{
  "abstract": "FINDING: Mock modular forms serve as Z-invariants for quantum 3-manifold invariants, bridging categorification, lattice theta functions, and quantum modularity. | MATH: Key objects: mock theta functions (Ramanujan), non-holomorphic modular forms (Zwegers: \\( \\hat{f}(\\tau) = f(\\tau) + \\frac{i}{2\\pi}\\int_{-\\bar{\\tau}}^{i\\infty} \\frac{\\Theta(w)}{\\sqrt{-i(w+\\tau)}} dw \\)), quantum modular forms (Zagier: functions \\( f: \\mathbb{Q} \\to \\mathbb{C} \\) with modular transformation errors that are \"nice\" — e.g., \\( f(x) - f(x+1) \\), \\( f(-1/x) - x^k f(x) \\) are real-analytic on \\( \\mathbb{R}\\setminus\\mathbb{Q} \\)). Z-invariants: partition functions of \\( \\text{SU}(2) \\) Chern–Simons theory on 3-manifolds, \\( Z(M) = \\sum_{j} \\frac{S_{0j}^2}{S_{0j}} \\dots \\) (WRT invariant), categorified to homological invariants. Even unimodular lattice theta: \\( \\Theta_\\Lambda(\\tau) = \\sum_{v\\in\\Lambda} q^{v\\cdot v/2} \\), with \\( \\Lambda \\) even unimodular (e.g., \\( E_8 \\), Leech), modular of weight \\( k = \\text{\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/9010zty0a1rw7.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490690",
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  "id": "9010zty0a1rw7",
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  "language": "eng",
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  "published": "2026-10-20",
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  "ris": "https://research.draconitic.com/paper/9010zty0a1rw7.ris",
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    {
      "first_seen": "2026-11-03T12:21:26Z",
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  "title": "Mock Modular Forms as Z-Invariants Bridging Quantum 3-Manifolds and Modularity — E8 Intelligence Research",
  "title_text": "Mock Modular Forms as Z-Invariants Bridging Quantum 3-Manifolds and Modularity — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:26Z",
  "url": "https://research.draconitic.com/paper/9010zty0a1rw7",
  "venue": "Zenodo",
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