Completeness of Canonical Closure Representations Is coNP-Complete

Precise statement

A finite closure system can be given by implications or by a list of subsets closed under intersection. Deciding whether one specification of each kind defines the same family had remained open in several settings; the paper proves the problem coNP-complete.

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

GPT-5.6 Pro

The disclosure states the main proof was obtained by GPT-5.6 Pro through ChatGPT and checked by the author.

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

Verification boundary

unreviewed

No independent review; the author reports checking the model's proof himself. Preprint, not refereed.

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

Timeline

1. 2026-07-20

   arXiv

   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.