{
  "annotation_id": "fe14d889-4a80-41b2-ac22-e84a946da7f3",
  "date_created": "2026-02-17T05:53:20.172000Z",
  "date_modified": "2026-02-17T05:53:20.172000Z",
  "file_hash": "9ff70d7e68105fe2d8b013828032ed09814be76b09fa0854cce022e07545b061",
  "private": false,
  "record": {
    "abstract": "We establish a foundational homotopical framework for ternary $\\Gamma$-modules by establishing that $\\mathcal{T}\\text{-Mod}$ is a Barr-exact, monoidal closed category. We resolve the long-standing \"additivity obstruction\" in non-binary algebra by constructing a cofibrantly generated Quillen model structure on the simplicial category $s(\\mathcal{T}\\text{-Mod})$. Our central discovery is that the derived category $D(\\mathcal{T}\\text{-Mod})$ constitutes a 3-angulated category, where the derived periodicity is governed by triadic quadrilaterals rather than binary triangles. We derive the 3-ary long exact sequence and characterize the connecting morphisms as invariants of the $\\Gamma$-parameter space. This framework provides a rigorous homological bridge to Nambu mechanics and absolute geometry over $\\mathbb{F}_1$.",
    "arxiv_id": "2601.08918",
    "authors": [
      "Chandrasekhar Gokavarapu"
    ],
    "categories": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Homotopical Foundations of Ternary Gamma Modules and Higher Structural Invariants",
    "url": "https://arxiv.org/abs/2601.08918",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9d7e9dec-a4bc-4c50-b3f5-2347ddf4f93a",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}