Exact butterfly parameter check

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verify/: Independent whole-conclusion examination and separate grade of the exact finite graph construction and its asymptotic consequence.

From the repository root run:

uv run --no-sync python wiki/research/graph_ramsey_interfaces/butterfly_degree_sum_certificate/evidence/main.py

The exact input specifies five part numerators, the common denominator, all six supported pairs and their density numerators, the comparison constant and the cutoff. The program uses integer and rational arithmetic only. It checks all ten triples of part labels, the handshaking identity, the exact two triangle sums, the positive edge-density surplus, the rational comparison with $2(\sqrt3-1)$, and the padding inequality at the cutoff. Monotonicity extends the latter check to every larger order, as proved on the owning page.

The run takes less than a second in the repository environment. It has no search parameters, external source input or generated witness. The construction and the reduction from rational parameters to actual graphs are proved in the native proof. This program supplies author arithmetic evidence. The independent recount, adversarial controls, whole-conclusion report and separate grade are retained in the verification record.

The handshaking diagnostic is forced by shared pair accumulation and has no independent checking weight. The program also does not validate arbitrary construction inputs: simultaneous sign reversal preserves its rational values while invalidating the finite-set parameters. The retained positive input and the full analytic proof are the subject of the accepted grade.