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ResearchMath Intake Lane

Purpose

ResearchMath-14k is useful to MATHFORGE as a sourcing corpus, not as a theorem oracle. Canonical intake now lives in MATHFORGE under forge/intake/researchmath14k/ and is imported here at an immutable protected commit through governance/mathforge_external_source_imports.json. This Programme fixture is a conformance mirror: it demonstrates the source-row, problem-card, and handoff contract but is not the authoritative source reconstruction.

The fixture is deliberately modest:

ResearchMath row
  -> source-row preservation
  -> audited problem card
  -> route classification
  -> MATHSOLVE handoff

Fixture 004

Fixture RM-DIO-004 ingests the ResearchMath viewer row whose original question asks for all integer pairs satisfying

x^2 - x = y^5 - y.

The row is pinned to Hugging Face repository commit f22d0f28b55e6e777acf82e722d97ae982dff02e, LFS data object 3f6c96d18925a47ac223555717226c5408cc9c75e07a1e96bddcffde8a06f029, config ResearchMath-14k, split test, row 0. It imports status unknown, which remains STATUS_UNVERIFIED_UNKNOWN; no independent current-status reconstruction is claimed.

Artifacts

Artifact Role
source_row.json Preserves the dataset row, provenance, taxonomy, evidence URL, and imported status.
problem_card.json Converts the row into a MATHFORGE problem card with canonical algebraic extraction.
mathsolve_handoff.json Produces a MATHSOLVE-ready Work Package seed and first executable step.
claim_ledger.json Marks only source reconstruction, route classification, and provisional handoff readiness.

Canonical extraction

The Diophantine equation is preserved as an integer-points problem over the affine plane curve

x^2 - x - y^5 + y = 0.

This is an extraction, not a solution. The polynomial object supports finite screens and route planning; it does not prove complete integer classification.

First executable MATHSOLVE step

The handoff proposes a finite exact sanity screen:

for y in {-1, 0, 1, 2, 3}:
    compute D = 1 + 4(y^5 - y)
    retain y only when D is a nonnegative square
    lift corresponding x values exactly

The output is a finite-screen ledger of small branches. It is not a proof of completeness.

CI rejection policy

The adversarial suite rejects attempts to:

  • change the imported unknown status to solved;
  • remove source provenance;
  • falsify artifact hashes;
  • allow status promotion;
  • alter the extracted polynomial;
  • remove the excluded inference;
  • mark the handoff solved;
  • remove the first executable step;
  • certify the provisional handoff;
  • remove forbidden promotions.

Boundary

MATHFORGE may preserve, audit, classify, and hand off. MATHSOLVE may open a Chaidez-style campaign and run exact bounded screens. MATHCERT has no theorem to certify from this fixture.

The value is the intake machinery itself: a noisy research-problem corpus can feed Forge triage without becoming an authority. Programme admission, campaign authority, and certification remain separate transitions.