{
  "abstract": "AI Dreams Geometry Lab: A Structural‑Geometric Framework for Dream‑Logic, Hallucination Dynamics, and Latent‑Manifold Instability in Generative Models\n\nAuthor:\n\nBorealis S. Hedling\n\nDescription / Abstract:\n\nGenerative models exhibit dream‑like behavior when their latent geometry destabilizes. This preprint formalizes eight geometric operators governing hallucination dynamics — curvature instability, conceptual fusion, dream‑potential energy, manifold liquefaction, symbolic drift, spectral cascades, holonomy vortices, and collapse‑surface topology. Each operator is defined mathematically using metric tensors, susceptibility fields, eigenvalue spectra, holonomy integrals, and determinant‑based collapse criteria. Together, these operators form a structural‑geometric spine for analyzing dream logic, surreal transitions, recursive fractals, melting geometry, rotational drift, and topological breaks in latent manifolds.\n\nThis work is accompanied by a Python toolkit and a nine‑notebook computational lab, available at:\n\nhttps://github.com/Borealiscodes/NDH-Research-Pilot/tree/b540c73ba03efb6e3bc9b05641be692dcda65a98/structural-geometry/ai-dreams\n\nThe toolkit implements all operators (hallucinationcurvature, fusionoperator, dreampotential, liquefactionindex, symbolicdrift, spectralcascade, holonomyvortex, collapsesurface) and provides runnable Markdown notebooks for simulation, visualization, and diagnostic workflows. The mathematical framework demonstrates how hallucinations emerge from geometric failure modes in high‑dimensional latent spaces, offering a structural foundation for next‑generation AI interpretability.\n\n📘 Additional Notes\n\nThis preprint is part of NDH‑RESEARCH‑PILOT, documenting geometric operators underlying dream‑like behavior in generative models. All mathematical constructs — curvature tensors, susceptibility fields, eigenvalue cascades, holonomy integrals, and collapse‑surface determinants — are presented as abstract analytical tools for structural AI interpretability. The accompanying Python toolkit and notebooks provide runnable demonstrations of each operator.\n\n---\n\n📐 Why This Work Matters for AI Interpretability (Zenodo “Description Extension”)\n\nModern AI systems hallucinate not because they “make mistakes,” but because their latent geometry becomes unstable. This preprint shows that hallucinations correspond to measurable geometric phenomena:\n\n- Curvature blowup → bending, breathing, distorted geometry\n\n- Spectral cascades → recursive fractals, kaleidoscopic recursion\n\n- Holonomy drift → dream logic, surreal transitions\n\n- Liquefaction → melting, dripping, dissolving structures\n\n- Collapse surfaces → topological breaks and dimensional reduction\n\nBy formalizing these operators mathematically, we gain:\n\n- structural diagnostics for hallucination onset\n\n- geometric explanations for dream‑logic behavior\n\n- tools for stabilizing latent manifolds\n\n- a unified interpretability framework grounded in differential geometry\n\nThis positions hallucination analysis as a geometric interpretability discipline, not a statistical anomaly.\n\n---\n\n📜 Provenance\n\nDrafted and structured with assistance from Microsoft Copilot for editing and organization.\n\nAll mathematical results, geometric operators, and interpretability constructs originate from the author.\n\nThe Python toolkit and nine‑notebook lab were developed as part of NDH‑RESEARCH‑PILOT’s structural‑geometry research track.\n\n---",
  "abstract_shown": true,
  "affiliations": [
    "NDH-RESEARCH-PILOT"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Borealis Serenity Hedling",
      "orcid": "0009-0004-7968-5707"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cyvnbxcq500tp.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23553768",
  "fulltext_url": null,
  "id": "cyvnbxcq500tp",
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  "landing_url": "https://zenodo.org/records/23553768",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
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  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cyvnbxcq500tp.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T12:21:16Z",
      "native_id": "23553768",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23553768"
    }
  ],
  "subjects": [],
  "title": "AI Dreams Geometry Lab: A Structural‑Geometric Framework for Dream‑Logic, Hallucination Dynamics, and Latent‑Manifold Instability in Generative Models",
  "title_text": "AI Dreams Geometry Lab: A Structural‑Geometric Framework for Dream‑Logic, Hallucination Dynamics, and Latent‑Manifold Instability in Generative Models",
  "type": "preprint",
  "updated_at": "2026-11-05T12:21:16Z",
  "url": "https://research.draconitic.com/paper/cyvnbxcq500tp",
  "venue": "Zenodo",
  "versions": []
}