Exact evidence for the thirteen-point fractional obstruction

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Run from the repository root:

uv run --no-sync python wiki/theory/integer_sequences/L211_fractional_half_cover_obstruction/evidence/main.py

The entry point uses Python integers and rational numbers, the standard library, and the shared tools checker. Its fixed input is the thirteen binary vectors and exact covering certificates. The vectors were located by a finite search; the checker reproduces no search and uses no optimization solver. It takes a few seconds and less than 32 MiB. The optional --quick performs the same complete check.

It enumerates all $2^{13}$ subset sums and, independently as an author cross-check, all $3^{13}$ ternary sums through two half-word tables. The resulting relation-support sets must agree. A separate scalar subset-sum check tests the base-sixteen encoding. Upward closure of relation supports gives every dissociated subset, and submask dynamic programming gives the largest dissociated size in every nonempty subset.

The checker exhausts all two-color partitions, verifies the displayed three-color partition, and checks the dual inequality on every dissociated subset and the primal coverage at every point. It also checks that deleting any point makes the set two-colorable. In particular, the critical-core separation bound applies to this example: its three-color separation threshold is at most six. This finite seed alone does not provide successive tensor color jumps.

Any false hereditary bound, proper two-coloring, invalid coloring class, undercovered point, or overweight dual independent set makes the program exit nonzero, including under python -O. No cached output is read. These are author checks of the finite claim, not independent verification of it or evidence for an unbounded family.