Zhi-Wei Sun's Conjecture 3.4 on a Truncated Legendre-Symbol Determinant

Precise statement

Zhi-Wei Sun conjectured a closed evaluation of a truncated Legendre-symbol determinant. For every prime $p \equiv 3 \pmod 4$ it equals $\lfloor (p-2)/3 \rfloor^2 x$, proved by reducing to inverse data for Chapman's full Legendre-symbol matrix and evaluating that with Vsemirnov's factorization and a Schur-Pfaffian resolvent identity.

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

The abstract states flatly that OpenAI's ChatGPT produced the proof, which the authors independently checked and confirmed. The authors separately used a GPT-assisted framework to develop Lean 4 formalizations of selected components.

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

Verification boundary

unreviewed

The authors report Lean 4 formalizations of selected proof components rather than the whole argument. arXiv preprint, not peer-reviewed.

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

Timeline

1. 2026-06-21

   arXiv:2606.22548 - A Proof of a Conjecture of Zhi-Wei Sun on a Truncated Legendre-Symbol Determinant

   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.