Evidence

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The entry point checks that the retained certificate assets/cube4.json is present and runs the probe util/check_cube4.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_963/evidence/main.py

The certificate proves that every 32-subset of the 40 nonzero antipodal representatives in the ternary four-dimensional cube contains a dissociated six-subset: it partitions the representatives into blocks of sizes 13, 13, and 14 and lists dissociated six-subsets whose pairwise unions cover every pair of each block. The probe recomputes the representative set, enumerates the 64 signed sums of every listed six-subset, and checks the pair covers. The proof sketch states how this excludes one proposed counterexample family; the certificate excludes this specific candidate family only.