Sun’s sign conjecture for trigonometric permanents
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Sun proposed two sign rules for integer-normalized sine and cosecant permanents at odd primes. Do the normalized quantities s_p and s′_p always have those predicted signs?
Why it matters and what counts as progress
Why it matters: Exact sign patterns test an arithmetic conjecture suggested by computations through p=23.
What counts as progress: A sign proof for every odd prime or exact evaluated permanents contradicting either rule, rather than numerical sign estimates.
How the problem developed
- 2021 · Conjecture [1]
Zhi-Wei Sun Proposed two sign rules for the integer-normalized sine and cosecant permanents at odd primes as part of Conjecture 4.6(ii).
- 12 Jun 2026 · Counterexample [2]
John Erlbacher, with Claude agents under his direction Reported exact values at p=29 that violate both sign rules in part (ii), while leaving the separate composite-number divisibility assertion in part (i) open.
- 18 Oct 2026 · Verification report [3]
AIProofWatch Recorded the p=29 values and the reported independent cyclotomic, subset-DP, and CRT checks; no replacement sign law was claimed.
AI contribution
AI-found values refute both sign clauses of Sun’s Conjecture 4.6(ii)
For the integer-normalized trigonometric permanents at prime p=29, s₂₉=1,053,859 is positive and s′₂₉=−4,806,838,304 is negative. These exact values contradict both sign predictions in Conjecture 4.6(ii).
Sources
- Zhi-Wei Sun, Arithmetic properties of some permanents
- John Erlbacher, Sun’s Conjecture 4.6(ii) on Sine Permanents, Refuted at p = 29
- AIProofWatch, AI-found values refute both sign clauses of Sun’s Conjecture 4.6(ii)
- Demonstrandum’s Sun 4.6(ii) values and checks
- Demonstrandum’s AI methods
- Sun’s original Conjecture 4.6
Website timeline
Publication dates and editorial changes.
AI-found values refute both sign clauses of Sun’s Conjecture 4.6(ii)