .x [protected] = %.loc5_18
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -1252,6 +1273,7 @@ class B {
 // CHECK:STDOUT:   .base = %.loc9
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   extend %A.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F[%self.param_patt: %B]() {
diff --git a/toolchain/check/testdata/class/init.carbon b/toolchain/check/testdata/class/init.carbon
index 5559263891fb..0c7597e4adc4 100644
--- a/toolchain/check/testdata/class/init.carbon
+++ b/toolchain/check/testdata/class/init.carbon
@@ -119,6 +119,7 @@ fn MakeReorder(n: i32, next: Class*) -> Class {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .n = %.loc12_8
 // CHECK:STDOUT:   .next = %.loc13_11
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Make(%n.param_patt: %i32, %next.param_patt: %.3) -> %return: %Class {
diff --git a/toolchain/check/testdata/class/init_adapt.carbon b/toolchain/check/testdata/class/init_adapt.carbon
index 2e33fba8b377..3571b044084a 100644
--- a/toolchain/check/testdata/class/init_adapt.carbon
+++ b/toolchain/check/testdata/class/init_adapt.carbon
@@ -192,6 +192,7 @@ var e: C = MakeAdaptC();
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .a = %.loc5_8
 // CHECK:STDOUT:   .b = %.loc6_8
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @AdaptC {
@@ -201,6 +202,7 @@ var e: C = MakeAdaptC();
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%AdaptC
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @MakeC() -> %C;
@@ -360,6 +362,7 @@ var e: C = MakeAdaptC();
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .a = %.loc5_8
 // CHECK:STDOUT:   .b = %.loc6_8
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @AdaptC {
@@ -369,6 +372,7 @@ var e: C = MakeAdaptC();
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%AdaptC
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @MakeC() -> %C;
diff --git a/toolchain/check/testdata/class/init_as.carbon b/toolchain/check/testdata/class/init_as.carbon
index e54e848c9235..31059fec8735 100644
--- a/toolchain/check/testdata/class/init_as.carbon
+++ b/toolchain/check/testdata/class/init_as.carbon
@@ -93,6 +93,7 @@ fn F() -> i32 {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .a = %.loc12_8
 // CHECK:STDOUT:   .b = %.loc13_8
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %i32 {
diff --git a/toolchain/check/testdata/class/init_nested.carbon b/toolchain/check/testdata/class/init_nested.carbon
index 1408aa9da6c6..f8fb860c2488 100644
--- a/toolchain/check/testdata/class/init_nested.carbon
+++ b/toolchain/check/testdata/class/init_nested.carbon
@@ -99,6 +99,7 @@ fn MakeOuter() -> Outer {
 // CHECK:STDOUT:   .Self = constants.%Inner
 // CHECK:STDOUT:   .a = %.loc12_8
 // CHECK:STDOUT:   .b = %.loc13_8
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Outer {
@@ -112,6 +113,7 @@ fn MakeOuter() -> Outer {
 // CHECK:STDOUT:   .Self = constants.%Outer
 // CHECK:STDOUT:   .c = %.loc19
 // CHECK:STDOUT:   .d = %.loc20
+// CHECK:STDOUT:   complete_type_witness = %.loc21
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @MakeInner() -> %Inner;
diff --git a/toolchain/check/testdata/class/method.carbon b/toolchain/check/testdata/class/method.carbon
index 4bd870492387..29099815ac34 100644
--- a/toolchain/check/testdata/class/method.carbon
+++ b/toolchain/check/testdata/class/method.carbon
@@ -315,6 +315,7 @@ fn CallGOnInitializingExpr() -> i32 {
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   .A = %A
 // CHECK:STDOUT:   .k = %.loc17_8
+// CHECK:STDOUT:   complete_type_witness = %.loc18
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F[%self.param_patt: %Class]() -> %i32 {
diff --git a/toolchain/check/testdata/class/nested.carbon b/toolchain/check/testdata/class/nested.carbon
index ef31d64bbd90..72a963381e98 100644
--- a/toolchain/check/testdata/class/nested.carbon
+++ b/toolchain/check/testdata/class/nested.carbon
@@ -123,6 +123,7 @@ fn F(a: Outer*) {
 // CHECK:STDOUT:   .po = %.loc36_9
 // CHECK:STDOUT:   .qo = %.loc37_9
 // CHECK:STDOUT:   .pi = %.loc38_9
+// CHECK:STDOUT:   complete_type_witness = %.loc39
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Inner {
@@ -144,6 +145,7 @@ fn F(a: Outer*) {
 // CHECK:STDOUT:   .po = %.loc20_11
 // CHECK:STDOUT:   .qi = %.loc21_11
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc28
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.1() {
diff --git a/toolchain/check/testdata/class/nested_name.carbon b/toolchain/check/testdata/class/nested_name.carbon
index 149a13595694..2cc1cc627aab 100644
--- a/toolchain/check/testdata/class/nested_name.carbon
+++ b/toolchain/check/testdata/class/nested_name.carbon
@@ -93,6 +93,7 @@ fn G(o: Outer) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Outer
 // CHECK:STDOUT:   .Inner = %Inner.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Inner {
@@ -106,6 +107,7 @@ fn G(o: Outer) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Inner
 // CHECK:STDOUT:   .n = %.loc13_10
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%oi.param_patt: %Inner) -> %i32 {
diff --git a/toolchain/check/testdata/class/no_prelude/export_name.carbon b/toolchain/check/testdata/class/no_prelude/export_name.carbon
index 7c2daad8bd9b..55c908e2aaf7 100644
--- a/toolchain/check/testdata/class/no_prelude/export_name.carbon
+++ b/toolchain/check/testdata/class/no_prelude/export_name.carbon
@@ -58,12 +58,15 @@ var c: C = {};
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- export.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -82,6 +85,7 @@ var c: C = {};
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- use_export.carbon
@@ -89,6 +93,7 @@ var c: C = {};
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -111,6 +116,7 @@ var c: C = {};
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/class/no_prelude/extern.carbon b/toolchain/check/testdata/class/no_prelude/extern.carbon
index 7ab66260d054..8101d8e93152 100644
--- a/toolchain/check/testdata/class/no_prelude/extern.carbon
+++ b/toolchain/check/testdata/class/no_prelude/extern.carbon
@@ -346,6 +346,7 @@ extern class C;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_decl_fn_in_extern.carbon
@@ -388,6 +389,7 @@ extern class C;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_extern_decl_after_extern_decl.carbon
@@ -445,6 +447,7 @@ extern class C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .D = %D.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D;
@@ -470,6 +473,7 @@ extern class C;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_extern_decl_after_decl.carbon
@@ -595,6 +599,8 @@ extern class C;
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -612,12 +618,15 @@ extern class C;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_extern_decl_after_import_def.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -635,5 +644,6 @@ extern class C;
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/no_prelude/generic_vs_params.carbon b/toolchain/check/testdata/class/no_prelude/generic_vs_params.carbon
index fc1646827223..fad17b3f501f 100644
--- a/toolchain/check/testdata/class/no_prelude/generic_vs_params.carbon
+++ b/toolchain/check/testdata/class/no_prelude/generic_vs_params.carbon
@@ -154,6 +154,7 @@ fn F(T:! type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%NotGenericNoParams
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @NotGenericButParams {
@@ -161,6 +162,7 @@ fn F(T:! type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%NotGenericButParams.2
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @GenericAndParams.1(%T.loc6_24.1: type) {
@@ -174,6 +176,7 @@ fn F(T:! type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%GenericAndParams.2
+// CHECK:STDOUT:     complete_type_witness = %.loc6
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -200,6 +203,7 @@ fn F(T:! type) {
 // CHECK:STDOUT:     .Self = constants.%C.2
 // CHECK:STDOUT:     .GenericNoParams = %GenericNoParams.decl
 // CHECK:STDOUT:     .GenericAndParams = %GenericAndParams.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc11
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -211,6 +215,7 @@ fn F(T:! type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%GenericNoParams.2
+// CHECK:STDOUT:     complete_type_witness = %.loc9
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -225,6 +230,7 @@ fn F(T:! type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%GenericAndParams.4
+// CHECK:STDOUT:     complete_type_witness = %.loc10
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -233,6 +239,7 @@ fn F(T:! type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%X
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -327,6 +334,7 @@ fn F(T:! type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A.2
+// CHECK:STDOUT:   complete_type_witness = %.loc8
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_non_generic_params.carbon
@@ -363,6 +371,7 @@ fn F(T:! type) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A.2
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc10_6.1: type) {
diff --git a/toolchain/check/testdata/class/no_prelude/implicit_import.carbon b/toolchain/check/testdata/class/no_prelude/implicit_import.carbon
index a7a3ac931c8e..279971cfa692 100644
--- a/toolchain/check/testdata/class/no_prelude/implicit_import.carbon
+++ b/toolchain/check/testdata/class/no_prelude/implicit_import.carbon
@@ -120,6 +120,7 @@ class B {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- redecl_after_def.carbon
@@ -142,12 +143,15 @@ class B {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_redecl_after_def.impl.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -166,6 +170,7 @@ class B {}
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- redef_after_def.carbon
@@ -188,6 +193,7 @@ class B {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_redef_after_def.impl.carbon
@@ -216,6 +222,7 @@ class B {}
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @.1 {
@@ -223,6 +230,7 @@ class B {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%.3
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- def_alias.carbon
@@ -274,5 +282,6 @@ class B {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%.1
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/no_prelude/import_access.carbon b/toolchain/check/testdata/class/no_prelude/import_access.carbon
index 9d2eb6e8cecd..89c49efa8c8c 100644
--- a/toolchain/check/testdata/class/no_prelude/import_access.carbon
+++ b/toolchain/check/testdata/class/no_prelude/import_access.carbon
@@ -155,6 +155,7 @@ private class Redecl {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Def
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- forward_with_def.carbon
@@ -178,6 +179,7 @@ private class Redecl {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%ForwardWithDef
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- forward.carbon
@@ -200,6 +202,7 @@ private class Redecl {}
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %Def: type = class_type @Def [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %Def = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -223,6 +226,7 @@ private class Redecl {}
 // CHECK:STDOUT: class @Def {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -293,6 +297,7 @@ private class Redecl {}
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %ForwardWithDef: type = class_type @ForwardWithDef [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %ForwardWithDef = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -316,6 +321,7 @@ private class Redecl {}
 // CHECK:STDOUT: class @ForwardWithDef {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -420,6 +426,7 @@ private class Redecl {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Forward
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%c.param_patt: %.1) {
@@ -512,5 +519,6 @@ private class Redecl {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Redecl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/no_prelude/indirect_import_member.carbon b/toolchain/check/testdata/class/no_prelude/indirect_import_member.carbon
index b629872b2a32..acde352ad2a1 100644
--- a/toolchain/check/testdata/class/no_prelude/indirect_import_member.carbon
+++ b/toolchain/check/testdata/class/no_prelude/indirect_import_member.carbon
@@ -124,6 +124,7 @@ var x: () = D.C.F();
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
@@ -148,6 +149,8 @@ var x: () = D.C.F();
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -168,6 +171,7 @@ var x: () = D.C.F();
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .F = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- d.carbon
@@ -215,12 +219,14 @@ var x: () = D.C.F();
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
 // CHECK:STDOUT:   .C = %C
+// CHECK:STDOUT:   complete_type_witness = %.loc8
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .F = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- f.carbon
@@ -241,6 +247,8 @@ var x: () = D.C.F();
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
 // CHECK:STDOUT: }
@@ -267,6 +275,7 @@ var x: () = D.C.F();
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .F = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F();
@@ -285,6 +294,8 @@ var x: () = D.C.F();
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
 // CHECK:STDOUT: }
@@ -311,6 +322,7 @@ var x: () = D.C.F();
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .F = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F();
@@ -329,6 +341,8 @@ var x: () = D.C.F();
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
 // CHECK:STDOUT: }
@@ -355,6 +369,7 @@ var x: () = D.C.F();
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .F = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F();
@@ -373,6 +388,8 @@ var x: () = D.C.F();
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %D: type = class_type @D [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
@@ -402,12 +419,14 @@ var x: () = D.C.F();
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .C = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
 // CHECK:STDOUT:   .F = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F();
@@ -427,6 +446,8 @@ var x: () = D.C.F();
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %D: type = class_type @D [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
@@ -456,12 +477,14 @@ var x: () = D.C.F();
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .C = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
 // CHECK:STDOUT:   .F = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F();
diff --git a/toolchain/check/testdata/class/no_prelude/no_definition_in_impl_file.carbon b/toolchain/check/testdata/class/no_prelude/no_definition_in_impl_file.carbon
index 69b296031a3e..b6f3a69617da 100644
--- a/toolchain/check/testdata/class/no_prelude/no_definition_in_impl_file.carbon
+++ b/toolchain/check/testdata/class/no_prelude/no_definition_in_impl_file.carbon
@@ -112,6 +112,7 @@ class D;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- use_decl_in_api.carbon
diff --git a/toolchain/check/testdata/class/no_prelude/syntactic_merge.carbon b/toolchain/check/testdata/class/no_prelude/syntactic_merge.carbon
index 540acc397435..3fad2802dd81 100644
--- a/toolchain/check/testdata/class/no_prelude/syntactic_merge.carbon
+++ b/toolchain/check/testdata/class/no_prelude/syntactic_merge.carbon
@@ -244,6 +244,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Foo(%a.loc7_11.1: %C) {
@@ -257,6 +258,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Foo.2
+// CHECK:STDOUT:     complete_type_witness = %.loc8
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -271,6 +273,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Bar.2
