Exact parity controls

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The entry point checks the finite controls for L273. It enumerates every two-, three- and four-element support at $(s,W)=(2,4),(2,8),(3,18)$, and every distinct rotation when averaging the block law. For both rotation conventions and mixture weights $0,1/2,1$, it checks the centered parity square, degree totals and positive renormalization denominators in exact rational arithmetic. The square coefficients are compared with direct edge pairings; balanced hypergeometric distributions give a separate calculation of the genuine moments. At $(s,W)=(2,4)$ it also enumerates every whole-set outcome of both laws and directly evaluates the original and zeroed square.

The checks do not require a negative square at these small parameters and do not prove the asymptotic estimate. That conclusion rests on the written proof. There are no external inputs or output files. From the repository root:

uv run --no-sync python wiki/theory/additive_bases/L273_sidon_parity_obstruction/evidence/main.py

Default and --quick have the same exhaustive coverage. Allow thirty seconds and 300 MB with one thread. The only dependencies are NumPy and the root tools package; all theorem-relevant arithmetic is integer or rational.