schema_version: 1
contribution_id: con_601b2fee3ffc4e3cb86297fb68212035
revision_id: rev_38b38d2206754e3f8dcee66a769a25cc
expected_predecessor: null
type: attempt
home_problem_id: prb_b51a5f11716a459db4afee0981061c8e
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  statement_revision_id: stm_718d219628714d7399b5541810f6c05b
  scope: whole_statement
title: Integer right inverses of a diagonal block augmented by arbitrary columns
profiles:
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claim:
  type: full_solution
  scope_statement: 'Complete characterization for every input in Math-3291 / TOP-3030: integer right inverses of [D X] exist exactly when X[I_p,:] has full row rank over F_p for every p dividing a diagonal entry, I_p={i:p divides d_i}. The rowwise gcd conjecture is false, with a two-row counterexample even when X is nonsingular over Q. Includes elementary proofs, constructions, certificates, all inverses, exact scope of the rowwise test, optimal column repair, finite counting, and executed checks. This applies classical integer-linear-algebra results; no new-theorem priority or previously unknown breakthrough is claimed. No unproved assumptions or remaining gap in the stated characterization.'
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  limitations: []
attribution:
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    github_id: 206281466
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    display_name: gavenren
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    authorship_confirmation: confirmed
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    github_id: 206281466
    login_at_event: gavenren
    display_name: gavenren
    roles:
    - prompting
    - submission
    authorship_confirmation: confirmed
  organisations: []
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  provenance:
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    evidence: []
lineage: []
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  path: files/attempt.md
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rights:
  licence: CC-BY-4.0
  redistribution: permitted
  holders:
  - gavenren
declarations:
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    actor: per_2c87cd934d2b42b5b2ba7bce1fd533f3
    recorded_at: '2026-10-18T00:24:23Z'
    evidence_url: https://github.com/We-Solve/research/issues/5
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    recorded_at: '2026-10-18T00:24:23Z'
    evidence_url: https://github.com/We-Solve/research/issues/5
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    evidence_url: https://github.com/We-Solve/research/issues/5