+// CHECK:STDOUT:     complete_type_witness = %.loc11
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -326,6 +329,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Foo(%a.loc6_17.1: %C) {
@@ -339,6 +343,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Foo.2
+// CHECK:STDOUT:     complete_type_witness = %.loc7
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -391,6 +396,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Foo(%a.loc6_11.1: %C) {
@@ -411,6 +417,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%.4
+// CHECK:STDOUT:     complete_type_witness = %.loc14
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -466,6 +473,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Foo(%a.loc6_11.1: %C) {
@@ -479,6 +487,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Foo.2
+// CHECK:STDOUT:     complete_type_witness = %.loc7
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -534,6 +543,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Foo(%a.loc7_11.1: %C) {
@@ -612,6 +622,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Foo(constants.%a: %C) {
@@ -625,6 +636,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Foo.2
+// CHECK:STDOUT:     complete_type_witness = %.loc4
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -639,6 +651,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Bar.2
+// CHECK:STDOUT:     complete_type_witness = %.loc5
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -701,6 +714,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Foo(%a.loc7_11.1: %C) {
@@ -721,6 +735,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%.4
+// CHECK:STDOUT:     complete_type_witness = %.loc15
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -781,6 +796,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Foo(%a.loc7_11.1: %C) {
@@ -801,6 +817,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%.4
+// CHECK:STDOUT:     complete_type_witness = %.loc15
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -861,6 +878,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Foo(%a.loc7_11.1: %C) {
@@ -881,6 +899,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%.4
+// CHECK:STDOUT:     complete_type_witness = %.loc15
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -927,6 +946,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Foo(%a.loc6_11.1: %C) {
@@ -982,6 +1002,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Foo(constants.%a: %C) {
@@ -995,6 +1016,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Foo.2
+// CHECK:STDOUT:     complete_type_witness = %.loc6
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1051,6 +1073,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @Foo(%a.loc6_11.1: %.3) {
@@ -1071,6 +1094,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%.5
+// CHECK:STDOUT:     complete_type_witness = %.loc18_33
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1137,6 +1161,7 @@ fn Base.F[addr self: Base*]() {
 // CHECK:STDOUT:   .Self = constants.%Base
 // CHECK:STDOUT:   .a = %.loc5_8
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc8
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F[addr %self.param_patt: %.2]();
diff --git a/toolchain/check/testdata/class/raw_self.carbon b/toolchain/check/testdata/class/raw_self.carbon
index 4cc8f9df033c..21e41a802c3f 100644
--- a/toolchain/check/testdata/class/raw_self.carbon
+++ b/toolchain/check/testdata/class/raw_self.carbon
@@ -168,6 +168,7 @@ fn Class.G[self: Self](r#self: i32) -> (i32, i32) {
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   .n = %.loc14_8
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F[addr %self.param_patt.loc17_21: %.1](%self.param_patt.loc17_36: %i32) {
diff --git a/toolchain/check/testdata/class/raw_self_type.carbon b/toolchain/check/testdata/class/raw_self_type.carbon
index 5cb13ca2a1a3..2eef1a946233 100644
--- a/toolchain/check/testdata/class/raw_self_type.carbon
+++ b/toolchain/check/testdata/class/raw_self_type.carbon
@@ -76,6 +76,7 @@ fn MemberNamedSelf.F(x: Self, y: r#Self) {}
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @MemberNamedSelf {
@@ -99,6 +100,7 @@ fn MemberNamedSelf.F(x: Self, y: r#Self) {}
 // CHECK:STDOUT:   .Self = constants.%MemberNamedSelf
 // CHECK:STDOUT:   .r#Self = %Self.decl
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc22
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Self {
@@ -106,6 +108,7 @@ fn MemberNamedSelf.F(x: Self, y: r#Self) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Self
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.1() {
diff --git a/toolchain/check/testdata/class/redeclaration.carbon b/toolchain/check/testdata/class/redeclaration.carbon
index 8d80e9ecf461..40cb75739491 100644
--- a/toolchain/check/testdata/class/redeclaration.carbon
+++ b/toolchain/check/testdata/class/redeclaration.carbon
@@ -82,6 +82,7 @@ fn Class.F[self: Self](b: bool) {}
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F[%self.param_patt: %Class](%b.param_patt: bool) {
diff --git a/toolchain/check/testdata/class/redeclaration_introducer.carbon b/toolchain/check/testdata/class/redeclaration_introducer.carbon
index b7de42984cd3..9874c233d1fb 100644
--- a/toolchain/check/testdata/class/redeclaration_introducer.carbon
+++ b/toolchain/check/testdata/class/redeclaration_introducer.carbon
@@ -54,6 +54,7 @@ abstract class C {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -61,6 +62,7 @@ abstract class C {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -68,5 +70,6 @@ abstract class C {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/reenter_scope.carbon b/toolchain/check/testdata/class/reenter_scope.carbon
index 0901d7c07f39..fb79106ea3a3 100644
--- a/toolchain/check/testdata/class/reenter_scope.carbon
+++ b/toolchain/check/testdata/class/reenter_scope.carbon
@@ -91,6 +91,7 @@ fn Class.F() -> i32 {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %i32 {
diff --git a/toolchain/check/testdata/class/reorder.carbon b/toolchain/check/testdata/class/reorder.carbon
index 22994849d5af..2fe4ee4d5d79 100644
--- a/toolchain/check/testdata/class/reorder.carbon
+++ b/toolchain/check/testdata/class/reorder.carbon
@@ -89,6 +89,7 @@ class Class {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @G() -> %i32 {
diff --git a/toolchain/check/testdata/class/reorder_qualified.carbon b/toolchain/check/testdata/class/reorder_qualified.carbon
index 12d7cb13b7d1..3e423a950afa 100644
--- a/toolchain/check/testdata/class/reorder_qualified.carbon
+++ b/toolchain/check/testdata/class/reorder_qualified.carbon
@@ -144,6 +144,7 @@ class A {
 // CHECK:STDOUT:   .B = %B.decl
 // CHECK:STDOUT:   .AF = %AF.decl
 // CHECK:STDOUT:   .a = %.loc46_8
+// CHECK:STDOUT:   complete_type_witness = %.loc47
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -161,6 +162,7 @@ class A {
 // CHECK:STDOUT:   .C = %C.decl
 // CHECK:STDOUT:   .BF = %BF.decl
 // CHECK:STDOUT:   .b = %.loc16_10
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -179,6 +181,7 @@ class A {
 // CHECK:STDOUT:   .D = %D.decl
 // CHECK:STDOUT:   .CF = %CF.decl
 // CHECK:STDOUT:   .c = %.loc42_10
+// CHECK:STDOUT:   complete_type_witness = %.loc43
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -196,6 +199,7 @@ class A {
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .DF = %DF.decl
 // CHECK:STDOUT:   .d = %.loc24_12
+// CHECK:STDOUT:   complete_type_witness = %.loc25
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @BF();
diff --git a/toolchain/check/testdata/class/scope.carbon b/toolchain/check/testdata/class/scope.carbon
index 246a842e18e5..f2cc716ee138 100644
--- a/toolchain/check/testdata/class/scope.carbon
+++ b/toolchain/check/testdata/class/scope.carbon
@@ -120,6 +120,7 @@ fn Run() {
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F.1() -> %i32 {
diff --git a/toolchain/check/testdata/class/self.carbon b/toolchain/check/testdata/class/self.carbon
index df488eee606a..31f727f048f0 100644
--- a/toolchain/check/testdata/class/self.carbon
+++ b/toolchain/check/testdata/class/self.carbon
@@ -157,6 +157,7 @@ class Class {
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
 // CHECK:STDOUT:   .n = %.loc8_8
+// CHECK:STDOUT:   complete_type_witness = %.loc9
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F[%self.param_patt: %Class]() -> %i32 {
@@ -225,6 +226,7 @@ class Class {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F[%self.param_patt: %Class]() -> <error>;
diff --git a/toolchain/check/testdata/class/self_conversion.carbon b/toolchain/check/testdata/class/self_conversion.carbon
index 33f577fe898c..04087963526d 100644
--- a/toolchain/check/testdata/class/self_conversion.carbon
+++ b/toolchain/check/testdata/class/self_conversion.carbon
@@ -141,6 +141,7 @@ fn Call(p: Derived*) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Base
 // CHECK:STDOUT:   .a = %.loc12_8
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Derived {
@@ -180,6 +181,7 @@ fn Call(p: Derived*) -> i32 {
 // CHECK:STDOUT:   .SelfBase = %SelfBase.decl
 // CHECK:STDOUT:   .AddrSelfBase = %AddrSelfBase.decl
 // CHECK:STDOUT:   extend %Base.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc20
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @SelfBase[%self.param_patt: %Base]() -> %i32 {
diff --git a/toolchain/check/testdata/class/self_type.carbon b/toolchain/check/testdata/class/self_type.carbon
index b017816cbebe..ec67af7b5431 100644
--- a/toolchain/check/testdata/class/self_type.carbon
+++ b/toolchain/check/testdata/class/self_type.carbon
@@ -108,6 +108,7 @@ fn Class.F[self: Self]() -> i32 {
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .Make = %Make.decl
 // CHECK:STDOUT:   .p = %.loc18_8
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F[%self.param_patt: %Class]() -> %i32 {
diff --git a/toolchain/check/testdata/class/static_method.carbon b/toolchain/check/testdata/class/static_method.carbon
index 2f2d8ec04b0e..fb204b65062c 100644
--- a/toolchain/check/testdata/class/static_method.carbon
+++ b/toolchain/check/testdata/class/static_method.carbon
@@ -79,6 +79,7 @@ fn Run() -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Class
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %i32;
diff --git a/toolchain/check/testdata/class/syntactic_merge_literal.carbon b/toolchain/check/testdata/class/syntactic_merge_literal.carbon
index 24a0ead008d4..168978ba2c10 100644
--- a/toolchain/check/testdata/class/syntactic_merge_literal.carbon
+++ b/toolchain/check/testdata/class/syntactic_merge_literal.carbon
@@ -130,6 +130,7 @@ class D(b:! C(1_000)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:     complete_type_witness = %.loc2_19
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -144,6 +145,7 @@ class D(b:! C(1_000)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%D.2
+// CHECK:STDOUT:     complete_type_witness = %.loc4_24
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -266,6 +268,7 @@ class D(b:! C(1_000)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:     complete_type_witness = %.loc2_19
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -287,6 +290,7 @@ class D(b:! C(1_000)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%.33
+// CHECK:STDOUT:     complete_type_witness = %.loc10_24
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/class/todo_access_modifiers.carbon b/toolchain/check/testdata/class/todo_access_modifiers.carbon
index e2bac3886fe8..4dc5c2cae75c 100644
--- a/toolchain/check/testdata/class/todo_access_modifiers.carbon
+++ b/toolchain/check/testdata/class/todo_access_modifiers.carbon
@@ -74,6 +74,7 @@ class Access {
 // CHECK:STDOUT:   .G [protected] = %G.decl
 // CHECK:STDOUT:   .k [private] = %.loc17_16
 // CHECK:STDOUT:   .l [protected] = %.loc19_18
+// CHECK:STDOUT:   complete_type_witness = %.loc20
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F();
diff --git a/toolchain/check/testdata/class/virtual_modifiers.carbon b/toolchain/check/testdata/class/virtual_modifiers.carbon
index 5f3a8623be10..37a13cae37a5 100644
--- a/toolchain/check/testdata/class/virtual_modifiers.carbon
+++ b/toolchain/check/testdata/class/virtual_modifiers.carbon
@@ -159,6 +159,7 @@ class Derived {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Base
 // CHECK:STDOUT:   .H = %H.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Abstract {
@@ -170,6 +171,7 @@ class Derived {
 // CHECK:STDOUT:   .Self = constants.%Abstract
 // CHECK:STDOUT:   .J = %J.decl
 // CHECK:STDOUT:   .K = %K.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: virtual fn @H();
@@ -185,6 +187,9 @@ class Derived {
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
 // CHECK:STDOUT:   %Base: type = class_type @Base [template]
+// CHECK:STDOUT:   %.1: type = ptr_type <vtable> [template]
+// CHECK:STDOUT:   %.2: type = struct_type {.<vptr>: %.1} [template]
+// CHECK:STDOUT:   %.3: <witness> = complete_type_witness %.2 [template]
 // CHECK:STDOUT:   %.5: type = unbound_element_type %Derived, %Base [template]
 // CHECK:STDOUT:   %.6: type = struct_type {.base: %Base} [template]
 // CHECK:STDOUT:   %.7: <witness> = complete_type_witness %.6 [template]
@@ -227,12 +232,14 @@ class Derived {
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .base = %.loc8
 // CHECK:STDOUT:   extend %Base.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc9
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Base {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .H = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.3
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: virtual fn @F();
@@ -243,6 +250,9 @@ class Derived {
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
 // CHECK:STDOUT:   %Base: type = class_type @Base [template]
+// CHECK:STDOUT:   %.1: type = ptr_type <vtable> [template]
+// CHECK:STDOUT:   %.2: type = struct_type {.<vptr>: %.1} [template]
+// CHECK:STDOUT:   %.3: <witness> = complete_type_witness %.2 [template]
 // CHECK:STDOUT:   %.5: type = struct_type {} [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -275,6 +285,7 @@ class Derived {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .H = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.3
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
@@ -332,6 +343,7 @@ class Derived {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A1
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @A2 {
@@ -345,6 +357,7 @@ class Derived {
 // CHECK:STDOUT:   .base = %.loc9
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   extend %A1.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: virtual fn @F.1();
@@ -401,6 +414,7 @@ class Derived {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B1
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B2 {
@@ -414,6 +428,7 @@ class Derived {
 // CHECK:STDOUT:   .base = %.loc9
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   extend %B1.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -427,6 +442,7 @@ class Derived {
 // CHECK:STDOUT:   .base = %.loc14
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   extend %B2.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: virtual fn @F.1();
@@ -469,6 +485,7 @@ class Derived {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc9
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: impl fn @F();
@@ -548,6 +565,7 @@ class Derived {
 // CHECK:STDOUT:   .m1 = %.loc5_9
 // CHECK:STDOUT:   .m2 = %.loc6_9
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc9
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: virtual fn @F.1();
@@ -656,6 +674,7 @@ class Derived {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Base
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @Derived {
@@ -669,6 +688,7 @@ class Derived {
 // CHECK:STDOUT:   .base = %.loc8
