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

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.

Result: Proved
Status: Resolved
AI contribution: AI-discovered
Method: Argument
Field: Number theory
Posed by: Zhi-Wei Sun
Year posed: 2024
Years open: 2y
Solved: 2026-06-21
Model: ChatGPT
Vendor: OpenAI
Collaborators: Yaoran Yang, Gaishi Yang, Yutong Zhang
Verification: Unreviewed
Publication: Preprint
Significance: 10 / 100
Disclosed cost: —
Wikipedia: No dedicated article

What the AI did

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.

Verification

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 arXiv preprint, not peer-reviewed.

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

What the AI did

Verification

Sources

Discussion