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.