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   extend %Base.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: impl fn @F();
diff --git a/toolchain/check/testdata/deduce/array.carbon b/toolchain/check/testdata/deduce/array.carbon
index d2d21996e413..73409cdd47a2 100644
--- a/toolchain/check/testdata/deduce/array.carbon
+++ b/toolchain/check/testdata/deduce/array.carbon
@@ -181,6 +181,7 @@ fn G() -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc6_6.1: type) {
@@ -354,6 +355,7 @@ fn G() -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%N.loc10_6.1: %i32) {
@@ -512,6 +514,7 @@ fn G() -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc10_6.1: type, %N.loc10_16.1: %i32) {
@@ -652,6 +655,7 @@ fn G() -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc6_6.1: type) {
@@ -828,6 +832,7 @@ fn G() -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -835,6 +840,7 @@ fn G() -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%N.loc10_6.1: %i32) {
diff --git a/toolchain/check/testdata/deduce/generic_type.carbon b/toolchain/check/testdata/deduce/generic_type.carbon
index 4e7c8d50077c..00852b1647b3 100644
--- a/toolchain/check/testdata/deduce/generic_type.carbon
+++ b/toolchain/check/testdata/deduce/generic_type.carbon
@@ -156,6 +156,7 @@ fn G() -> i32 {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:     complete_type_witness = %.loc4
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -164,6 +165,7 @@ fn G() -> i32 {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc7_6.1: type) {
@@ -330,6 +332,7 @@ fn G() -> i32 {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%I.2
+// CHECK:STDOUT:     complete_type_witness = %.loc4
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -338,6 +341,7 @@ fn G() -> i32 {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc7_6.1: type) {
@@ -545,6 +549,7 @@ fn G() -> i32 {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Outer.2
 // CHECK:STDOUT:     .Inner = %Inner.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc6
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -559,6 +564,7 @@ fn G() -> i32 {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Inner.2
+// CHECK:STDOUT:     complete_type_witness = %.loc5
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -567,6 +573,7 @@ fn G() -> i32 {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc8
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -574,6 +581,7 @@ fn G() -> i32 {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc9
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc13_6.1: type, %U.loc13_16.1: type) {
@@ -820,6 +828,7 @@ fn G() -> i32 {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%WithNontype.2
+// CHECK:STDOUT:     complete_type_witness = %.loc4_29
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/deduce/tuple.carbon b/toolchain/check/testdata/deduce/tuple.carbon
index 2e46895795fd..d226c75c86c2 100644
--- a/toolchain/check/testdata/deduce/tuple.carbon
+++ b/toolchain/check/testdata/deduce/tuple.carbon
@@ -139,6 +139,7 @@ fn G(pair: (C, D)) -> D {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -146,6 +147,7 @@ fn G(pair: (C, D)) -> D {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc7_6.1: type, %U.loc7_16.1: type) {
@@ -373,6 +375,7 @@ fn G(pair: (C, D)) -> D {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%HasPair.2
+// CHECK:STDOUT:     complete_type_witness = %.loc4_35
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -527,6 +530,7 @@ fn G(pair: (C, D)) -> D {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -534,6 +538,7 @@ fn G(pair: (C, D)) -> D {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc7_6.1: type) {
diff --git a/toolchain/check/testdata/deduce/type_operator.carbon b/toolchain/check/testdata/deduce/type_operator.carbon
index aa3658b50f20..49b323088a1c 100644
--- a/toolchain/check/testdata/deduce/type_operator.carbon
+++ b/toolchain/check/testdata/deduce/type_operator.carbon
@@ -135,6 +135,7 @@ fn G(p: C*) -> const C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc6_6.1: type) {
@@ -268,6 +269,7 @@ fn G(p: C*) -> const C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc6_6.1: type) {
@@ -404,6 +406,7 @@ fn G(p: C*) -> const C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc6_6.1: type) {
@@ -536,6 +539,7 @@ fn G(p: C*) -> const C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc6_6.1: type) {
diff --git a/toolchain/check/testdata/function/call/prefer_unqualified_lookup.carbon b/toolchain/check/testdata/function/call/prefer_unqualified_lookup.carbon
index fa88b0618d53..1333a3b9a103 100644
--- a/toolchain/check/testdata/function/call/prefer_unqualified_lookup.carbon
+++ b/toolchain/check/testdata/function/call/prefer_unqualified_lookup.carbon
@@ -104,6 +104,7 @@ fn Class(F:! type).Inner.G() -> i32 { return F(); }
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Class.2
 // CHECK:STDOUT:     .Inner = %Inner.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc11
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -144,6 +145,7 @@ fn Class(F:! type).Inner.G() -> i32 { return F(); }
 // CHECK:STDOUT:     .Self = constants.%Inner.2
 // CHECK:STDOUT:     .F = %F.decl
 // CHECK:STDOUT:     .G = %G.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc10
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/function/declaration/no_prelude/extern.carbon b/toolchain/check/testdata/function/declaration/no_prelude/extern.carbon
index 9ab6dfccba5e..7ecffbb6cf69 100644
--- a/toolchain/check/testdata/function/declaration/no_prelude/extern.carbon
+++ b/toolchain/check/testdata/function/declaration/no_prelude/extern.carbon
@@ -199,6 +199,7 @@ extern library "basic" fn F();
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F();
diff --git a/toolchain/check/testdata/function/declaration/no_prelude/fail_import_incomplete_return.carbon b/toolchain/check/testdata/function/declaration/no_prelude/fail_import_incomplete_return.carbon
index 31efd2ae70ed..d5da403f0c3a 100644
--- a/toolchain/check/testdata/function/declaration/no_prelude/fail_import_incomplete_return.carbon
+++ b/toolchain/check/testdata/function/declaration/no_prelude/fail_import_incomplete_return.carbon
@@ -157,6 +157,7 @@ fn CallFAndGIncomplete() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc37
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @ReturnCUnused() -> %C;
@@ -189,6 +190,8 @@ fn CallFAndGIncomplete() {
 // CHECK:STDOUT:   %ReturnDUnused.type: type = fn_type @ReturnDUnused [template]
 // CHECK:STDOUT:   %ReturnDUnused: %ReturnDUnused.type = struct_value () [template]
 // CHECK:STDOUT:   %D: type = class_type @D [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %ReturnDUsed.type: type = fn_type @ReturnDUsed [template]
 // CHECK:STDOUT:   %ReturnDUsed: %ReturnDUsed.type = struct_value () [template]
 // CHECK:STDOUT: }
@@ -224,6 +227,7 @@ fn CallFAndGIncomplete() {
 // CHECK:STDOUT: class @D {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.8
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @CallFAndGIncomplete() {
diff --git a/toolchain/check/testdata/function/definition/no_prelude/syntactic_merge.carbon b/toolchain/check/testdata/function/definition/no_prelude/syntactic_merge.carbon
index a57b8a080a8c..3751bbcf283f 100644
--- a/toolchain/check/testdata/function/definition/no_prelude/syntactic_merge.carbon
+++ b/toolchain/check/testdata/function/definition/no_prelude/syntactic_merge.carbon
@@ -229,6 +229,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo(%a.param_patt: %C) {
@@ -280,6 +281,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo[](%a.param_patt: %C) {
@@ -328,6 +330,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo(%a.param_patt: %C);
@@ -376,6 +379,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo(%a.param_patt: %C) {
@@ -428,6 +432,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo(%a.param_patt: %C);
@@ -438,6 +443,8 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %Foo.type: type = fn_type @Foo [template]
 // CHECK:STDOUT:   %Foo: %Foo.type = struct_value () [template]
 // CHECK:STDOUT:   %Bar.type: type = fn_type @Bar [template]
@@ -480,6 +487,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo(%a.param_patt: %C) {
@@ -536,6 +544,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo(%a.param_patt: %C);
@@ -589,6 +598,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo(%a.param_patt: %C);
@@ -644,6 +654,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @Foo(%a.loc7_8.1: %C) {
@@ -718,6 +729,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo() -> %return: %C {
@@ -759,6 +771,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo(%a.param_patt: %C);
@@ -767,6 +780,8 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %Foo.type: type = fn_type @Foo [template]
 // CHECK:STDOUT:   %Foo: %Foo.type = struct_value () [template]
 // CHECK:STDOUT: }
@@ -799,6 +814,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo(%a.param_patt: %C) {
@@ -851,6 +867,7 @@ fn Foo(a: const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo(%a.param_patt: %.3);
diff --git a/toolchain/check/testdata/function/generic/deduce.carbon b/toolchain/check/testdata/function/generic/deduce.carbon
index 9313b05d5e0c..75d02ca2bf21 100644
--- a/toolchain/check/testdata/function/generic/deduce.carbon
+++ b/toolchain/check/testdata/function/generic/deduce.carbon
@@ -572,6 +572,7 @@ fn CallImplicitNotDeducible() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @ExplicitAndAlsoDeduced(%T.loc6_27.1: type) {
diff --git a/toolchain/check/testdata/function/generic/no_prelude/call.carbon b/toolchain/check/testdata/function/generic/no_prelude/call.carbon
index 997c07d64f14..9e57a62e7ed4 100644
--- a/toolchain/check/testdata/function/generic/no_prelude/call.carbon
+++ b/toolchain/check/testdata/function/generic/no_prelude/call.carbon
@@ -156,6 +156,7 @@ fn CallSpecific(x: C) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @Function(%T.loc4_13.1: type) {
@@ -370,6 +371,7 @@ fn CallSpecific(x: C) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @Function(%T.loc4_13.1: type) {
diff --git a/toolchain/check/testdata/function/generic/no_prelude/import_specific.carbon b/toolchain/check/testdata/function/generic/no_prelude/import_specific.carbon
index cb7cecd5f0c4..85017f7ba8bd 100644
--- a/toolchain/check/testdata/function/generic/no_prelude/import_specific.carbon
+++ b/toolchain/check/testdata/function/generic/no_prelude/import_specific.carbon
@@ -156,6 +156,7 @@ fn H() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @H() {
diff --git a/toolchain/check/testdata/function/generic/return_slot.carbon b/toolchain/check/testdata/function/generic/return_slot.carbon
index 2992066bf2e0..71641a423a05 100644
--- a/toolchain/check/testdata/function/generic/return_slot.carbon
+++ b/toolchain/check/testdata/function/generic/return_slot.carbon
@@ -109,6 +109,7 @@ fn G() {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%Wrap.2
 // CHECK:STDOUT:     .Make = %Make.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc13
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -125,6 +126,7 @@ fn G() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .arr = %.loc15_18
+// CHECK:STDOUT:   complete_type_witness = %.loc15_32
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @Make(@Wrap.%T.loc11_12.1: type) {
diff --git a/toolchain/check/testdata/global/class_obj.carbon b/toolchain/check/testdata/global/class_obj.carbon
index 50de3d6ea5b4..bd47e30661e1 100644
--- a/toolchain/check/testdata/global/class_obj.carbon
+++ b/toolchain/check/testdata/global/class_obj.carbon
@@ -45,6 +45,7 @@ var a: A = {};
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/global/class_with_fun.carbon b/toolchain/check/testdata/global/class_with_fun.carbon
index 5f350ca82fd8..f8191618964d 100644
--- a/toolchain/check/testdata/global/class_with_fun.carbon
+++ b/toolchain/check/testdata/global/class_with_fun.carbon
@@ -60,6 +60,7 @@ var a: A = {};
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @ret_a() -> %return: %A {
diff --git a/toolchain/check/testdata/if_expr/fail_not_in_function.carbon b/toolchain/check/testdata/if_expr/fail_not_in_function.carbon
index 7814a1bbe377..e11768b45bb8 100644
--- a/toolchain/check/testdata/if_expr/fail_not_in_function.carbon
+++ b/toolchain/check/testdata/if_expr/fail_not_in_function.carbon
@@ -79,6 +79,7 @@ class C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .n = <unexpected>.inst+369.loc37_8
+// CHECK:STDOUT:   complete_type_witness = <unexpected>.inst+371.loc38_1
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/impl/extend_impl.carbon b/toolchain/check/testdata/impl/extend_impl.carbon
index 7f228cf3752c..7b57ff749ac9 100644
--- a/toolchain/check/testdata/impl/extend_impl.carbon
+++ b/toolchain/check/testdata/impl/extend_impl.carbon
@@ -101,6 +101,7 @@ fn G(c: C) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   extend @impl.%HasF.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@HasF.%Self: %HasF.type) {
diff --git a/toolchain/check/testdata/impl/extend_impl_generic.carbon b/toolchain/check/testdata/impl/extend_impl_generic.carbon
index b3cbdcef73cc..be69e01c7eb1 100644
--- a/toolchain/check/testdata/impl/extend_impl_generic.carbon
+++ b/toolchain/check/testdata/impl/extend_impl_generic.carbon
@@ -189,6 +189,7 @@ class X(U:! type) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Param
 // CHECK:STDOUT:   .x = %.loc9_8
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -203,6 +204,7 @@ class X(U:! type) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   extend @impl.1.%HasF.type
+// CHECK:STDOUT:   complete_type_witness = %.loc18
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@HasF.%T.loc4_16.1: type, @HasF.%Self.1: @HasF.%HasF.type (%HasF.type.2)) {
@@ -449,6 +451,7 @@ class X(U:! type) {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%X.2
 // CHECK:STDOUT:     extend %.loc9
+// CHECK:STDOUT:     complete_type_witness = %.loc12
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/fail_extend_impl_forall.carbon b/toolchain/check/testdata/impl/fail_extend_impl_forall.carbon
index b57784c22981..d6f3c3fa4e31 100644
--- a/toolchain/check/testdata/impl/fail_extend_impl_forall.carbon
+++ b/toolchain/check/testdata/impl/fail_extend_impl_forall.carbon
@@ -143,6 +143,7 @@ class C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   has_error
+// CHECK:STDOUT:   complete_type_witness = %.loc22
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@GenericInterface.%T.loc11_28.1: type, @GenericInterface.%Self.1: @GenericInterface.%GenericInterface.type (%GenericInterface.type.2)) {
diff --git a/toolchain/check/testdata/impl/fail_extend_impl_type_as.carbon b/toolchain/check/testdata/impl/fail_extend_impl_type_as.carbon
index 8119ac7b5b85..6a4872e4bae5 100644
--- a/toolchain/check/testdata/impl/fail_extend_impl_type_as.carbon
+++ b/toolchain/check/testdata/impl/fail_extend_impl_type_as.carbon
@@ -116,6 +116,7 @@ class E {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   has_error
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -128,6 +129,7 @@ class E {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
 // CHECK:STDOUT:   extend @impl.2.%I.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc30
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @E {
@@ -140,5 +142,6 @@ class E {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%E
 // CHECK:STDOUT:   extend @impl.3.%I.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc40
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/fail_extend_non_interface.carbon b/toolchain/check/testdata/impl/fail_extend_non_interface.carbon
index ce074594007f..0898cb98b5d5 100644
