Evidence

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The entry point checks the finite statements behind the notes of this folder. It verifies the explicit degree-two family of the linear-capacity note in exact rational arithmetic at sample sizes, every constraint included, with a floating-point eigenvalue control and a negative control just beyond the family's limit. It checks the integer parameter conditions of the proof on the whole closed-form range for $48\le N\le 200000$, and the window inequality at the sample points. For the rotated perturbed lattice it computes the exact expected difference counts of the unconditioned process at two sample sizes and checks them, with the conditioning factor of the proof, against the capacities. For the perfect-difference note it builds Singer sets for $q\in\{5,7,11,13,17\}$, checks the perfect difference property and checks every arc of every unit dilate against the ceiling. The full run also brackets an auxiliary circulant linear-program threshold at $N=1000$ between the coefficients $0.583$ and $0.596$. This program omits sum capacities; its floating-point solver reports are uncertified and do not establish feasibility of the full relaxation. The lattice convolution uses exact integer autocorrelation counts and a second-difference recurrence, checked against direct enumeration on a small input. Its capacity comparisons are rational. The parameter-range scan likewise uses integer inequalities.

The short-count covariance formulas are checked against every outcome of the unrotated block law at $(s,W)=(2,4),(3,4),(3,6),(4,6)$. All means, covariance entries and the two-kernel decomposition are compared in exact rational arithmetic. Both run modes include these four complete sample spaces, the largest of which has $\binom{6}{4}^4=50625$ outcomes. This finite check supports the exposed counting formulas; it is not a positivity certificate for a Sidon repair.

The fixed-seed short-pair simulation is exploratory: it permits coincident labeled positions and does not certify a repaired moment functional. The precise quartic obstruction has its own exact finite witness and direct-enumeration control.

Run from the repository root with uv run --no-sync python wiki/research/sidon_extremal_error/evidence/main.py; the full run takes about a minute and uses under 3 GiB, with one thread; --quick uses smaller samples and takes a few seconds. These are finite checks of stated samples. The statements for all $N$ rest on the written proofs.