Add an independent replay path for materialized Jacobian-syzygy coefficient ledgers

[yuelgrace1810-ops]

Observed gap

polynomial.jacobian_syzygy.minimum_degree.compute intentionally rejects coefficient_map_detail: "SPARSE_ENTRIES" and directs callers to polynomial.jacobian_syzygy.coefficients.materialize. The materialized operation says the full sparse graded coefficient ledger is retained as explicit bulk evidence for independent replay, but it exposes no reciprocal verifier relationship.

The existing polynomial.jacobian_syzygy.minimum_degree.verify is an inline verifier for the ordinary compute operation. It accepts the exact producer input and inline candidate; it cannot consume the materialized ledger's result_uri.

Held-out reproduction

A weak-model audit used Abe–Denham's 2026 G(3,3,3) counterexample polynomial

h=(x^3-y^3)(y^3-z^3)(x^3-z^3)

with max_degree=4 and requested full sparse coefficient maps. On current main 614fdc40:

1. the compact compute operation returned POLYNOMIAL_OPERATION_NOT_APPLICABLE and correctly pointed to the coefficient-ledger capability;
2. polynomial.jacobian_syzygy.coefficients.materialize completed on the exact six-term polynomial and returned bound input_uri / result_uri artifacts;
3. discovery exposed only the inline minimum-degree verifier, which could not accept the opaque materialized result;
4. the original 240-second arm timed out after repeated invalid handoff attempts.

A validation against draft PR #917 correctly advertised the inline input_and_candidate contract, but the full-ledger route still ended at a COMPUTED artifact with no authorized replay. It completed in 101.04 s / 8 MCP calls / 322,605 input tokens and explicitly withheld verification.

Desired outcome

Give the intentionally durable coefficient ledger a coherent independent replay boundary. For example, expose a dedicated typed verifier that accepts this producer's exact result_uri, resolves its input/result lineage, independently rebuilds the graded maps/ranks/minors/first kernel, and returns a bound verification record. Producer and verifier should link reciprocally.

Acceptance criteria

• polynomial.jacobian_syzygy.coefficients.materialize advertises the exact verifier and input field that actually consume its result.
• The verifier accepts the producer's returned result_uri without copying or reshaping opaque artifact contents.
• Replay checks the full sparse-entry ledger as well as the compact rank/kernel claims.
• Successful replay produces a verification record bound to the exact stored input/result; malformed, cross-producer, or forged artifacts fail closed.
• MCP composition tests cover producer → linked verifier and verifier → producer navigation.
• The ordinary compact compute → inline verifier path fixed by PR Fix syzygy verifier handoff metadata #917 remains unchanged.

Design note

This appears to need maintainer review rather than a small metadata-only patch: the current GradedJacobianSyzygyResult has a single verifier ID/input-field self-description, while compact inline results and durable sparse ledgers now require different transport contracts. The checker entrypoint also currently binds replay to polynomial.jacobian_syzygy.minimum_degree.compute. This issue should preserve the deliberate bulk-artifact policy described in #874 rather than forcing the ledger inline.

[morluto]

Confirmed as the concrete failure of the current one-producer/one-derived-verifier model. The compact inline result and the durable sparse coefficient ledger require distinct verification transports and obligations; adding another untyped string field would not make the handoff safe.

Canonical architecture owner: #1025. Keep this issue as the polynomial-ledger acceptance fixture: the returned result_uri must map directly into a schema-valid verifier request, preserve lineage, and replay the full ledger without copying or reshaping opaque contents.

[morluto]

Closing as superseded by #1513/#1514. The materialized artifact ledger, artifact handles, generic verifier records, and replayable artifact store were intentionally removed. Current operations return bounded typed mathematical values directly; any domain-specific residual or certificate belongs in that result model rather than a generic materialization verifier.