--- a/toolchain/check/testdata/impl/fail_extend_non_interface.carbon
+++ b/toolchain/check/testdata/impl/fail_extend_non_interface.carbon
@@ -59,5 +59,6 @@ class C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   has_error
+// CHECK:STDOUT:   complete_type_witness = %.loc16
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/fail_extend_partially_defined_interface.carbon b/toolchain/check/testdata/impl/fail_extend_partially_defined_interface.carbon
index 28d21dee44fd..0ed43a4da1d2 100644
--- a/toolchain/check/testdata/impl/fail_extend_partially_defined_interface.carbon
+++ b/toolchain/check/testdata/impl/fail_extend_partially_defined_interface.carbon
@@ -79,6 +79,7 @@ interface I {
 // CHECK:STDOUT:     .Self = constants.%C.2
 // CHECK:STDOUT:     extend %.loc19
 // CHECK:STDOUT:     has_error
+// CHECK:STDOUT:     complete_type_witness = %.loc20
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/fail_extend_undefined_interface.carbon b/toolchain/check/testdata/impl/fail_extend_undefined_interface.carbon
index ea4b1a0d9ae6..d07de12820e7 100644
--- a/toolchain/check/testdata/impl/fail_extend_undefined_interface.carbon
+++ b/toolchain/check/testdata/impl/fail_extend_undefined_interface.carbon
@@ -98,6 +98,7 @@ fn F(c: C) {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   extend @impl.%I.ref
 // CHECK:STDOUT:   has_error
+// CHECK:STDOUT:   complete_type_witness = %.loc22
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%c.param_patt: %C) {
diff --git a/toolchain/check/testdata/impl/fail_impl_bad_assoc_fn.carbon b/toolchain/check/testdata/impl/fail_impl_bad_assoc_fn.carbon
index 928cea065638..60289bc373ed 100644
--- a/toolchain/check/testdata/impl/fail_impl_bad_assoc_fn.carbon
+++ b/toolchain/check/testdata/impl/fail_impl_bad_assoc_fn.carbon
@@ -805,6 +805,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%NoF
+// CHECK:STDOUT:   complete_type_witness = %.loc22
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @FNotFunction {
@@ -816,6 +817,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%FNotFunction
+// CHECK:STDOUT:   complete_type_witness = %.loc35
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @F.16;
@@ -829,6 +831,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%FAlias
+// CHECK:STDOUT:   complete_type_witness = %.loc51
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @FExtraParam {
@@ -840,6 +843,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%FExtraParam
+// CHECK:STDOUT:   complete_type_witness = %.loc64
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @FExtraImplicitParam {
@@ -851,6 +855,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%FExtraImplicitParam
+// CHECK:STDOUT:   complete_type_witness = %.loc77
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @FExtraReturnType {
@@ -862,6 +867,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%FExtraReturnType
+// CHECK:STDOUT:   complete_type_witness = %.loc91
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @FMissingParam {
@@ -873,6 +879,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%FMissingParam
+// CHECK:STDOUT:   complete_type_witness = %.loc106
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @FMissingImplicitParam {
@@ -884,6 +891,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%FMissingImplicitParam
+// CHECK:STDOUT:   complete_type_witness = %.loc119
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @FMissingReturnType {
@@ -895,6 +903,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%FMissingReturnType
+// CHECK:STDOUT:   complete_type_witness = %.loc132
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @FDifferentParamType {
@@ -906,6 +915,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%FDifferentParamType
+// CHECK:STDOUT:   complete_type_witness = %.loc145
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @FDifferentImplicitParamType {
@@ -917,6 +927,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%FDifferentImplicitParamType
+// CHECK:STDOUT:   complete_type_witness = %.loc158
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @FDifferentReturnType {
@@ -928,6 +939,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%FDifferentReturnType
+// CHECK:STDOUT:   complete_type_witness = %.loc171
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @FDifferentParamName {
@@ -939,6 +951,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%FDifferentParamName
+// CHECK:STDOUT:   complete_type_witness = %.loc185
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @SelfNestedBadParam {
@@ -950,6 +963,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%SelfNestedBadParam
+// CHECK:STDOUT:   complete_type_witness = %.loc202
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @SelfNestedBadReturnType {
@@ -961,6 +975,7 @@ class SelfNestedBadReturnType {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%SelfNestedBadReturnType
+// CHECK:STDOUT:   complete_type_witness = %.loc214
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@I.%Self: %I.type) {
diff --git a/toolchain/check/testdata/impl/fail_self_type_mismatch.carbon b/toolchain/check/testdata/impl/fail_self_type_mismatch.carbon
index e4cf2f798550..8cfa57d80086 100644
--- a/toolchain/check/testdata/impl/fail_self_type_mismatch.carbon
+++ b/toolchain/check/testdata/impl/fail_self_type_mismatch.carbon
@@ -143,6 +143,7 @@ impl i32 as I {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:     complete_type_witness = %.loc11
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/impl_as.carbon b/toolchain/check/testdata/impl/impl_as.carbon
index 9bad9ade8550..3055680f08fa 100644
--- a/toolchain/check/testdata/impl/impl_as.carbon
+++ b/toolchain/check/testdata/impl/impl_as.carbon
@@ -87,6 +87,7 @@ class C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc22
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@Simple.%Self: %Simple.type) {
diff --git a/toolchain/check/testdata/impl/lookup/alias.carbon b/toolchain/check/testdata/impl/lookup/alias.carbon
index 2f8772cbb695..3d4491aae516 100644
--- a/toolchain/check/testdata/impl/lookup/alias.carbon
+++ b/toolchain/check/testdata/impl/lookup/alias.carbon
@@ -106,6 +106,7 @@ fn G(c: C) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .G = %G
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@HasF.%Self: %HasF.type) {
diff --git a/toolchain/check/testdata/impl/lookup/fail_alias_impl_not_found.carbon b/toolchain/check/testdata/impl/lookup/fail_alias_impl_not_found.carbon
index bf1ba69bd5d4..fb25ae355a1a 100644
--- a/toolchain/check/testdata/impl/lookup/fail_alias_impl_not_found.carbon
+++ b/toolchain/check/testdata/impl/lookup/fail_alias_impl_not_found.carbon
@@ -91,6 +91,7 @@ fn F(c: C) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .F = %F
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@I.%Self: %I.type) {
diff --git a/toolchain/check/testdata/impl/lookup/fail_todo_undefined_impl.carbon b/toolchain/check/testdata/impl/lookup/fail_todo_undefined_impl.carbon
index 1b796f4d9350..cfafb5193b1b 100644
--- a/toolchain/check/testdata/impl/lookup/fail_todo_undefined_impl.carbon
+++ b/toolchain/check/testdata/impl/lookup/fail_todo_undefined_impl.carbon
@@ -119,6 +119,7 @@ impl C as I {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   extend @impl.1.%I.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@I.%Self: %I.type) {
diff --git a/toolchain/check/testdata/impl/lookup/generic.carbon b/toolchain/check/testdata/impl/lookup/generic.carbon
index e75fd2a674aa..d3ba4b692736 100644
--- a/toolchain/check/testdata/impl/lookup/generic.carbon
+++ b/toolchain/check/testdata/impl/lookup/generic.carbon
@@ -594,6 +594,7 @@ fn G(x: A) {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:     complete_type_witness = %.loc8
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1165,6 +1166,7 @@ fn G(x: A) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -1172,6 +1174,7 @@ fn G(x: A) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@HasF.%T.loc4_16.1: type, @HasF.%Self.1: @HasF.%HasF.type (%HasF.type.2)) {
diff --git a/toolchain/check/testdata/impl/lookup/instance_method.carbon b/toolchain/check/testdata/impl/lookup/instance_method.carbon
index 54b2ca1e9c45..b39f4d2deec7 100644
--- a/toolchain/check/testdata/impl/lookup/instance_method.carbon
+++ b/toolchain/check/testdata/impl/lookup/instance_method.carbon
@@ -148,6 +148,7 @@ fn F(c: C) -> i32 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   extend @impl.%I.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc21
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@I.%Self: %I.type) {
diff --git a/toolchain/check/testdata/impl/lookup/no_prelude/impl_forall.carbon b/toolchain/check/testdata/impl/lookup/no_prelude/impl_forall.carbon
index d148c9bae908..966ddab86cee 100644
--- a/toolchain/check/testdata/impl/lookup/no_prelude/impl_forall.carbon
+++ b/toolchain/check/testdata/impl/lookup/no_prelude/impl_forall.carbon
@@ -265,6 +265,7 @@ fn TestSpecific(a: A({})) -> {} {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%A.2
 // CHECK:STDOUT:     .n = %.loc3_8.1
+// CHECK:STDOUT:     complete_type_witness = %.loc4_1.1
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/lookup/no_prelude/import.carbon b/toolchain/check/testdata/impl/lookup/no_prelude/import.carbon
index 0c94f8c57fa9..6510ab97aa0d 100644
--- a/toolchain/check/testdata/impl/lookup/no_prelude/import.carbon
+++ b/toolchain/check/testdata/impl/lookup/no_prelude/import.carbon
@@ -249,6 +249,7 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc8
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@HasF.%Self: %HasF.type) {
@@ -385,11 +386,13 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @G.1(@HasG.%Self: %HasG.type) {
@@ -431,6 +434,8 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %TestCF.type: type = fn_type @TestCF [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %TestCF: %TestCF.type = struct_value () [template]
@@ -493,6 +498,7 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestCF(%c.param_patt: %C) {
@@ -519,6 +525,8 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %D: type = class_type @D [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %TestDF.type: type = fn_type @TestDF [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %TestDF: %TestDF.type = struct_value () [template]
@@ -623,11 +631,13 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT: class @D {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.8
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestDF(%d.param_patt: %D) {
@@ -654,6 +664,8 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %TestCG.type: type = fn_type @TestCG [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %TestCG: %TestCG.type = struct_value () [template]
@@ -758,11 +770,13 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.17
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestCG(%c.param_patt: %C) {
@@ -789,6 +803,8 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %D: type = class_type @D [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %TestDG.type: type = fn_type @TestDG [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %TestDG: %TestDG.type = struct_value () [template]
@@ -880,11 +896,13 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT: class @D {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.8
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestDG(%d.param_patt: %D) {
@@ -1104,6 +1122,7 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%AnyParam.2
+// CHECK:STDOUT:     complete_type_witness = %.loc4
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1138,6 +1157,7 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:   %AnyParam.type: type = generic_class_type @AnyParam [template]
 // CHECK:STDOUT:   %AnyParam.1: %AnyParam.type = struct_value () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T, 0 [symbolic]
 // CHECK:STDOUT:   %X.1: %T = bind_symbolic_name X, 1 [symbolic]
 // CHECK:STDOUT:   %X.2: @AnyParam.%T (%T) = bind_symbolic_name X, 1 [symbolic]
@@ -1242,6 +1262,7 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:   class {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.2
+// CHECK:STDOUT:     complete_type_witness = constants.%.2
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1322,6 +1343,7 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:   %AnyParam.type: type = generic_class_type @AnyParam [template]
 // CHECK:STDOUT:   %AnyParam.1: %AnyParam.type = struct_value () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T, 0 [symbolic]
 // CHECK:STDOUT:   %X.1: %T = bind_symbolic_name X, 1 [symbolic]
 // CHECK:STDOUT:   %X.2: @AnyParam.%T (%T) = bind_symbolic_name X, 1 [symbolic]
@@ -1406,6 +1428,7 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:   class {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.2
+// CHECK:STDOUT:     complete_type_witness = constants.%.2
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1652,6 +1675,7 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:     complete_type_witness = %.loc13
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1684,6 +1708,8 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C.type: type = generic_class_type @C [template]
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T, 0 [symbolic]
 // CHECK:STDOUT:   %T.patt: type = symbolic_binding_pattern T, 0 [symbolic]
 // CHECK:STDOUT:   %C.3: type = class_type @C, @C(type) [template]
@@ -1818,6 +1844,7 @@ fn Test(c: HasExtraInterfaces.C(type)) {
 // CHECK:STDOUT:   class {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.2
+// CHECK:STDOUT:     complete_type_witness = constants.%.2
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/multiple_extend.carbon b/toolchain/check/testdata/impl/multiple_extend.carbon
index 68d31847f53a..0fd4398a0a8a 100644
--- a/toolchain/check/testdata/impl/multiple_extend.carbon
+++ b/toolchain/check/testdata/impl/multiple_extend.carbon
@@ -274,6 +274,7 @@ fn P(o: O) {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   extend @impl.1.%HasF.ref
 // CHECK:STDOUT:   extend @impl.2.%HasG.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@HasF.%Self: %HasF.type) {
@@ -439,6 +440,7 @@ fn P(o: O) {
 // CHECK:STDOUT:   .Self = constants.%D
 // CHECK:STDOUT:   extend @impl.1.%HasA1.ref
 // CHECK:STDOUT:   extend @impl.2.%HasA2.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc19
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @A.1(@HasA1.%Self: %HasA1.type) {
@@ -561,6 +563,7 @@ fn P(o: O) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
 // CHECK:STDOUT:   .J = %J.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @E {
@@ -577,6 +580,7 @@ fn P(o: O) {
 // CHECK:STDOUT:   .base = %.loc13
 // CHECK:STDOUT:   extend %B.ref
 // CHECK:STDOUT:   extend @impl.%HasI.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @I.1(@HasI.%Self: %HasI.type) {
@@ -699,6 +703,7 @@ fn P(o: O) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Base
 // CHECK:STDOUT:   .K = %K.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @L {
@@ -715,6 +720,7 @@ fn P(o: O) {
 // CHECK:STDOUT:   .base = %.loc13
 // CHECK:STDOUT:   extend %Base.ref
 // CHECK:STDOUT:   extend @impl.%HasK.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @K.1() {
@@ -862,6 +868,7 @@ fn P(o: O) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%NBase
 // CHECK:STDOUT:   .N = %N.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @O {
@@ -885,6 +892,7 @@ fn P(o: O) {
 // CHECK:STDOUT:   extend %NBase.ref
 // CHECK:STDOUT:   extend @impl.1.%HasN1.ref
 // CHECK:STDOUT:   extend @impl.2.%HasN2.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc25
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @N.1() {
