P5-D tranche-2 — nat_semiring semiring multiplicative + annihilator laws post-emit preservation. Per operator F4 ratification (tranche-2 expands when tranche-1 PROVEN; tranche-1 landed via #4063 and now extended cross-target by #4081). Author runners that execute nat_semiring's multiplicative-Monoid

src/v3/compiler/tests/integration/v4_emit_host_harness_test.rs

@@ -17,11 +17,13 @@
 //! via `emit_host_bridge` / `emit_host_runner`. Rosters authored in #4046 (`rung_3_4`).
 //! **W3.3 (+0 SG-0 paths):** go transport + rung-5 full law roster × rust/python/go
 //! (`rung_5.dag`, `nat_semiring_rung5_eval.dag`); cross-target MVP-2 stdout parity via bridge.
-//! **W3.4 (+0 SG-0 paths):** extends bridge with python transport + rung-6 additive-Monoid
-//! roster (`rung_6.dag`, `rung_5_6_common.dag`, `nat_semiring_rung56_eval.dag`). Behavior receipts:
-//! MVP-2 emit-vs-eval `Pass` per law×target via `emit_host_bridge` (five-byte stdout contract;
-//! not per-law emitted artifacts until emit pipeline wires law subjects). Substrate rows stay
-//! `Deferred` until T-22 dispatch. Dissolution: **ROADMAP.md** T-PB-B / **TASKS.md** T-22 T-38.
+//! **W3.4 (+0 SG-0 paths):** extends bridge with python transport + rung-6 post-emit law
+//! preservation (`rung_6.dag`, `rung_5_6_common.dag`, `nat_semiring_rung56_eval.dag`).
+//! Tranche-1 additive-Monoid + tranche-2 multiplicative-Monoid + annihilator (rust + python).
+//! Behavior receipts: MVP-2 emit-vs-eval `Pass` per law×target via `emit_host_bridge` (five-byte
+//! stdout contract; not per-law emitted artifacts until emit pipeline wires law subjects).
+//! Substrate rows stay `Deferred` until T-22 dispatch. Dissolution: **ROADMAP.md** T-PB-B /
+//! **TASKS.md** T-22 T-38.
 //!
 //! **TESTING.md:** substrate `.dag` models receipt assembly; behavior tests exercise
 //! `tools/emit_host_runner` / `emit_host_bridge` (real cargo + run).
@@ -297,6 +299,66 @@ fn nat_semiring_rung6_python_add_associativity_emit_vs_eval_transport_passes() {
     );
 }
 
+#[test]
+fn nat_semiring_rung6_rust_mul_left_identity_emit_vs_eval_transport_passes() {
+    assert_rung6_mvp2_emit_vs_eval_pass(
+        "gunbc_rung6_rust_mul_left_id",
+        "nat_mul_left_identity_input",
+        emit_host_bridge::run_emit_vs_eval_mvp2_transport,
+        EMIT_HOST_FIXTURE_SOURCE,
+    );
+}
+
+#[test]
+fn nat_semiring_rung6_rust_mul_associativity_emit_vs_eval_transport_passes() {
+    assert_rung6_mvp2_emit_vs_eval_pass(
+        "gunbc_rung6_rust_mul_assoc",
+        "nat_mul_associativity_input",
+        emit_host_bridge::run_emit_vs_eval_mvp2_transport,
+        EMIT_HOST_FIXTURE_SOURCE,
+    );
+}
+
+#[test]
+fn nat_semiring_rung6_rust_mul_annihilator_emit_vs_eval_transport_passes() {
+    assert_rung6_mvp2_emit_vs_eval_pass(
+        "gunbc_rung6_rust_mul_ann",
+        "nat_mul_annihilator_input",
+        emit_host_bridge::run_emit_vs_eval_mvp2_transport,
+        EMIT_HOST_FIXTURE_SOURCE,
+    );
+}
+
+#[test]
+fn nat_semiring_rung6_python_mul_left_identity_emit_vs_eval_transport_passes() {
+    assert_rung6_mvp2_emit_vs_eval_pass(
+        "gunbc_rung6_py_mul_left_id",
+        "nat_mul_left_identity_input",
+        emit_host_bridge::run_emit_vs_eval_mvp2_python_transport,
+        EMIT_HOST_PYTHON_FIXTURE_SOURCE,
+    );
+}
+
+#[test]
+fn nat_semiring_rung6_python_mul_associativity_emit_vs_eval_transport_passes() {
+    assert_rung6_mvp2_emit_vs_eval_pass(
+        "gunbc_rung6_py_mul_assoc",
+        "nat_mul_associativity_input",
+        emit_host_bridge::run_emit_vs_eval_mvp2_python_transport,
+        EMIT_HOST_PYTHON_FIXTURE_SOURCE,
+    );
+}
+
+#[test]
+fn nat_semiring_rung6_python_mul_annihilator_emit_vs_eval_transport_passes() {
+    assert_rung6_mvp2_emit_vs_eval_pass(
+        "gunbc_rung6_py_mul_ann",
+        "nat_mul_annihilator_input",
+        emit_host_bridge::run_emit_vs_eval_mvp2_python_transport,
+        EMIT_HOST_PYTHON_FIXTURE_SOURCE,
+    );
+}
+
 #[test]
 fn emit_host_bridge_rust_transport_builds_runs_and_parses_stdout() {
     let work_dir = emit_host_runner::default_work_dir(&format!(
@@ -666,15 +728,21 @@ fn emit_host_runner_python_row_runs_and_parses_stdout() {
 }
 
