Exact checks of Ramsey–Graham tensor layers

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Purpose, input, and finite range

These checks verify the published tensor-layer data on the base $X=S_3\otimes S_5$.

Run, from the repository root,

uv run --no-sync python wiki/research/erdos_774/evidence/tensor_layers/main.py

The checker uses explicit eight-coordinate integer vectors and checks 29 layers with at most eight vectors each, enumerating at most $3^8$ ternary sums per layer. Every arithmetic operation is exact; it uses the standard library and the shared root tools checker and finishes in a few seconds. Its named checks are that every layer is dissociated, that each final signed-span intersection is zero and that the successive intersection sizes below are reproduced; a failed clause exits nonzero. The layer lists come from Ramsey–Graham, Planar Sidonicity and quasi-independence for multiplicative subgroups of the roots of unity, Example 7.3 and Appendix (printed pages 356 and 358), checked in the held copy at those pages. The checker verifies the data rather than assuming the reported computational outcome.

Checked witnesses

For a 52-element subset of $X\otimes S_7$, all seven layers are dissociated and the successive signed-span intersection sizes are

The final intersection is $\{0\}$, so the subset is dissociated by the layer criterion. For two complementary subsets of $X\otimes S_{11}$, of sizes 82 and 83, both final intersections are again $\{0\}$.