diff --git a/toolchain/check/testdata/impl/no_prelude/basic.carbon b/toolchain/check/testdata/impl/no_prelude/basic.carbon
index 08478d30b5c5..04c2b0eb4bc3 100644
--- a/toolchain/check/testdata/impl/no_prelude/basic.carbon
+++ b/toolchain/check/testdata/impl/no_prelude/basic.carbon
@@ -74,6 +74,7 @@ impl C as Simple {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@Simple.%Self: %Simple.type) {
diff --git a/toolchain/check/testdata/impl/no_prelude/fail_alias.carbon b/toolchain/check/testdata/impl/no_prelude/fail_alias.carbon
index 9e201b7d6164..678bb27cdea6 100644
--- a/toolchain/check/testdata/impl/no_prelude/fail_alias.carbon
+++ b/toolchain/check/testdata/impl/no_prelude/fail_alias.carbon
@@ -75,5 +75,6 @@ impl AC as AI {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/no_prelude/fail_undefined_interface.carbon b/toolchain/check/testdata/impl/no_prelude/fail_undefined_interface.carbon
index a3e1cfaafdb5..7d7d22c9bba9 100644
--- a/toolchain/check/testdata/impl/no_prelude/fail_undefined_interface.carbon
+++ b/toolchain/check/testdata/impl/no_prelude/fail_undefined_interface.carbon
@@ -96,5 +96,6 @@ impl C as J {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/no_prelude/import_extend_impl.carbon b/toolchain/check/testdata/impl/no_prelude/import_extend_impl.carbon
index 35bfe49cf6e3..ed2b52f3f800 100644
--- a/toolchain/check/testdata/impl/no_prelude/import_extend_impl.carbon
+++ b/toolchain/check/testdata/impl/no_prelude/import_extend_impl.carbon
@@ -90,6 +90,7 @@ fn G(c: C) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   extend @impl.%I.ref
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@I.%Self: %I.type) {
@@ -110,6 +111,8 @@ fn G(c: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %G.type: type = fn_type @G [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %G: %G.type = struct_value () [template]
@@ -169,6 +172,7 @@ fn G(c: C) {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
 // CHECK:STDOUT:   extend imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @G(%c.param_patt: %C) {
diff --git a/toolchain/check/testdata/impl/no_prelude/import_generic.carbon b/toolchain/check/testdata/impl/no_prelude/import_generic.carbon
index 17f99626af61..06b0b68e0464 100644
--- a/toolchain/check/testdata/impl/no_prelude/import_generic.carbon
+++ b/toolchain/check/testdata/impl/no_prelude/import_generic.carbon
@@ -138,6 +138,7 @@ impl forall [T:! type] C as I(T*) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @I(constants.%T) {
@@ -191,6 +192,8 @@ impl forall [T:! type] C as I(T*) {}
 // CHECK:STDOUT:   %I.type.2: type = facet_type <@I, @I(%T)> [symbolic]
 // CHECK:STDOUT:   %T.patt: type = symbolic_binding_pattern T, 0 [symbolic]
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %Self.2: %I.type.2 = bind_symbolic_name Self, 1 [symbolic]
 // CHECK:STDOUT:   %.3: type = ptr_type %T [symbolic]
 // CHECK:STDOUT:   %I.type.3: type = facet_type <@I, @I(%.3)> [symbolic]
@@ -273,6 +276,7 @@ impl forall [T:! type] C as I(T*) {}
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @I(constants.%T) {
@@ -326,6 +330,8 @@ impl forall [T:! type] C as I(T*) {}
 // CHECK:STDOUT:   %I.type.2: type = facet_type <@I, @I(%T)> [symbolic]
 // CHECK:STDOUT:   %T.patt: type = symbolic_binding_pattern T, 0 [symbolic]
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %Self.2: %I.type.2 = bind_symbolic_name Self, 1 [symbolic]
 // CHECK:STDOUT:   %.3: type = ptr_type %T [symbolic]
 // CHECK:STDOUT:   %I.type.3: type = facet_type <@I, @I(%.3)> [symbolic]
@@ -401,6 +407,7 @@ impl forall [T:! type] C as I(T*) {}
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @I(constants.%T) {
diff --git a/toolchain/check/testdata/impl/no_prelude/import_use_generic.carbon b/toolchain/check/testdata/impl/no_prelude/import_use_generic.carbon
index ba615cb3efc3..7eb813e4cf42 100644
--- a/toolchain/check/testdata/impl/no_prelude/import_use_generic.carbon
+++ b/toolchain/check/testdata/impl/no_prelude/import_use_generic.carbon
@@ -129,6 +129,7 @@ fn F() -> c.(I.F)() {}
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:     complete_type_witness = %.loc4
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -186,6 +187,7 @@ fn F() -> c.(I.F)() {}
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T, 0 [symbolic]
 // CHECK:STDOUT:   %C.2: type = class_type @C, @C(%T) [symbolic]
 // CHECK:STDOUT:   %T.patt: type = symbolic_binding_pattern T, 0 [symbolic]
@@ -283,6 +285,7 @@ fn F() -> c.(I.F)() {}
 // CHECK:STDOUT:   class {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.3
+// CHECK:STDOUT:     complete_type_witness = constants.%.2
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/impl/no_prelude/interface_args.carbon b/toolchain/check/testdata/impl/no_prelude/interface_args.carbon
index 54a2d55613ee..7ccd50148539 100644
--- a/toolchain/check/testdata/impl/no_prelude/interface_args.carbon
+++ b/toolchain/check/testdata/impl/no_prelude/interface_args.carbon
@@ -182,6 +182,7 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc8
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -189,6 +190,7 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc9
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -196,6 +198,7 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @Op.1(@Action.%T.loc4_18.1: type, @Action.%Self.1: @Action.%Action.type (%Action.type.2)) {
@@ -252,6 +255,8 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %B: type = class_type @B [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %Action.type.1: type = generic_interface_type @Action [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %Action: %Action.type.1 = struct_value () [template]
@@ -346,11 +351,13 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT: class @B {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.6
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @A {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.10
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @Op.1(constants.%T: type, constants.%Self.1: @Action.%Action.type (%Action.type.2)) {
@@ -402,6 +409,8 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %B: type = class_type @B [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %Action.type.1: type = generic_interface_type @Action [template]
 // CHECK:STDOUT:   %Action: %Action.type.1 = struct_value () [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T, 0 [symbolic]
@@ -499,16 +508,19 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT: class @B {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.6
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @A {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.10
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.17
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @Op(constants.%T: type, constants.%Self.1: @Action.%Action.type (%Action.type.2)) {
@@ -668,6 +680,7 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc8
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -675,6 +688,7 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc9
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @Make.1(@Factory.%T.loc4_19.1: type, @Factory.%Self.1: @Factory.%Factory.type (%Factory.type.2)) {
@@ -720,6 +734,8 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %B: type = class_type @B [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %Factory.type.1: type = generic_interface_type @Factory [template]
 // CHECK:STDOUT:   %Factory: %Factory.type.1 = struct_value () [template]
 // CHECK:STDOUT:   %T: type = bind_symbolic_name T, 0 [symbolic]
@@ -814,11 +830,13 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT: class @B {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @A {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.8
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @Make.1(constants.%T: type, constants.%Self.1: @Factory.%Factory.type (%Factory.type.2)) {
@@ -975,11 +993,13 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT: class @B {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @A {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.8
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -987,6 +1007,7 @@ fn MakeC(a: A) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @Make(constants.%T: type, constants.%Self.1: @Factory.%Factory.type (%Factory.type.2)) {
diff --git a/toolchain/check/testdata/impl/no_prelude/self_in_class.carbon b/toolchain/check/testdata/impl/no_prelude/self_in_class.carbon
index d60b7ab1048a..3d124caa7e65 100644
--- a/toolchain/check/testdata/impl/no_prelude/self_in_class.carbon
+++ b/toolchain/check/testdata/impl/no_prelude/self_in_class.carbon
@@ -95,6 +95,7 @@ class A {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @A {
@@ -106,6 +107,7 @@ class A {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc23
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @Make.1(@DefaultConstructible.%Self: %DefaultConstructible.type) {
diff --git a/toolchain/check/testdata/impl/no_prelude/self_in_signature.carbon b/toolchain/check/testdata/impl/no_prelude/self_in_signature.carbon
index 87ebbacedc68..1151d69497b8 100644
--- a/toolchain/check/testdata/impl/no_prelude/self_in_signature.carbon
+++ b/toolchain/check/testdata/impl/no_prelude/self_in_signature.carbon
@@ -283,6 +283,7 @@ impl D as SelfNested {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -290,6 +291,7 @@ impl D as SelfNested {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@UseSelf.%Self: %UseSelf.type) {
diff --git a/toolchain/check/testdata/impl/redeclaration.carbon b/toolchain/check/testdata/impl/redeclaration.carbon
index e4fb52d79037..fed0e3c593fa 100644
--- a/toolchain/check/testdata/impl/redeclaration.carbon
+++ b/toolchain/check/testdata/impl/redeclaration.carbon
@@ -95,5 +95,6 @@ impl i32 as I {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%X
+// CHECK:STDOUT:   complete_type_witness = %.loc17
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interface/fail_todo_define_default_fn_out_of_line.carbon b/toolchain/check/testdata/interface/fail_todo_define_default_fn_out_of_line.carbon
index e685eb2c6782..7e6c403b570d 100644
--- a/toolchain/check/testdata/interface/fail_todo_define_default_fn_out_of_line.carbon
+++ b/toolchain/check/testdata/interface/fail_todo_define_default_fn_out_of_line.carbon
@@ -303,6 +303,7 @@ fn Interface.C.F[self: Self](U:! type, u: U) -> U { return u; }
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
 // CHECK:STDOUT:     .F = %F.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc15
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interface/no_prelude/default_fn.carbon b/toolchain/check/testdata/interface/no_prelude/default_fn.carbon
index ef846ade5b0b..f02468f11919 100644
--- a/toolchain/check/testdata/interface/no_prelude/default_fn.carbon
+++ b/toolchain/check/testdata/interface/no_prelude/default_fn.carbon
@@ -81,6 +81,7 @@ class C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .I = %I.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc24
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@I.%Self: %I.type) {
diff --git a/toolchain/check/testdata/interface/no_prelude/generic.carbon b/toolchain/check/testdata/interface/no_prelude/generic.carbon
index ba39bae97e6d..e5c989ef51d2 100644
--- a/toolchain/check/testdata/interface/no_prelude/generic.carbon
+++ b/toolchain/check/testdata/interface/no_prelude/generic.carbon
@@ -250,6 +250,7 @@ fn G(T:! Generic(B)) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%X
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C {
@@ -269,6 +270,7 @@ fn G(T:! Generic(B)) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc20
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(@WithAssocFn.%T.loc8_23.1: type, @WithAssocFn.%Self.1: @WithAssocFn.%WithAssocFn.type (%WithAssocFn.type.2)) {
@@ -469,6 +471,7 @@ fn G(T:! Generic(B)) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @B {
@@ -476,6 +479,7 @@ fn G(T:! Generic(B)) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%T.loc9_6.1: %Generic.type.3) {
diff --git a/toolchain/check/testdata/interface/no_prelude/generic_import.carbon b/toolchain/check/testdata/interface/no_prelude/generic_import.carbon
index fc8aad9cdb98..f883094dbb02 100644
--- a/toolchain/check/testdata/interface/no_prelude/generic_import.carbon
+++ b/toolchain/check/testdata/interface/no_prelude/generic_import.carbon
@@ -181,6 +181,7 @@ impl C as AddWith(C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F.1(constants.%T: type, constants.%Self.1: @AddWith.%AddWith.type (%AddWith.type.2)) {
diff --git a/toolchain/check/testdata/interface/no_prelude/generic_vs_params.carbon b/toolchain/check/testdata/interface/no_prelude/generic_vs_params.carbon
index 97cf4f6ca3b9..62892ec8a834 100644
--- a/toolchain/check/testdata/interface/no_prelude/generic_vs_params.carbon
+++ b/toolchain/check/testdata/interface/no_prelude/generic_vs_params.carbon
@@ -268,6 +268,7 @@ interface A(T: type) {}
 // CHECK:STDOUT:     .Self = constants.%C.2
 // CHECK:STDOUT:     .GenericNoParams = %GenericNoParams.decl
 // CHECK:STDOUT:     .GenericAndParams = %GenericAndParams.decl
+// CHECK:STDOUT:     complete_type_witness = %.loc11
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -276,6 +277,7 @@ interface A(T: type) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%X
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @GenericAndParams.1(constants.%T) {
diff --git a/toolchain/check/testdata/interface/no_prelude/syntactic_merge.carbon b/toolchain/check/testdata/interface/no_prelude/syntactic_merge.carbon
index 0a3219e92ff5..411ec7fffd1c 100644
--- a/toolchain/check/testdata/interface/no_prelude/syntactic_merge.carbon
+++ b/toolchain/check/testdata/interface/no_prelude/syntactic_merge.carbon
@@ -286,6 +286,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Foo(constants.%a) {
@@ -368,6 +369,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Foo(constants.%a) {
@@ -449,6 +451,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Foo(constants.%a) {
@@ -526,6 +529,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Foo(constants.%a) {
@@ -599,6 +603,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Foo(constants.%a) {
@@ -615,6 +620,8 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %a: %C = bind_symbolic_name a, 0 [symbolic]
 // CHECK:STDOUT:   %a.patt: %C = symbolic_binding_pattern a, 0 [symbolic]
 // CHECK:STDOUT:   %Foo.type: type = generic_interface_type @Foo [template]
@@ -717,6 +724,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Foo(constants.%a) {
@@ -823,6 +831,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Foo(constants.%a) {
@@ -912,6 +921,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Foo(constants.%a) {
@@ -1001,6 +1011,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Foo(constants.%a) {
@@ -1058,6 +1069,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Foo(constants.%a) {
@@ -1069,6 +1081,8 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %a: %C = bind_symbolic_name a, 0 [symbolic]
 // CHECK:STDOUT:   %a.patt: %C = symbolic_binding_pattern a, 0 [symbolic]
 // CHECK:STDOUT:   %Foo.type: type = generic_interface_type @Foo [template]
@@ -1132,6 +1146,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Foo(constants.%a) {
@@ -1222,6 +1237,7 @@ interface Foo(a:! const (const C)) {}
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: specific @Foo(constants.%a) {
diff --git a/toolchain/check/testdata/let/compile_time_bindings.carbon b/toolchain/check/testdata/let/compile_time_bindings.carbon
index 2bbe443443d8..82b5b5067593 100644
--- a/toolchain/check/testdata/let/compile_time_bindings.carbon
+++ b/toolchain/check/testdata/let/compile_time_bindings.carbon
