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Sun's Conjecture 4.6(ii) on Trigonometric Permanents

Number theory · posed by Zhi-Wei Sun, 2021 · disproved

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Statement

For an odd prime pp, do Sun's normalized trigonometric permanents satisfy sp<0  ⟺  p≡5(mod12)s_p < 0 \iff p \equiv 5 \pmod{12} and sp′<0  ⟺  p≡7(mod8)s'_p < 0 \iff p \equiv 7 \pmod 8? Exact computation at p=29p = 29 refutes both sign laws.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Demonstrandum multi-agent pipeline

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
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    — the result was found by a model.

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

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