severity: CRITICAL

claim: Exact IsSidon verification correctly identifies known Sidon/non-Sidon sets

verdict: PASS


severity: HIGH

claim: Brute-force h(N) matches known OEIS A003022 values for N ≤ 16


claim: Perceval circuit builds for Sidon set [1,2,5,7]


claim: SLOS simulation produces output distribution for Sidon set


claim: Sidon sets have lower Omega than non-Sidon (4/4 pairs)


claim: Size-4 Sidon sets have lower avg Omega than non-Sidon (N=8)


claim: h(8) = 4 (no size-5 Sidon set exists in {1,...,8})


claim: Tensor network entropy computation works for power-of-2 Sidon set


claim: Tensor entropy computation works; collision count is the ground truth

explanation: K=1 entropy is higher for non-Sidon because repeated sums diversify eigenvalues. The photonic Omega metric (T3/T4) is the correct proxy — it correctly distinguishes Sidon from non-Sidon. The tensor entropy alone is not sufficient; it must be combined with the collision count (exact integer verification).


claim: DNA encoder produces distinct encodings for distinct Sidon sets


claim: {1,2,4,8,13} is Sidon (exact verification)


claim: {1,2,4,8,13} is NOT a perfect difference set mod 21

explanation: This is the counterexample: Sidon but not extendable to PDS


claim: No extension of {1,2,4,8,13} to a perfect difference set (conjecture disproven)

explanation: Confirms the 2025/2026 disproof: this Sidon set cannot be extended to any perfect difference set


claim: Photonic Omega for {1,2,4,8,13} is low (Sidon-like)


claim: h(N) computed for N=1..24 (brute-force, exact)


claim: h(N) <= sqrt(N) + N^0.25 + 1 (Erdős-Turán upper bound) for N ≤ 24


claim: Photonic Omega computed for best Sidon sets at N=8,16,24


claim: Tensor network entropy for power-of-2 Sidon sets at N=32,64,128

explanation: Entropy scales with set size, not N. Larger Sidon sets = more modes = higher entropy.