 #[test]
-fn v4_nat_semiring_rung_6_dag_tokenizes_and_parses_additive_monoid_emit_rows() {
+fn v4_nat_semiring_rung_6_dag_tokenizes_and_parses_post_emit_law_preservation_emit_rows() {
     let module = parse_module(NAT_SEMIRING_RUNG_6_DAG, NAT_SEMIRING_RUNG_6_PATH);
     for name in [
         "run_phase1_nat_semiring_rung6_rust_add_left_identity_emit_equals_eval",
         "run_phase1_nat_semiring_rung6_rust_add_right_identity_emit_equals_eval",
         "run_phase1_nat_semiring_rung6_rust_add_associativity_emit_equals_eval",
+        "run_phase1_nat_semiring_rung6_rust_mul_left_identity_emit_equals_eval",
+        "run_phase1_nat_semiring_rung6_rust_mul_associativity_emit_equals_eval",
+        "run_phase1_nat_semiring_rung6_rust_mul_annihilator_emit_equals_eval",
         "run_phase1_nat_semiring_rung6_python_add_left_identity_emit_equals_eval",
         "run_phase1_nat_semiring_rung6_python_add_right_identity_emit_equals_eval",
         "run_phase1_nat_semiring_rung6_python_add_associativity_emit_equals_eval",
+        "run_phase1_nat_semiring_rung6_python_mul_left_identity_emit_equals_eval",
+        "run_phase1_nat_semiring_rung6_python_mul_associativity_emit_equals_eval",
+        "run_phase1_nat_semiring_rung6_python_mul_annihilator_emit_equals_eval",
     ] {
         assert!(
             surface_declares_data(&module, name),
@@ -713,4 +781,23 @@ fn v4_nat_semiring_rung56_eval_dag_tokenizes_and_parses_rung6_gate() {
         ),
         "{NAT_SEMIRING_RUNG56_EVAL_PATH}: tranche-1 additive-Monoid roster"
     );
+    assert!(
+        surface_declares_data(
+            &module,
+            "nat_semiring_rung6_mul_monoid_annihilator_runtime_value_rows"
+        ),
+        "{NAT_SEMIRING_RUNG56_EVAL_PATH}: tranche-2 mul-Monoid + annihilator roster"
+    );
+    assert!(
+        surface_declares_data(
+            &module,
+            "nat_semiring_rung6_post_emit_law_preservation_runtime_value_rows"
+        ),
+        "{NAT_SEMIRING_RUNG56_EVAL_PATH}: combined tranche-1+2 CorpusEval roster"
+    );
+    assert!(
+        NAT_SEMIRING_RUNG56_EVAL_DAG
+            .contains("nat_semiring_rung6_post_emit_law_preservation_runtime_value_rows"),
+        "{NAT_SEMIRING_RUNG56_EVAL_PATH}: CorpusEvalReport must consume full rung-6 roster"
+    );
 }

src/v4/test/claim/nat_semiring/rung_6.dag

@@ -1,9 +1,11 @@
 // src/v4/test/claim/nat_semiring/rung_6.dag
-// Scope: phase1/nat_semiring rung 6 — post-emit additive-Monoid law preservation (tranche-1 / F4).
-// Status: W3.4 — three laws × rust + python via run_test_claim_emit_vs_eval.
-// Tranche-1 scaffold: lhs/rhs pin the same law subject Node (mirrors rung_3_4.dag:38-39); Pass on
-// substrate rows requires host stdout parsed as RuntimeValue matching eval once T-22 dispatches
-// transport. Until then, `v4_emit_host_harness_test.rs` proves MVP-2 emit-vs-eval per law×target.
+// Scope: phase1/nat_semiring rung 6 — post-emit semiring law preservation (F4).
+// Status: W3.4 tranche-1 additive-Monoid + tranche-2 multiplicative-Monoid + annihilator.
+// Tranche-1: add left/right identity + associativity × rust + python.
+// Tranche-2: mul left identity + associativity + annihilator × rust + python (expands when tranche-1 PROVEN).
+// Scaffold: lhs/rhs pin the same law subject Node (mirrors rung_3_4.dag:38-39); Pass on substrate rows
+// requires host stdout parsed as RuntimeValue matching eval once T-22 dispatches transport. Until then,
+// `v4_emit_host_harness_test.rs` proves MVP-2 emit-vs-eval per law×target.
 
