Contact Order ≥ 4 at the Rank-22 Obstruction Locus of 3×3 Matrix Multiplication

Zenodo (CERN European Organization for Nuclear Research) 2026 Preprint Open access

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Authors: Stefan Beuchert
DOI: 10.5281/zenodo.20583479
Cited by: 4

Abstract

We present a computational-algebraic characterization of the rank-22 barrier for M₃ (3×3 matrix multiplication)through a gate-verified L1-obstruction triangle and a complete contact order sequence. Contact order ≥ 4 is established empirically (57,155 null-space triples, THIRD_ORDER_FULL_C3_VANISHES) and algebraically(Macaulay2 Betti [0,233,0,233]). Results exemplify the cactus barrier theory of Buczyński (2026). A German version is included. ORCID: 0009-0002-3883-5540 Mail: sb@sb-forschung.com

Fields of Study & Subjects

Polynomial and algebraic computation Tensor decomposition and applications Matrix Theory and Algorithms

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
7 June 2026
Language
EN
Document type
Preprint