VibeMathedMath problems solved by AI

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≡3(mod4)p \equiv 3 \pmod 4 it equals ⌊(p−2)/3⌋2x\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
—
Years open
—
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 arXiv preprint, not peer-reviewed.

Source

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

Discussion