@@ -212,6 +212,7 @@ impl i32 as Empty {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .x = %x
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %empty_tuple.type {
@@ -270,6 +271,7 @@ impl i32 as Empty {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .x = %x
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %empty_tuple.type {
@@ -364,6 +366,7 @@ impl i32 as Empty {
 // CHECK:STDOUT:   .a = %a
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .d = %d
+// CHECK:STDOUT:   complete_type_witness = %.loc23
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @F(%b.loc10_8.2: %tuple.type.1) {
@@ -518,6 +521,7 @@ impl i32 as Empty {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .F = %F.decl
 // CHECK:STDOUT:   .x = %x
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %empty_tuple.type {
@@ -798,6 +802,7 @@ impl i32 as Empty {
 // CHECK:STDOUT:   .Self = constants.%I
 // CHECK:STDOUT:   .T = %T
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> <error>;
diff --git a/toolchain/check/testdata/namespace/merging_with_indirections.carbon b/toolchain/check/testdata/namespace/merging_with_indirections.carbon
index 9ce07cb5c9c5..365bfdf6104b 100644
--- a/toolchain/check/testdata/namespace/merging_with_indirections.carbon
+++ b/toolchain/check/testdata/namespace/merging_with_indirections.carbon
@@ -73,6 +73,7 @@ fn Run() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%A
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- b.carbon
@@ -130,11 +131,13 @@ fn Run() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%B
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @A {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %return: %A {
@@ -153,6 +156,8 @@ fn Run() {
 // CHECK:STDOUT:   %F.type: type = fn_type @F [template]
 // CHECK:STDOUT:   %F: %F.type = struct_value () [template]
 // CHECK:STDOUT:   %A: type = class_type @A [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -191,6 +196,7 @@ fn Run() {
 // CHECK:STDOUT: class @A {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Run() {
diff --git a/toolchain/check/testdata/operators/overloaded/add.carbon b/toolchain/check/testdata/operators/overloaded/add.carbon
index 3de7f2fd0b20..6f289696485d 100644
--- a/toolchain/check/testdata/operators/overloaded/add.carbon
+++ b/toolchain/check/testdata/operators/overloaded/add.carbon
@@ -174,6 +174,7 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C](%other.param_patt: %C) -> %return: %C {
diff --git a/toolchain/check/testdata/operators/overloaded/bit_and.carbon b/toolchain/check/testdata/operators/overloaded/bit_and.carbon
index f8626527e3c5..57d956f834b2 100644
--- a/toolchain/check/testdata/operators/overloaded/bit_and.carbon
+++ b/toolchain/check/testdata/operators/overloaded/bit_and.carbon
@@ -174,6 +174,7 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C](%other.param_patt: %C) -> %return: %C {
diff --git a/toolchain/check/testdata/operators/overloaded/bit_complement.carbon b/toolchain/check/testdata/operators/overloaded/bit_complement.carbon
index 823cff0861e1..e2ac1e7e8920 100644
--- a/toolchain/check/testdata/operators/overloaded/bit_complement.carbon
+++ b/toolchain/check/testdata/operators/overloaded/bit_complement.carbon
@@ -103,6 +103,7 @@ fn TestOp(a: C) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C]() -> %return: %C {
diff --git a/toolchain/check/testdata/operators/overloaded/bit_or.carbon b/toolchain/check/testdata/operators/overloaded/bit_or.carbon
index 22dfb0787700..239013d2d110 100644
--- a/toolchain/check/testdata/operators/overloaded/bit_or.carbon
+++ b/toolchain/check/testdata/operators/overloaded/bit_or.carbon
@@ -174,6 +174,7 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C](%other.param_patt: %C) -> %return: %C {
diff --git a/toolchain/check/testdata/operators/overloaded/bit_xor.carbon b/toolchain/check/testdata/operators/overloaded/bit_xor.carbon
index d2e1933c5aed..f36186645570 100644
--- a/toolchain/check/testdata/operators/overloaded/bit_xor.carbon
+++ b/toolchain/check/testdata/operators/overloaded/bit_xor.carbon
@@ -174,6 +174,7 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C](%other.param_patt: %C) -> %return: %C {
diff --git a/toolchain/check/testdata/operators/overloaded/dec.carbon b/toolchain/check/testdata/operators/overloaded/dec.carbon
index 31c9028497a0..3a86b2f4cf1b 100644
--- a/toolchain/check/testdata/operators/overloaded/dec.carbon
+++ b/toolchain/check/testdata/operators/overloaded/dec.carbon
@@ -89,6 +89,7 @@ fn TestOp() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[addr %self.param_patt: %.3]();
diff --git a/toolchain/check/testdata/operators/overloaded/div.carbon b/toolchain/check/testdata/operators/overloaded/div.carbon
index 13fee7181db8..716a42714a22 100644
--- a/toolchain/check/testdata/operators/overloaded/div.carbon
+++ b/toolchain/check/testdata/operators/overloaded/div.carbon
@@ -174,6 +174,7 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C](%other.param_patt: %C) -> %return: %C {
diff --git a/toolchain/check/testdata/operators/overloaded/eq.carbon b/toolchain/check/testdata/operators/overloaded/eq.carbon
index 8059f5d719e3..3c7c0d7b132e 100644
--- a/toolchain/check/testdata/operators/overloaded/eq.carbon
+++ b/toolchain/check/testdata/operators/overloaded/eq.carbon
@@ -224,6 +224,7 @@ fn TestLhsBad(a: D, b: C) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Equal.1[%self.param_patt: %C](%other.param_patt: %C) -> bool;
@@ -333,6 +334,7 @@ fn TestLhsBad(a: D, b: C) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestEqual(%a.param_patt: %D, %b.param_patt: %D) -> bool {
@@ -494,6 +496,7 @@ fn TestLhsBad(a: D, b: C) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -501,6 +504,7 @@ fn TestLhsBad(a: D, b: C) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Equal.1[%self.param_patt: %C](%other.param_patt: %C) -> bool;
diff --git a/toolchain/check/testdata/operators/overloaded/fail_assign_non_ref.carbon b/toolchain/check/testdata/operators/overloaded/fail_assign_non_ref.carbon
index 228798c0c158..7cf4bc33be7c 100644
--- a/toolchain/check/testdata/operators/overloaded/fail_assign_non_ref.carbon
+++ b/toolchain/check/testdata/operators/overloaded/fail_assign_non_ref.carbon
@@ -163,6 +163,7 @@ fn TestAddAssignNonRef(a: C, b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[addr %self.param_patt: %.3]();
diff --git a/toolchain/check/testdata/operators/overloaded/fail_no_impl.carbon b/toolchain/check/testdata/operators/overloaded/fail_no_impl.carbon
index 15eb8687910f..cdbc08e9ae3e 100644
--- a/toolchain/check/testdata/operators/overloaded/fail_no_impl.carbon
+++ b/toolchain/check/testdata/operators/overloaded/fail_no_impl.carbon
@@ -123,6 +123,7 @@ fn TestRef(b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestUnary(%a.param_patt: %C) -> %return: %C {
diff --git a/toolchain/check/testdata/operators/overloaded/fail_no_impl_for_arg.carbon b/toolchain/check/testdata/operators/overloaded/fail_no_impl_for_arg.carbon
index 0ef223d0c9df..5e1f970d8e3c 100644
--- a/toolchain/check/testdata/operators/overloaded/fail_no_impl_for_arg.carbon
+++ b/toolchain/check/testdata/operators/overloaded/fail_no_impl_for_arg.carbon
@@ -189,6 +189,7 @@ fn TestAssign(b: D) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -196,6 +197,7 @@ fn TestAssign(b: D) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C](%other.param_patt: %C) -> %C;
diff --git a/toolchain/check/testdata/operators/overloaded/implicit_as.carbon b/toolchain/check/testdata/operators/overloaded/implicit_as.carbon
index f3545ae95960..85ac590672bd 100644
--- a/toolchain/check/testdata/operators/overloaded/implicit_as.carbon
+++ b/toolchain/check/testdata/operators/overloaded/implicit_as.carbon
@@ -204,6 +204,7 @@ fn Test() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%X
 // CHECK:STDOUT:   .n = %.loc12_8
+// CHECK:STDOUT:   complete_type_witness = %.loc13
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Convert.2[%self.param_patt: %i32]() -> %return: %X {
diff --git a/toolchain/check/testdata/operators/overloaded/inc.carbon b/toolchain/check/testdata/operators/overloaded/inc.carbon
index de618de75688..357ab34ff891 100644
--- a/toolchain/check/testdata/operators/overloaded/inc.carbon
+++ b/toolchain/check/testdata/operators/overloaded/inc.carbon
@@ -89,6 +89,7 @@ fn TestOp() {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[addr %self.param_patt: %.3]();
diff --git a/toolchain/check/testdata/operators/overloaded/index.carbon b/toolchain/check/testdata/operators/overloaded/index.carbon
index a30eea47ff0f..b92f8a43a1d5 100644
--- a/toolchain/check/testdata/operators/overloaded/index.carbon
+++ b/toolchain/check/testdata/operators/overloaded/index.carbon
@@ -163,6 +163,7 @@ let x: i32 = c[0];
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @ElementType {
@@ -170,6 +171,7 @@ let x: i32 = c[0];
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%ElementType.1
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @SubscriptType {
@@ -177,6 +179,7 @@ let x: i32 = c[0];
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%SubscriptType.1
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @At.2[%self.param_patt: %C](%subscript.param_patt: %SubscriptType.1) -> %return: %ElementType.1 {
@@ -471,6 +474,7 @@ let x: i32 = c[0];
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @ElementType {
@@ -478,6 +482,7 @@ let x: i32 = c[0];
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%ElementType.1
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @SubscriptType {
@@ -485,6 +490,7 @@ let x: i32 = c[0];
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%SubscriptType.1
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @At.2[%self.param_patt: %C](%subscript.param_patt: %SubscriptType.1) -> %return: %ElementType.1 {
@@ -561,6 +567,7 @@ let x: i32 = c[0];
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/operators/overloaded/left_shift.carbon b/toolchain/check/testdata/operators/overloaded/left_shift.carbon
index aff25ef48035..81e4243cb09b 100644
--- a/toolchain/check/testdata/operators/overloaded/left_shift.carbon
+++ b/toolchain/check/testdata/operators/overloaded/left_shift.carbon
@@ -174,6 +174,7 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C](%other.param_patt: %C) -> %return: %C {
diff --git a/toolchain/check/testdata/operators/overloaded/mod.carbon b/toolchain/check/testdata/operators/overloaded/mod.carbon
index 8a7addff3648..4e2a18f3def1 100644
--- a/toolchain/check/testdata/operators/overloaded/mod.carbon
+++ b/toolchain/check/testdata/operators/overloaded/mod.carbon
@@ -174,6 +174,7 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C](%other.param_patt: %C) -> %return: %C {
diff --git a/toolchain/check/testdata/operators/overloaded/mul.carbon b/toolchain/check/testdata/operators/overloaded/mul.carbon
index c04768559fdd..fd899dc13bf4 100644
--- a/toolchain/check/testdata/operators/overloaded/mul.carbon
+++ b/toolchain/check/testdata/operators/overloaded/mul.carbon
@@ -174,6 +174,7 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C](%other.param_patt: %C) -> %return: %C {
diff --git a/toolchain/check/testdata/operators/overloaded/negate.carbon b/toolchain/check/testdata/operators/overloaded/negate.carbon
index 4090978232a2..4323f636de3d 100644
--- a/toolchain/check/testdata/operators/overloaded/negate.carbon
+++ b/toolchain/check/testdata/operators/overloaded/negate.carbon
@@ -103,6 +103,7 @@ fn TestOp(a: C) -> C {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C]() -> %return: %C {
diff --git a/toolchain/check/testdata/operators/overloaded/no_prelude/index.carbon b/toolchain/check/testdata/operators/overloaded/no_prelude/index.carbon
index faded026022b..91ba9117e23c 100644
--- a/toolchain/check/testdata/operators/overloaded/no_prelude/index.carbon
+++ b/toolchain/check/testdata/operators/overloaded/no_prelude/index.carbon
@@ -79,6 +79,7 @@ fn F() { ()[()]; }
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%IndexWith
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() {
diff --git a/toolchain/check/testdata/operators/overloaded/ordered.carbon b/toolchain/check/testdata/operators/overloaded/ordered.carbon
index 1b5435baa09e..789fd7cab554 100644
--- a/toolchain/check/testdata/operators/overloaded/ordered.carbon
+++ b/toolchain/check/testdata/operators/overloaded/ordered.carbon
@@ -310,6 +310,7 @@ fn TestGreaterEqual(a: D, b: D) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Less.1[%self.param_patt: %C](%other.param_patt: %C) -> bool;
@@ -493,6 +494,7 @@ fn TestGreaterEqual(a: D, b: D) -> bool {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @TestLess(%a.param_patt: %D, %b.param_patt: %D) -> bool {
diff --git a/toolchain/check/testdata/operators/overloaded/right_shift.carbon b/toolchain/check/testdata/operators/overloaded/right_shift.carbon
index 20352ecdcd86..8a1cbfff3e5d 100644
--- a/toolchain/check/testdata/operators/overloaded/right_shift.carbon
+++ b/toolchain/check/testdata/operators/overloaded/right_shift.carbon
@@ -174,6 +174,7 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C](%other.param_patt: %C) -> %return: %C {
diff --git a/toolchain/check/testdata/operators/overloaded/sub.carbon b/toolchain/check/testdata/operators/overloaded/sub.carbon
index 4a419e1d206e..e36d7e6abfc1 100644
--- a/toolchain/check/testdata/operators/overloaded/sub.carbon
+++ b/toolchain/check/testdata/operators/overloaded/sub.carbon
@@ -174,6 +174,7 @@ fn TestAssign(a: C*, b: C) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc15
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Op.1[%self.param_patt: %C](%other.param_patt: %C) -> %return: %C {
diff --git a/toolchain/check/testdata/package_expr/syntax.carbon b/toolchain/check/testdata/package_expr/syntax.carbon
index 578a6330fda3..71d354849bee 100644
--- a/toolchain/check/testdata/package_expr/syntax.carbon
+++ b/toolchain/check/testdata/package_expr/syntax.carbon
@@ -233,6 +233,7 @@ fn Main() {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .Foo = %Foo.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc8
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Foo() {
diff --git a/toolchain/check/testdata/packages/no_prelude/cross_package_export.carbon b/toolchain/check/testdata/packages/no_prelude/cross_package_export.carbon
index 94350fc2c87c..ff256650e7e7 100644
--- a/toolchain/check/testdata/packages/no_prelude/cross_package_export.carbon
+++ b/toolchain/check/testdata/packages/no_prelude/cross_package_export.carbon
@@ -217,6 +217,7 @@ alias C = Other.C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .x = %.loc5_8
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- conflict.carbon
@@ -281,6 +282,9 @@ alias C = Other.C;
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
+// CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -301,12 +305,16 @@ alias C = Other.C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- export_name_copy.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
+// CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -327,12 +335,16 @@ alias C = Other.C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- export_name_indirect.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
+// CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -353,6 +365,7 @@ alias C = Other.C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- use_export_import.carbon
