Evidence

../

The entry point checks that the retained certificate assets/couplings.json is present and runs the probe util/verify.py in its own interpreter, failing when the probe exits nonzero. It uses the root Python environment and the shared failure harness, reads only the certificate, and writes no output files. Run it from the repository root:

uv run --no-sync python wiki/research/erdos_644/evidence/main.py

The probe uses only the Python standard library and exact rational arithmetic. It examines all $\binom{15}{7}=6435$ active-constraint choices for the seven-dimensional probability polytope $Q_3$, discards singular and infeasible bases, and finds exactly 52 distinct vertices. The certificate supplies one representative of each of their 16 orbits under permutations of the three seed points. Every representative is expressed as a convex combination of vectors $(4\delta_I+2\delta_J+\delta_K)/7$, with $I,J,K$ pairwise disjoint.

States are bit masks in the order $\varnothing,1,2,12,3,13,23,123$, namely integers 0 through 7. Each coupling entry is [rational coefficient, [I, J, K]].

This is a finite, exhaustive, rational computational certificate, not a proof-assistant formalization. Its mathematical reduction and the integral rounding argument are in constant-composition families. No numerical linear-programming solver or floating-point calculation is used by the probe. The certificate checks only the finite three-point polytope inclusion and does not certify either unrestricted assertion of Problem 644.