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Graffiti's Residue Problem for Common-Divisor Graphs

Combinatorics · posed by Graffiti (S. Fajtlowicz's program); studied by Erdős and Staton · solved

1 attempt

Statement

A problem from Fajtlowicz's Graffiti program, studied by Erdős and Staton, on the Havel-Hakimi residue of common-divisor graphs. The paper resolves the problem and extends it, determining the residue's first-order scale and its nontrivial constant from the degree sequence.

Context

A machine-generated Graffiti conjecture, the band the scoring ladder pins at 5, though this one carries Erdős and Staton's names in its history.

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Attempts

1 attempt

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  • #1

    Attempt 1

    proof attemptTheo-Conjecture, OpenAI Codex with Randy Davila ·
    AI involvement
    ai assisted
    a person led the work and used a model along the way.
    models
    Theo-Conjecture, OpenAI Codex
    people
    Randy Davila

    The study deliberately retained Graffiti's conjecture-example-proof workflow through the TxGraffiti / Theo-Conjecture line: the systems supported registry construction, conjecture generation, exact stress testing, proof search and proof auditing, with the surviving conjecture selected by discrepancy tracking against a quarter-million-graph registry.

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