Evidence

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The entry point runs every retained certificate under util/ in its own interpreter and fails when any certificate exits nonzero. It uses the root Python environment and the shared failure harness, reads no input files, and writes no output files; the certificates that need NumPy or SymPy say so and fail when the package is missing, and neither package is declared by the repository, so the command supplies both. Run it from the repository root:

uv run --no-sync --with numpy --with sympy python wiki/research/erdos_940/evidence/main.py

The quintic first-moment certificate preserves the exact integer convolutions and rational inequalities used in the quintic barrier theorem. Its combined file runs and passes under the entry point above. It requires NumPy and SymPy.

The quartic residue certificate was reconstructed during the independent-record comparison. It uses only the Python standard library and proves the restricted 32-prescription objective exceeds 1.08. It does not obstruct the quartic complement argument.

The four-unit quintic extension uses only the Python standard library. Its 70 integer convolutions modulo 25 give primitive minimum nine, and its rational arithmetic certifies the strengthened uniform unordered mean $385732347/156250000>2.468$ in the quintic note.

The cubic matrix certificate uses SymPy to verify polynomial identities in a nine-dimensional matrix algebra, reducing coefficients modulo $z^2+z+1$. It checks every coefficient, not sampled inputs. The accompanying composition note gives the trace obstructions and the analytic bounds for the remaining scalar repairs.

The representation-count diagnostic preserves the one exact computation through $100000$ made in the count-congruence attempt. It requires NumPy, finds counterexamples in every residue class for six specified pairs of target and count moduli, and fails if any tested class lacks a witness. It excludes only universal congruences of those particular forms, not eventual congruences.

This directory stores supporting material only. See the main research index for established results and unresolved questions.