{
  "abstract": "Let ${\\mathbb K}$ be an arbitrary field. We study tensor degenerations for square matrix multiplication over the field ${\\mathbb K}$, and mainly prove for any integer $n\\ge5$ the uniform dyadic estimate \\[ \\underline{\\mathrm R}_{\\mathbb K}({\\mathsf M}_{2^n}) \\le 2^{2n+1}\\] which implies that $ω(\\mathbb K)\\le 2+1/n$, where the border rank $\\underline{\\mathrm R}_{\\mathbb K}(T)$ is the least $r$ for which the scalar extension of $T$ to an algebraic closure of $\\mathbb K$ lies in the Zariski closure of the tensors of rank at most $r$, and $ω(\\mathbb K)$ is the matrix multiplication exponent over the field ${\\mathbb K}$. This improves the current best record $ω(\\mathbb K)<2.371177$ greatly, and answers affirmatively the long-standing open question whether the value $ω({\\mathbb K})$ is exactly $2$. The implementation disclosure and appendices in this paper give fixed source maps, interpolation data, terminal incidence ledgers, and deterministic check counts for independent reconstruction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13971",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhi-Wei Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f40k92k08erbj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13971",
  "fulltext_url": null,
  "id": "f40k92k08erbj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13971",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GM"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7221834137",
  "pdf_url": "https://arxiv.org/pdf/2610.13971",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f40k92k08erbj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.13971",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13971"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GM",
      "subfield": "general"
    }
  ],
  "title": "Tensor Degenerations for Matrix Multiplication",
  "title_text": "Tensor Degenerations for Matrix Multiplication",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/f40k92k08erbj",
  "venue": "arXiv",
  "versions": []
}