Exact fourteen-point Sidon certificate

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From the repository root run:

uv run --no-sync python wiki/research/four_point_sidon_certificates/evidence/main.py

The exact input fourteen_points.json is the set and eight-point witness in Ma–Tang, arXiv:2602.23282v2, Lemma 5.1. The owning account gives the source link and the distinction between strong Sidon and the four-point hypothesis.

Using integer arithmetic, the program checks all 1001 four-subsets for at least five positive differences, all 2002 nine-subsets for a strong Sidon violation, and the contained eight-point witness for all 36 distinct pair sums including diagonals. The maximum strong Sidon cardinality of this one set is therefore exactly eight, since the property is hereditary. Boundary checks distinguish repeated summands and the weak convention.

Expected runtime is a few seconds or less in the repository environment. There is no discovery search, assertion of optimality of $4/7$, or independent review. The checker exits nonzero on any failed obligation, also under optimized Python.