Fix syzygy verifier handoff metadata

src/jacobian/contracts/jacobian_syzygy.py

@@ -229,7 +229,9 @@ class GradedJacobianSyzygyResult(ContractModel):
     verification_capability_id: Literal[
         "polynomial.jacobian_syzygy.minimum_degree.verify"
     ] = "polynomial.jacobian_syzygy.minimum_degree.verify"
-    verification_input_field: Literal["result_uri"] = "result_uri"
+    verification_input_field: Literal["input_and_complete_output_result"] = (
+        "input_and_complete_output_result"
+    )
 
     @model_validator(mode="after")
     def bind_first_kernel_and_finite_scope(self) -> Self:

src/jacobian/domains/polynomial/checkers.py

@@ -25,8 +25,8 @@
         verification_title="Verify a first graded Jacobian syzygy degree",
         verification_description=(
             "Independently reconstruct every bounded homogeneous coefficient map, "
-            "rank ledger, nonzero minor, and first kernel from a stored producer "
-            "result."
+            "rank ledger, nonzero minor, and first kernel from the exact producer "
+            "input and the complete, unmodified producer output.result object."
         ),
         verification_tags=(
             "verification",

src/jacobian_checkers/jacobian_syzygy.py

@@ -568,7 +568,7 @@ def _expected_result(source: dict[str, Any]) -> dict[str, Any]:
         "verification_capability_id": (
             "polynomial.jacobian_syzygy.minimum_degree.verify"
         ),
-        "verification_input_field": "result_uri",
+        "verification_input_field": "input_and_complete_output_result",
     }
 
 

tests/composition/runtime/test_frontier_capabilities.py

@@ -264,6 +264,7 @@ def test_graded_jacobian_syzygy_finds_and_verifies_the_first_kernel(
     result = _result_payload(frontier_services, computed)
     assert result["status"] == "FOUND"
     assert result["first_syzygy_degree"] == 1
+    assert result["verification_input_field"] == "input_and_complete_output_result"
     assert [(item["rank"], item["nullity"]) for item in result["degree_maps"]] == [
         (3, 0),
         (7, 2),
@@ -288,6 +289,16 @@ def test_graded_jacobian_syzygy_finds_and_verifies_the_first_kernel(
     assert verified.execution.status is ExecutionStatus.COMPLETED
     assert verified.output["status"] == "VERIFIED"
 
+    verifier = next(
+        descriptor
+        for descriptor in frontier_services.core.capabilities.catalog().capabilities
+        if descriptor.capability_id
+        == "polynomial.jacobian_syzygy.minimum_degree.verify"
+    )
+    assert "complete, unmodified producer output.result object" in (
+        verifier.description
+    )
+
 
 def test_graded_jacobian_syzygy_handles_a_zero_partial_derivative(
     frontier_services: DomainTestServices,