@@ -361,6 +374,7 @@ alias C = Other.C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -392,6 +406,7 @@ alias C = Other.C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -413,6 +428,7 @@ alias C = Other.C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -445,6 +461,7 @@ alias C = Other.C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -466,6 +483,7 @@ alias C = Other.C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -498,6 +516,7 @@ alias C = Other.C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -519,6 +538,7 @@ alias C = Other.C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -549,6 +569,7 @@ alias C = Other.C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -570,6 +591,7 @@ alias C = Other.C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -601,6 +623,7 @@ alias C = Other.C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -622,6 +645,7 @@ alias C = Other.C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -652,6 +676,7 @@ alias C = Other.C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -673,6 +698,7 @@ alias C = Other.C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -709,6 +735,7 @@ alias C = Other.C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -791,6 +818,9 @@ alias C = Other.C;
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
+// CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -819,5 +849,6 @@ alias C = Other.C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/packages/no_prelude/export_import.carbon b/toolchain/check/testdata/packages/no_prelude/export_import.carbon
index d20629d7f652..68878d905ca1 100644
--- a/toolchain/check/testdata/packages/no_prelude/export_import.carbon
+++ b/toolchain/check/testdata/packages/no_prelude/export_import.carbon
@@ -192,6 +192,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .x = %.loc5_8
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- export.carbon
@@ -271,6 +272,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -296,6 +298,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -317,6 +320,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -343,6 +347,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -364,6 +369,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -390,6 +396,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -411,6 +418,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -436,6 +444,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -457,6 +466,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -482,6 +492,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -503,6 +514,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -528,6 +540,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -549,6 +562,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -574,6 +588,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -595,6 +610,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -620,6 +636,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -641,6 +658,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -666,6 +684,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -698,6 +717,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -723,6 +743,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -744,6 +765,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -771,6 +793,7 @@ var indirect_c: C = {.x = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
 // CHECK:STDOUT:   .x = imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/packages/no_prelude/export_mixed.carbon b/toolchain/check/testdata/packages/no_prelude/export_mixed.carbon
index 6746c9eb57ee..0e94da2f29f7 100644
--- a/toolchain/check/testdata/packages/no_prelude/export_mixed.carbon
+++ b/toolchain/check/testdata/packages/no_prelude/export_mixed.carbon
@@ -145,6 +145,7 @@ var d: D = {.y = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .x = %.loc5_8
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
@@ -156,6 +157,7 @@ var d: D = {.y = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
 // CHECK:STDOUT:   .y = %.loc9_8
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- export_import.carbon
@@ -177,6 +179,9 @@ var d: D = {.y = ()};
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
+// CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -199,12 +204,16 @@ var d: D = {.y = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
 // CHECK:STDOUT:   .x = imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- export_name.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
+// CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -227,6 +236,7 @@ var d: D = {.y = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
 // CHECK:STDOUT:   .x = imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- export_name_then_import.carbon
@@ -248,6 +258,7 @@ var d: D = {.y = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -273,6 +284,7 @@ var d: D = {.y = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -294,6 +306,7 @@ var d: D = {.y = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -319,6 +332,7 @@ var d: D = {.y = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -340,6 +354,7 @@ var d: D = {.y = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -365,6 +380,7 @@ var d: D = {.y = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -416,6 +432,7 @@ var d: D = {.y = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -441,6 +458,7 @@ var d: D = {.y = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -462,10 +480,12 @@ var d: D = {.y = ()};
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct.1: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT:   %D: type = class_type @D [template]
 // CHECK:STDOUT:   %.4: type = struct_type {.y: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.5: <witness> = complete_type_witness %.4 [template]
 // CHECK:STDOUT:   %struct.2: %D = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -498,12 +518,14 @@ var d: D = {.y = ()};
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
 // CHECK:STDOUT:   .x = imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @D {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.5
 // CHECK:STDOUT:   .y = imports.%import_ref.6
+// CHECK:STDOUT:   complete_type_witness = constants.%.5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/packages/no_prelude/export_name.carbon b/toolchain/check/testdata/packages/no_prelude/export_name.carbon
index 3a19fa4cc010..32f055a4fcf3 100644
--- a/toolchain/check/testdata/packages/no_prelude/export_name.carbon
+++ b/toolchain/check/testdata/packages/no_prelude/export_name.carbon
@@ -235,6 +235,7 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .x = %.loc5_8
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @NSC {
@@ -246,13 +247,19 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%NSC
 // CHECK:STDOUT:   .y = %.loc10_8
+// CHECK:STDOUT:   complete_type_witness = %.loc11
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- export.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
+// CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %NSC: type = class_type @NSC [template]
+// CHECK:STDOUT:   %.3: type = struct_type {.y: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.4: <witness> = complete_type_witness %.3 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -282,12 +289,14 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
 // CHECK:STDOUT:   .x = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @NSC {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.6
 // CHECK:STDOUT:   .y = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- not_reexporting.carbon
@@ -312,7 +321,12 @@ private export C;
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
+// CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %NSC: type = class_type @NSC [template]
+// CHECK:STDOUT:   %.3: type = struct_type {.y: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.4: <witness> = complete_type_witness %.3 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -342,12 +356,14 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
 // CHECK:STDOUT:   .x = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @NSC {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.6
 // CHECK:STDOUT:   .y = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- export_in_impl.carbon
@@ -362,10 +378,12 @@ private export C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct.1: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT:   %NSC: type = class_type @NSC [template]
 // CHECK:STDOUT:   %.4: type = struct_type {.y: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.5: <witness> = complete_type_witness %.4 [template]
 // CHECK:STDOUT:   %struct.2: %NSC = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -403,12 +421,14 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
 // CHECK:STDOUT:   .x = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @NSC {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.6
 // CHECK:STDOUT:   .y = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -438,10 +458,12 @@ private export C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct.1: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT:   %NSC: type = class_type @NSC [template]
 // CHECK:STDOUT:   %.4: type = struct_type {.y: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.5: <witness> = complete_type_witness %.4 [template]
 // CHECK:STDOUT:   %struct.2: %NSC = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -480,12 +502,14 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
 // CHECK:STDOUT:   .x = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @NSC {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.6
 // CHECK:STDOUT:   .y = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -515,10 +539,12 @@ private export C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct.1: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT:   %NSC: type = class_type @NSC [template]
 // CHECK:STDOUT:   %.4: type = struct_type {.y: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.5: <witness> = complete_type_witness %.4 [template]
 // CHECK:STDOUT:   %struct.2: %NSC = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -556,12 +582,14 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
 // CHECK:STDOUT:   .x = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @NSC {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.6
 // CHECK:STDOUT:   .y = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -623,12 +651,16 @@ private export C;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Local
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_export_member.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
+// CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -653,6 +685,7 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
 // CHECK:STDOUT:   .x = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- import_both.carbon
@@ -661,10 +694,12 @@ private export C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct.1: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT:   %NSC: type = class_type @NSC [template]
 // CHECK:STDOUT:   %.4: type = struct_type {.y: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.5: <witness> = complete_type_witness %.4 [template]
 // CHECK:STDOUT:   %struct.2: %NSC = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -702,12 +737,14 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
 // CHECK:STDOUT:   .x = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @NSC {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.6
 // CHECK:STDOUT:   .y = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -737,10 +774,12 @@ private export C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct.1: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT:   %NSC: type = class_type @NSC [template]
 // CHECK:STDOUT:   %.4: type = struct_type {.y: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.5: <witness> = complete_type_witness %.4 [template]
 // CHECK:STDOUT:   %struct.2: %NSC = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -778,12 +817,14 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
 // CHECK:STDOUT:   .x = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @NSC {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.6
 // CHECK:STDOUT:   .y = imports.%import_ref.7
+// CHECK:STDOUT:   complete_type_witness = constants.%.5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -826,6 +867,9 @@ private export C;
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
+// CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -851,6 +895,7 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
 // CHECK:STDOUT:   .x = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- use_repeat_export.carbon
@@ -859,6 +904,7 @@ private export C;
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
 // CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %empty_tuple: %empty_tuple.type = tuple_value () [template]
 // CHECK:STDOUT:   %struct: %C = struct_value (%empty_tuple) [template]
 // CHECK:STDOUT: }
@@ -884,6 +930,7 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .x = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -903,6 +950,9 @@ private export C;
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %empty_tuple.type: type = tuple_type () [template]
+// CHECK:STDOUT:   %.1: type = struct_type {.x: %empty_tuple.type} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -928,5 +978,6 @@ private export C;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
 // CHECK:STDOUT:   .x = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/packages/no_prelude/fail_export_name_member.carbon b/toolchain/check/testdata/packages/no_prelude/fail_export_name_member.carbon
index 8cfd6bf40858..2f206d903584 100644
--- a/toolchain/check/testdata/packages/no_prelude/fail_export_name_member.carbon
+++ b/toolchain/check/testdata/packages/no_prelude/fail_export_name_member.carbon
@@ -59,12 +59,16 @@ export C.n;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .n = %.loc5_8
+// CHECK:STDOUT:   complete_type_witness = %.loc6
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- fail_b.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
+// CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: type = struct_type {.n: %.1} [template]
+// CHECK:STDOUT:   %.3: <witness> = complete_type_witness %.2 [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: imports {
@@ -84,5 +88,6 @@ export C.n;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
 // CHECK:STDOUT:   .n = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.3
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/packages/no_prelude/implicit_imports_entities.carbon b/toolchain/check/testdata/packages/no_prelude/implicit_imports_entities.carbon
index 35949c288aa5..56445e69c6a9 100644
--- a/toolchain/check/testdata/packages/no_prelude/implicit_imports_entities.carbon
+++ b/toolchain/check/testdata/packages/no_prelude/implicit_imports_entities.carbon
@@ -184,6 +184,7 @@ import Other library "o1";
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C1
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- c2.carbon
@@ -206,6 +207,7 @@ import Other library "o1";
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C2
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- ns.carbon
@@ -231,6 +233,7 @@ import Other library "o1";
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- o1.carbon
@@ -253,6 +256,7 @@ import Other library "o1";
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%O1
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- o2.carbon
@@ -275,6 +279,7 @@ import Other library "o1";
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%O2
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- local_other.carbon
@@ -297,6 +302,7 @@ import Other library "o1";
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Other
+// CHECK:STDOUT:   complete_type_witness = %.loc4
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: --- mix_current_package.carbon
