Sun's Conjecture 4.6(ii) on Trigonometric Permanents

Precise statement

For an odd prime $p$, do Sun's normalized trigonometric permanents satisfy $s_p < 0 \iff p \equiv 5 \pmod{12}$ and $s'_p < 0 \iff p \equiv 7 \pmod 8$? Exact computation at $p = 29$ refutes both sign laws.

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

Demonstrandum multi-agent pipeline

Found by the Demonstrandum multi-agent pipeline; every refutation ships a finite certificate, a mutation-tested checker, and an independent clean-room recomputation.

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

Verification boundary

unreviewed

Both sign clauses refuted by exact calculations in multiple independent implementations; public artifacts. Not externally refereed.

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

Timeline

1. 2026-06-12

   Demonstrandum artifacts repository (RESULTS.md)

   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

construction (source-reported)

Source-reported tools: construction.

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.