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A proof of the Regts–Sevenster conjecture, formalized

William Whistler

Palomar Registrypalomar/PALOMAR-2026-08-19-000003Sep 6, 2026math.COscore 0

A Lean 4 proof of the Regts–Sevenster conjecture. A complex-valued graph parameter, normalized at the empty graph and invariant under isomorphism, has exponentially bounded edge-connection rank if and only if it is a mixed partition function. For a natural rank base R, a representing model can be chosen with k even and 2ℓ odd colours satisfying k + 2ℓ ≤ R. The development also proves the even connection-rank growth limit, minimum total colour dimension, minimal parity formulas and prescribed-dimension criterion. Schrijver's factorial argument supplies nilpotent-trace vanishing;…

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