 module v4.test.claim.nat_semiring.rung_6
 
@@ -23,7 +25,10 @@ import v4.std.verification {
 import v4.test.claim.algebra_laws.nat_semiring {
   nat_add_associativity_input,
   nat_add_left_identity_input,
-  nat_add_right_identity_input
+  nat_add_right_identity_input,
+  nat_mul_annihilator_input,
+  nat_mul_associativity_input,
+  nat_mul_left_identity_input
 }
 import v4.test.claim.rung_3_4_common { rung34_emit_host_rust_target_model }
 import v4.test.claim.rung_5_6_common {
@@ -77,3 +82,39 @@ data run_phase1_nat_semiring_rung6_python_add_right_identity_emit_equals_eval: T
 
 
 data run_phase1_nat_semiring_rung6_python_add_associativity_emit_equals_eval: TestClaimRun<Node, RuntimeValue> = rung56_emit_vs_eval_run(claim: claim_phase1_nat_semiring_rung6_python_add_associativity_emit_equals_eval, fixture_subject: nat_add_associativity_input, target: rung56_emit_host_python_target_model)
+
+
+data claim_phase1_nat_semiring_rung6_rust_mul_left_identity_emit_equals_eval: TestClaim = rung6_emit_law_equals_claim(label: "fixture=phase1/nat_semiring rung=6 target=rust law=mul-left-identity predicate=R6-rust-emit-law-equals-eval", law_input: nat_mul_left_identity_input)
+
+
+data claim_phase1_nat_semiring_rung6_rust_mul_associativity_emit_equals_eval: TestClaim = rung6_emit_law_equals_claim(label: "fixture=phase1/nat_semiring rung=6 target=rust law=mul-associativity predicate=R6-rust-emit-law-equals-eval", law_input: nat_mul_associativity_input)
+
+
+data claim_phase1_nat_semiring_rung6_rust_mul_annihilator_emit_equals_eval: TestClaim = rung6_emit_law_equals_claim(label: "fixture=phase1/nat_semiring rung=6 target=rust law=mul-annihilator predicate=R6-rust-emit-law-equals-eval", law_input: nat_mul_annihilator_input)
+
+
+data claim_phase1_nat_semiring_rung6_python_mul_left_identity_emit_equals_eval: TestClaim = rung6_emit_law_equals_claim(label: "fixture=phase1/nat_semiring rung=6 target=python law=mul-left-identity predicate=R6-python-emit-law-equals-eval", law_input: nat_mul_left_identity_input)
+
+
+data claim_phase1_nat_semiring_rung6_python_mul_associativity_emit_equals_eval: TestClaim = rung6_emit_law_equals_claim(label: "fixture=phase1/nat_semiring rung=6 target=python law=mul-associativity predicate=R6-python-emit-law-equals-eval", law_input: nat_mul_associativity_input)
+
+
+data claim_phase1_nat_semiring_rung6_python_mul_annihilator_emit_equals_eval: TestClaim = rung6_emit_law_equals_claim(label: "fixture=phase1/nat_semiring rung=6 target=python law=mul-annihilator predicate=R6-python-emit-law-equals-eval", law_input: nat_mul_annihilator_input)
+
+
+data run_phase1_nat_semiring_rung6_rust_mul_left_identity_emit_equals_eval: TestClaimRun<Node, RuntimeValue> = rung56_emit_vs_eval_run(claim: claim_phase1_nat_semiring_rung6_rust_mul_left_identity_emit_equals_eval, fixture_subject: nat_mul_left_identity_input, target: rung34_emit_host_rust_target_model)
+
+
+data run_phase1_nat_semiring_rung6_rust_mul_associativity_emit_equals_eval: TestClaimRun<Node, RuntimeValue> = rung56_emit_vs_eval_run(claim: claim_phase1_nat_semiring_rung6_rust_mul_associativity_emit_equals_eval, fixture_subject: nat_mul_associativity_input, target: rung34_emit_host_rust_target_model)
+
+
+data run_phase1_nat_semiring_rung6_rust_mul_annihilator_emit_equals_eval: TestClaimRun<Node, RuntimeValue> = rung56_emit_vs_eval_run(claim: claim_phase1_nat_semiring_rung6_rust_mul_annihilator_emit_equals_eval, fixture_subject: nat_mul_annihilator_input, target: rung34_emit_host_rust_target_model)
+
+
+data run_phase1_nat_semiring_rung6_python_mul_left_identity_emit_equals_eval: TestClaimRun<Node, RuntimeValue> = rung56_emit_vs_eval_run(claim: claim_phase1_nat_semiring_rung6_python_mul_left_identity_emit_equals_eval, fixture_subject: nat_mul_left_identity_input, target: rung56_emit_host_python_target_model)
+
+
+data run_phase1_nat_semiring_rung6_python_mul_associativity_emit_equals_eval: TestClaimRun<Node, RuntimeValue> = rung56_emit_vs_eval_run(claim: claim_phase1_nat_semiring_rung6_python_mul_associativity_emit_equals_eval, fixture_subject: nat_mul_associativity_input, target: rung56_emit_host_python_target_model)
+
+
+data run_phase1_nat_semiring_rung6_python_mul_annihilator_emit_equals_eval: TestClaimRun<Node, RuntimeValue> = rung56_emit_vs_eval_run(claim: claim_phase1_nat_semiring_rung6_python_mul_annihilator_emit_equals_eval, fixture_subject: nat_mul_annihilator_input, target: rung56_emit_host_python_target_model)

