{
  "abstract": "Under the conditional framework breaking the longstanding O(n log n) integer multiplication barrier (originating from OpenAI Preprint #109), the asymptotic time complexity exponent T(n) = O(n (log n)^{1-κ}) is governed by bounding the second moment E[X^2] < 1 of recursive branching processes over trilinear tensor carrier graphs. In this work, we present a constructive combinatorial optimization over the alternating carrier bipartite matching graphs of the Schönhage trilinear tensor decomposition at dimensions h=23 and h=25. Through an alternating augmenting path search, we uncover a non-trivial cluster-unlocking cascade that eliminates 185 carrier roles (95 roles in h=23 and 90 roles in h=25), reducing the global physical wire width by 377,890 wires from the reviewed baseline W = 177,284,805 down to W = 176,906,915. Evaluated over the exact 10^{-14} rational grid, this wire reduction certifies an improved second-moment coefficient AB = 5,164,059 / 125,000,000,000 and establishes the sharpened conditional exponent κ= 826,215,307 / 20,000,000,000,000 \\approx 4.131076535 \\times 10^{-5}, strictly surpassing the preceding record on this architecture (κ\\approx 4.123864 \\times 10^{-5}). All 47 polynomial constraints and 7 rational security margins are audited in exact Q-arithmetic with zero floating-point error, and the fundamental wire reduction identity is formally verified in the Lean 4 interactive theorem prover without unproven axioms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14263",
  "author_total": 3,
  "authors": [
    {
      "name": "Volkan Dağlı"
    },
    {
      "name": "Zerrin Dağlı"
    },
    {
      "name": "Dağhan Dağlı"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a49ef5vz255cy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14263",
  "fulltext_url": null,
  "id": "a49ef5vz255cy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14263",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7221756888",
  "pdf_url": "https://arxiv.org/pdf/2610.14263",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a49ef5vz255cy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14263",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14263"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Bipartite Carrier Compression and Machine-Certified Bounds in Schönhage Trilinear Multiplication Tensors",
  "title_text": "Bipartite Carrier Compression and Machine-Certified Bounds in Schönhage Trilinear Multiplication Tensors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/a49ef5vz255cy",
  "venue": "arXiv",
  "versions": []
}