Problem detail · source-aware

The Coxeter Code Minimum Distance Conjecture

resolvedconfidence 70%

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Precise statement

Coble and Barg introduced binary Coxeter codes, the span of indicators of standard cosets of fixed rank in a finite Coxeter system, generalizing Reed-Muller codes, and proposed a conjectural value for the minimum distance of a general Coxeter code. The conjecture is true, and it yields a decoding consequence.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

ChatGPT-5.4, Claude Sonnet 4.6

The authors say the models were used as exploratory tools in connection with the problem, and bound that use explicitly: brainstorming, discussion of possible approaches, and preliminary checking of ideas.

Provider: OpenAI / Anthropic · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

arXiv preprint; not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

  1. arXiv:2607.10774 - Minimum distance and decoding of Coxeter codes

    VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

  • VibeMath has not independently verified the mathematical claim.
  • AI-attempt independence and training-data exposure are unknown unless explicitly documented.
  • VibeMath has not independently audited the mathematical statement, proof, or novelty claim.