Exact affine-fiber boundary diagnostics

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The checker is author evidence for L269. It constructs the original integer simplex tensor columns; no matrix entry is reduced to the characteristic of the field indexing the points.

Run from the repository root:

uv run --no-sync python wiki/theory/integer_sequences/L269_simplex_affine_fiber_threshold/evidence/main.py

For $q=3,4$, every $1\le k<q$, every affine value and each of two specified nonzero normals (one when these coincide), the program checks full column rank modulo 65521. This certifies rational independence of all 29 tested fibers. The non-prime field is $\mathbb F_4=\mathbb F_2[X]/(X^2+X+1)$.

At $k=q$ and $k=q+1$, it constructs the proof's difference of two codimension-two fibers for both normals and every affine value. For all 28 trades it checks the support size $2q^{q-2}$, disjointness of the two terms, and a zero image under the actual integer tensor matrix. Each term separately has nonzero image, checking the cancellation at the heart of the construction. The extra coordinate is fixed in the $k=q+1$ cases.

The input domain is fixed in the code. Arithmetic is exact; only the standard library and repository tools package are needed. The run takes under ten seconds and less than 32 MiB; --quick runs the same complete fixed domain. Failure gives a nonzero exit code. These checks are diagnostics, not a finite reduction of the general theorem. Its Fourier proof supplies the all-parameter argument.