Exhaustive check of the two-parabola sets for small q

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From the repository root run:

uv run --no-sync python wiki/theory/additive_bases/L208_two_parabola_maximal_sidon/evidence/main.py

The program builds $\mathbb F_q$ for $q\in\{3,5,7,9,11,13,17,19,23,25,27,49\}$ from explicit irreducible polynomials, whose irreducibility it checks, and forms the set $A$ of the claim for every non-square $\mu$. For each pair $(q,\mu)$ it checks that $|A|=2q-1$, that all unordered pair sums with doubles are distinct, that every point of $\mathbb F_q^3$ outside $A$ is of the form $a+b-c$ with $c\notin\{a,b\}$, and that the three explicit witness formulas of the proof produce valid witnesses for every such point. As a control, for every non-zero square $\mu$ it finds the repeated sum $P(t)+P(-t)=C(u)+C(-u)$ that the proof excludes for non-squares.

All arithmetic is exact. The program uses the repository's evidence harness and the Python standard library; it runs in about ten seconds and has no quick mode. Any failed obligation gives a nonzero exit, also under optimized Python. The check covers these finite fields only; the statement for every odd prime power rests on the proof.