@@ -317,6 +323,7 @@ import Other library "o1";
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C1: type = class_type @C1 [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct.1: %C1 = struct_value () [template]
 // CHECK:STDOUT:   %C2: type = class_type @C2 [template]
 // CHECK:STDOUT:   %struct.2: %C2 = struct_value () [template]
@@ -349,11 +356,13 @@ import Other library "o1";
 // CHECK:STDOUT: class @C1 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @C2 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -387,6 +396,7 @@ import Other library "o1";
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C1: type = class_type @C1 [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C1 = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -410,6 +420,7 @@ import Other library "o1";
 // CHECK:STDOUT: class @C1 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -442,6 +453,7 @@ import Other library "o1";
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %C: type = class_type @C [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %C = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -470,6 +482,7 @@ import Other library "o1";
 // CHECK:STDOUT: class @C {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -501,6 +514,7 @@ import Other library "o1";
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %O1: type = class_type @O1 [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct.1: %O1 = struct_value () [template]
 // CHECK:STDOUT:   %O2: type = class_type @O2 [template]
 // CHECK:STDOUT:   %struct.2: %O2 = struct_value () [template]
@@ -541,11 +555,13 @@ import Other library "o1";
 // CHECK:STDOUT: class @O1 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: class @O2 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.4
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
@@ -581,6 +597,7 @@ import Other library "o1";
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %O1: type = class_type @O1 [template]
 // CHECK:STDOUT:   %.1: type = struct_type {} [template]
+// CHECK:STDOUT:   %.2: <witness> = complete_type_witness %.1 [template]
 // CHECK:STDOUT:   %struct: %O1 = struct_value () [template]
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -610,6 +627,7 @@ import Other library "o1";
 // CHECK:STDOUT: class @O1 {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = imports.%import_ref.2
+// CHECK:STDOUT:   complete_type_witness = constants.%.2
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/packages/no_prelude/missing_prelude.carbon b/toolchain/check/testdata/packages/no_prelude/missing_prelude.carbon
index 97da0799336b..908748dfe9a1 100644
--- a/toolchain/check/testdata/packages/no_prelude/missing_prelude.carbon
+++ b/toolchain/check/testdata/packages/no_prelude/missing_prelude.carbon
@@ -487,6 +487,7 @@ var n: {} = i32;
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%Core
 // CHECK:STDOUT:   .Int = %Int.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic fn @Int(%T.loc6_10.2: type, %N.loc6_20.2: @Int.%T.loc6_10.1 (%T)) {
diff --git a/toolchain/check/testdata/pointer/arrow.carbon b/toolchain/check/testdata/pointer/arrow.carbon
index 7629d2cf68d6..4646723f27ff 100644
--- a/toolchain/check/testdata/pointer/arrow.carbon
+++ b/toolchain/check/testdata/pointer/arrow.carbon
@@ -82,6 +82,7 @@ fn Foo(ptr: C*) {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .Member = %Member.decl
 // CHECK:STDOUT:   .field = %.loc13_12
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Member[%self.param_patt: %C]();
diff --git a/toolchain/check/testdata/return/fail_return_with_returned_var.carbon b/toolchain/check/testdata/return/fail_return_with_returned_var.carbon
index 39c87fe6d628..48876f46f8a7 100644
--- a/toolchain/check/testdata/return/fail_return_with_returned_var.carbon
+++ b/toolchain/check/testdata/return/fail_return_with_returned_var.carbon
@@ -123,6 +123,7 @@ fn G() -> C {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .a = %.loc23_16
 // CHECK:STDOUT:   .b = %.loc23_28
+// CHECK:STDOUT:   complete_type_witness = %.loc23_35
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %i32 {
diff --git a/toolchain/check/testdata/return/no_prelude/import_convert_function.carbon b/toolchain/check/testdata/return/no_prelude/import_convert_function.carbon
index 157c31ac6652..7f728bf2b8ea 100644
--- a/toolchain/check/testdata/return/no_prelude/import_convert_function.carbon
+++ b/toolchain/check/testdata/return/no_prelude/import_convert_function.carbon
@@ -739,6 +739,7 @@ fn F0(n: i32) -> P.D {
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:     complete_type_witness = %.loc6_19
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -759,6 +760,7 @@ fn F0(n: i32) -> P.D {
 // CHECK:STDOUT:   .Self = constants.%D
 // CHECK:STDOUT:   .n = %.loc7_16
 // CHECK:STDOUT:   .m = %.loc7_28
+// CHECK:STDOUT:   complete_type_witness = %.loc7_35
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @Int(%N.param_patt: Core.IntLiteral) -> type = "int.make_type_signed";
@@ -1033,12 +1035,15 @@ fn F0(n: i32) -> P.D {
 // CHECK:STDOUT:   %Int: %Int.type = struct_value () [template]
 // CHECK:STDOUT:   %i32: type = int_type signed, %.1 [template]
 // CHECK:STDOUT:   %D: type = class_type @D [template]
+// CHECK:STDOUT:   %.2: type = struct_type {.n: %i32, .m: %i32} [template]
+// CHECK:STDOUT:   %.3: <witness> = complete_type_witness %.2 [template]
 // CHECK:STDOUT:   %F0.type: type = fn_type @F0 [template]
 // CHECK:STDOUT:   %F0: %F0.type = struct_value () [template]
 // CHECK:STDOUT:   %.5: bool = bool_literal false [template]
 // CHECK:STDOUT:   %.6: type = struct_type {} [template]
 // CHECK:STDOUT:   %C.type: type = generic_class_type @C [template]
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
+// CHECK:STDOUT:   %.7: <witness> = complete_type_witness %.6 [template]
 // CHECK:STDOUT:   %N: %i32 = bind_symbolic_name N, 0 [symbolic]
 // CHECK:STDOUT:   %N.patt: %i32 = symbolic_binding_pattern N, 0 [symbolic]
 // CHECK:STDOUT:   %.8: Core.IntLiteral = int_value 0 [template]
@@ -1283,6 +1288,7 @@ fn F0(n: i32) -> P.D {
 // CHECK:STDOUT:   .Self = imports.%import_ref.3
 // CHECK:STDOUT:   .n = imports.%import_ref.4
 // CHECK:STDOUT:   .m = imports.%import_ref.5
+// CHECK:STDOUT:   complete_type_witness = constants.%.3
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: generic class @C(constants.%N: %i32) {
@@ -1294,6 +1300,7 @@ fn F0(n: i32) -> P.D {
 // CHECK:STDOUT:   class {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.7
+// CHECK:STDOUT:     complete_type_witness = constants.%.7
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/return/returned_var.carbon b/toolchain/check/testdata/return/returned_var.carbon
index 4dada89ec2e5..dce7877be91b 100644
--- a/toolchain/check/testdata/return/returned_var.carbon
+++ b/toolchain/check/testdata/return/returned_var.carbon
@@ -114,6 +114,7 @@ fn G() -> i32 {
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .a = %.loc12_8
 // CHECK:STDOUT:   .b = %.loc13_8
+// CHECK:STDOUT:   complete_type_witness = %.loc14
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %return: %C {
diff --git a/toolchain/check/testdata/struct/import.carbon b/toolchain/check/testdata/struct/import.carbon
index b7bb4b14f81e..51869135fc15 100644
--- a/toolchain/check/testdata/struct/import.carbon
+++ b/toolchain/check/testdata/struct/import.carbon
@@ -200,6 +200,7 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:     complete_type_witness = %.loc8_34
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -341,6 +342,8 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   %.24: type = struct_type {.a: %.23, .d: %i32} [template]
 // CHECK:STDOUT:   %C.type: type = generic_class_type @C [template]
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
+// CHECK:STDOUT:   %.28: type = struct_type {} [template]
+// CHECK:STDOUT:   %.29: <witness> = complete_type_witness %.28 [template]
 // CHECK:STDOUT:   %.30: type = struct_type {.a: %i32, .b: %i32} [template]
 // CHECK:STDOUT:   %S: %.30 = bind_symbolic_name S, 0 [symbolic]
 // CHECK:STDOUT:   %S.patt: %.30 = symbolic_binding_pattern S, 0 [symbolic]
@@ -657,6 +660,7 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   class {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.40
+// CHECK:STDOUT:     complete_type_witness = constants.%.29
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1155,6 +1159,8 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   %.20: <witness> = interface_witness (%Convert.12) [symbolic]
 // CHECK:STDOUT:   %C.type: type = generic_class_type @C [template]
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
+// CHECK:STDOUT:   %.21: type = struct_type {} [template]
+// CHECK:STDOUT:   %.22: <witness> = complete_type_witness %.21 [template]
 // CHECK:STDOUT:   %.23: Core.IntLiteral = int_value 32 [template]
 // CHECK:STDOUT:   %i32: type = int_type signed, %.23 [template]
 // CHECK:STDOUT:   %.24: type = struct_type {.a: %i32, .b: %i32} [template]
@@ -1416,6 +1422,7 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   class {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.39
+// CHECK:STDOUT:     complete_type_witness = constants.%.22
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1853,6 +1860,8 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   %.20: <witness> = interface_witness (%Convert.12) [symbolic]
 // CHECK:STDOUT:   %C.type: type = generic_class_type @C [template]
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
+// CHECK:STDOUT:   %.21: type = struct_type {} [template]
+// CHECK:STDOUT:   %.22: <witness> = complete_type_witness %.21 [template]
 // CHECK:STDOUT:   %.23: Core.IntLiteral = int_value 32 [template]
 // CHECK:STDOUT:   %i32: type = int_type signed, %.23 [template]
 // CHECK:STDOUT:   %.24: type = struct_type {.a: %i32, .b: %i32} [template]
@@ -2152,6 +2161,7 @@ var c_bad: C({.a = 3, .b = 4}) = F();
 // CHECK:STDOUT:   class {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.39
+// CHECK:STDOUT:     complete_type_witness = constants.%.22
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/tuple/import.carbon b/toolchain/check/testdata/tuple/import.carbon
index 3049aca20abc..650501bedd54 100644
--- a/toolchain/check/testdata/tuple/import.carbon
+++ b/toolchain/check/testdata/tuple/import.carbon
@@ -217,6 +217,7 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = constants.%C.2
+// CHECK:STDOUT:     complete_type_witness = %.loc7_26
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -373,6 +374,8 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   %tuple.type.8: type = tuple_type (%tuple.type.6, %tuple.type.7) [template]
 // CHECK:STDOUT:   %C.type: type = generic_class_type @C [template]
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
+// CHECK:STDOUT:   %.25: type = struct_type {} [template]
+// CHECK:STDOUT:   %.26: <witness> = complete_type_witness %.25 [template]
 // CHECK:STDOUT:   %X: %tuple.type.7 = bind_symbolic_name X, 0 [symbolic]
 // CHECK:STDOUT:   %X.patt: %tuple.type.7 = symbolic_binding_pattern X, 0 [symbolic]
 // CHECK:STDOUT:   %.27: Core.IntLiteral = int_value 1 [template]
@@ -697,6 +700,7 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   class {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.40
+// CHECK:STDOUT:     complete_type_witness = constants.%.26
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1203,6 +1207,8 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   %.20: <witness> = interface_witness (%Convert.12) [symbolic]
 // CHECK:STDOUT:   %C.type: type = generic_class_type @C [template]
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
+// CHECK:STDOUT:   %.21: type = struct_type {} [template]
+// CHECK:STDOUT:   %.22: <witness> = complete_type_witness %.21 [template]
 // CHECK:STDOUT:   %.23: Core.IntLiteral = int_value 32 [template]
 // CHECK:STDOUT:   %i32: type = int_type signed, %.23 [template]
 // CHECK:STDOUT:   %tuple.type.1: type = tuple_type (%i32, %i32) [template]
@@ -1466,6 +1472,7 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   class {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.39
+// CHECK:STDOUT:     complete_type_witness = constants.%.22
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
@@ -1903,6 +1910,8 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   %.20: <witness> = interface_witness (%Convert.12) [symbolic]
 // CHECK:STDOUT:   %C.type: type = generic_class_type @C [template]
 // CHECK:STDOUT:   %C.1: %C.type = struct_value () [template]
+// CHECK:STDOUT:   %.21: type = struct_type {} [template]
+// CHECK:STDOUT:   %.22: <witness> = complete_type_witness %.21 [template]
 // CHECK:STDOUT:   %.23: Core.IntLiteral = int_value 32 [template]
 // CHECK:STDOUT:   %i32: type = int_type signed, %.23 [template]
 // CHECK:STDOUT:   %tuple.type.1: type = tuple_type (%i32, %i32) [template]
@@ -2202,6 +2211,7 @@ var c_bad: C((3, 4)) = F();
 // CHECK:STDOUT:   class {
 // CHECK:STDOUT:   !members:
 // CHECK:STDOUT:     .Self = imports.%import_ref.39
+// CHECK:STDOUT:     complete_type_witness = constants.%.22
 // CHECK:STDOUT:   }
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/var/fail_not_copyable.carbon b/toolchain/check/testdata/var/fail_not_copyable.carbon
index 7f1fee9e4969..732f7a9a4500 100644
--- a/toolchain/check/testdata/var/fail_not_copyable.carbon
+++ b/toolchain/check/testdata/var/fail_not_copyable.carbon
@@ -68,6 +68,7 @@ fn F(x: X) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%X
+// CHECK:STDOUT:   complete_type_witness = %.loc12
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%x.param_patt: %X) {
diff --git a/toolchain/check/testdata/where_expr/constraints.carbon b/toolchain/check/testdata/where_expr/constraints.carbon
index 7c120c1bb48a..35be548f7144 100644
--- a/toolchain/check/testdata/where_expr/constraints.carbon
+++ b/toolchain/check/testdata/where_expr/constraints.carbon
@@ -851,6 +851,7 @@ let B: type where .Self impls A = D;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
+// CHECK:STDOUT:   complete_type_witness = %.loc7
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @DoesNotImplI() {
@@ -956,6 +957,7 @@ let B: type where .Self impls A = D;
 // CHECK:STDOUT:
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
+// CHECK:STDOUT:   complete_type_witness = %.loc5
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @__global_init() {
diff --git a/toolchain/check/testdata/where_expr/designator.carbon b/toolchain/check/testdata/where_expr/designator.carbon
index b4dd57fb4c79..5be359271cf5 100644
--- a/toolchain/check/testdata/where_expr/designator.carbon
+++ b/toolchain/check/testdata/where_expr/designator.carbon
@@ -418,6 +418,7 @@ class D {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%C
 // CHECK:STDOUT:   .F = %F.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc10
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F() -> %return: %C {
@@ -466,6 +467,7 @@ class D {
 // CHECK:STDOUT: !members:
 // CHECK:STDOUT:   .Self = constants.%D
 // CHECK:STDOUT:   .G = %G.decl
+// CHECK:STDOUT:   complete_type_witness = %.loc9
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @G() -> <error> {
diff --git a/toolchain/sem_ir/formatter.cpp b/toolchain/sem_ir/formatter.cpp
index c7eea04a60e6..f5ec0b805d0b 100644
--- a/toolchain/sem_ir/formatter.cpp
+++ b/toolchain/sem_ir/formatter.cpp
@@ -264,6 +264,12 @@ class FormatterImpl {
       OpenBrace();
       FormatCodeBlock(class_info.body_block_id);
       FormatNameScope(class_info.scope_id, "!members:\n");
+
+      Indent();
+      out_ << "complete_type_witness = ";
+      FormatName(class_info.complete_type_witness_id);
+      out_ << "\n";
+
       CloseBrace();
       out_ << '\n';
     } else {