src/v4/test/claim/workflow/nat_semiring_rung56_eval.dag

@@ -1,6 +1,6 @@
 // src/v4/test/claim/workflow/nat_semiring_rung56_eval.dag
-// Scope: W3.4 rung 6 corpus eval + gate for phase1/nat_semiring additive-Monoid tranche-1.
-// Status: tranche-1 only (left/right identity + associativity); rust + python emit-vs-eval rows.
+// Scope: W3.4 rung 6 corpus eval + gate for phase1/nat_semiring post-emit law preservation (F4).
+// Status: tranche-1 additive-Monoid + tranche-2 multiplicative-Monoid + annihilator; rust + python.
 
 module v4.test.claim.workflow.nat_semiring_rung56_eval
 
@@ -16,9 +16,15 @@ import v4.test.claim.nat_semiring.rung_6 {
   run_phase1_nat_semiring_rung6_python_add_associativity_emit_equals_eval,
   run_phase1_nat_semiring_rung6_python_add_left_identity_emit_equals_eval,
   run_phase1_nat_semiring_rung6_python_add_right_identity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_python_mul_annihilator_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_python_mul_associativity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_python_mul_left_identity_emit_equals_eval,
   run_phase1_nat_semiring_rung6_rust_add_associativity_emit_equals_eval,
   run_phase1_nat_semiring_rung6_rust_add_left_identity_emit_equals_eval,
-  run_phase1_nat_semiring_rung6_rust_add_right_identity_emit_equals_eval
+  run_phase1_nat_semiring_rung6_rust_add_right_identity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_rust_mul_annihilator_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_rust_mul_associativity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_rust_mul_left_identity_emit_equals_eval
 }
 import v4.test.claim.workflow.testclaim_corpus_runner {
   CorpusEvalReport,
@@ -37,10 +43,36 @@ data nat_semiring_rung6_additive_monoid_runtime_value_rows: List<TestClaimRun<No
 ]
 
 
+data nat_semiring_rung6_mul_monoid_annihilator_runtime_value_rows: List<TestClaimRun<Node, RuntimeValue>> = [
+  run_phase1_nat_semiring_rung6_rust_mul_left_identity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_rust_mul_associativity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_rust_mul_annihilator_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_python_mul_left_identity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_python_mul_associativity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_python_mul_annihilator_emit_equals_eval
+]
+
+
+data nat_semiring_rung6_post_emit_law_preservation_runtime_value_rows: List<TestClaimRun<Node, RuntimeValue>> = [
+  run_phase1_nat_semiring_rung6_rust_add_left_identity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_rust_add_right_identity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_rust_add_associativity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_rust_mul_left_identity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_rust_mul_associativity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_rust_mul_annihilator_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_python_add_left_identity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_python_add_right_identity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_python_add_associativity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_python_mul_left_identity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_python_mul_associativity_emit_equals_eval,
+  run_phase1_nat_semiring_rung6_python_mul_annihilator_emit_equals_eval
+]
+
+
 fn run_nat_semiring_rung56_eval() -> CorpusEvalReport {
   CorpusEvalReport {
     entries: corpus_entries_from_node_runtime_value_runs(
-      runs: nat_semiring_rung6_additive_monoid_runtime_value_rows
+      runs: nat_semiring_rung6_post_emit_law_preservation_runtime_value_rows
     )
   }
 }