Rank-7 toy Rota Basis conjecture and de-randomization

Let MM be a rank-77 binary matroid instance from the circuit-rich pool template described in the source, including trap instances and conjugation by GL(7,2)\operatorname{GL}(7,2). Rank-7 toy Rota Basis conjecture. The evolved policy succeeds with probability 11 over its internal randomness, and there is a deterministic de-randomization, obtained by removing the noise and using deterministic tie-breaking, that succeeds on the same class. This is an experiment-specific computational claim rather than a theorem about all rank-77 matroids, and the supplied text does not establish it mathematically.

Sources & referencesView supporting material

Primary source

Gergely Bérczi, “Evolving Local Corrections for Global Constructions in Combinatorics”, arXiv:2603.06692 (2026).

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