Sun's Conjecture 4.6(ii) on Trigonometric Permanents

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.

Result: Disproved
Status: Resolved
AI contribution: AI-discovered
Method: Construction
Field: Experimental number theory
Posed by: Zhi-Wei Sun
Year posed: 2021
Years open: 5y
Solved: 2026-06-12
Model: Demonstrandum multi-agent pipeline
Vendor: —
Collaborators: —
Verification: Unreviewed
Publication: Announced
Significance: 5 / 100
Disclosed cost: —
Wikipedia: No dedicated article

What the AI did

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

Verification

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

Source

Demonstrandum artifacts repository (RESULTS.md)

Sun's Conjecture 4.6(ii) on Trigonometric Permanents

What the AI did

Verification

Source

Discussion