Evidence

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The entry point main.py builds every member of eight small block families and five small substitutions and checks, in exact rational arithmetic, the containment bound of Lemma 3, the spread recursion of Lemma 2, and the spread of $B(2,4)$ and $B(2,2)^2$. It covers finite instances only; the general statement and the thinning part rest on the written proof. Run it from the repository root with uv run --no-sync python wiki/theory/set_systems/L214_spread_intersecting_families/evidence/main.py; it takes a few seconds and exits with status 0 when every check passes.