A 55-Addition Rank-23 Scheme for 3×3 Matrix Multiplication — artifacts, verifier, and machine-checked proof

Artifacts for the first 55-addition, 23-multiplication exact 3×3 matrix-multiplication scheme (previous record: 56 additions; Y. Sun, arXiv:2604.27645). The scheme uses ±1 coefficients, binary ± additions with free negation, no change of basis, and is valid over any ring (fully non-commutative; recurses on block matrices). Included: the explicit 55-operation straight-line program; an independent verifier (exact integer and non-commutative block trials, operation count); a runnable Rust transcription with fuzz tests against the naive 27-multiplication algorithm; a sorry-free Lean 4 + Mathlib proof that the program computes the matrix product over a general non-commutative ring; and the paper, which also proves that no 54-addition scheme exists anywhere in the published Heule–Kauers–Seidl catalogue (17,376 de Groote classes, every representative, every sign model). Developed in an extended interactive collaboration with Claude (Anthropic); every claim is mechanically checkable by the included tools.