{
  "abstract": "Published October 20, 2026 | Version v1\n\nRelational Horizon Dynamics (RHD):\n\nSeam Fusion: Complete Mathematical Research Dossier to-date:\n\nFormal Seam Fusion, Marked Unfusion, and q-Scaled Emergent Kernel Geometry: 10/20/2026 v-1.0\n\nSole Author/Creator: TODD M. SISCA\n\nDescription:\n\nRelational Horizon Dynamics | Complete Mathematical Research Dossier | Formal Seam Fusion, Marked Unfusion, and q-Scaled Emergent Kernel Geometry, v-1.0, 10/20/2026\n\nTodd M. Sisca\n\nThis 126-page mathematical research volume contained herein - along with full framework Forcing Alignment Protocol audit - consolidates Relational Horizon Dynamics (RHD), a research program investigating relationships between set-theoretic forcing, Borel equivalence relations, von Neumann algebras, modular theory, and analytic geometry.\n\nThe foundational framework examines Cohen forcing through finite labelled directed graphs and Factorization-Disrupting Density (FDD), random-generic equivalence relations and Feldman–Moore factors, hyperfinite adjunction, and quasi-free CAR horizon-seam constructions.\n\nIts subsequent development introduces recursive dyadic singular measures, a critical measure transition at α = 1/2, positive-singular-measure seam fusion, marked unfusion, and q-dependent singular inner functions.\n\nThe unified construction investigates how fused seam measures determine projective reproducing-kernel metrics, how those geometries distinguish configurations sharing coarser algebraic invariants, and how marked data retain information lost under unmarked fusion.\n\nThe volume includes the foundational research manuscripts, six supporting seam-development papers, an additional q-scaled research note, mathematical visualizations, source code, computational checks, and historical and supplemental Forcing Alignment Protocol (FAP) auditing records.\n\nThe current 216-item FAP-format audit reports 196 passes, two documented corrected defects, and 18 incomplete verification obligations. - according, that is, to RHD's own internal self-regulating Forcing Alignment (audit) Protocol (FAP) - I call myself to task first and last wherever necessary: I don't need anyone else to do it for me...Thanks very much. These audit results are not independent mathematical peer-review certification.\n\n...supersedes \"Complete dossier\" of 105 pages, which had previously been published in chronological order while having the same date of 10/20/2026.\n\nThe author of the framework has TBIs, double vision, and trigemial neuralgia; and directs all research with AI reading and collaborative-assist.\n\nThe research is directed by Todd M. Sisca with AI-assisted mathematical development, computation, technical drafting, and adversarial checking.\n\nResearch status: Mathematical working research requiring independent specialist examination. Physical spacetime emergence, a physical DSSYK regulator identification, and the broader physical interpretations remain unproved.",
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  "authors": [
    {
      "name": "TODD SISCA"
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  "doi": "10.5281/zenodo.23535687",
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  "published": "2026-10-21",
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  "title": "Relational Horizon Dynamics: Seam Fusion: Complete Mathematical Research Dossier to-date: Formal Seam Fusion, Marked Unfusion, and q-Scaled Emergent Kernel Geometry, v-1.0, 10/20/2026",
  "title_text": "Relational Horizon Dynamics: Seam Fusion: Complete Mathematical Research Dossier to-date: Formal Seam Fusion, Marked Unfusion, and q-Scaled Emergent Kernel Geometry, v-1.0, 10/20/2026",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:07Z",
  "url": "https://research.draconitic.com/paper/bvdvfbke0t99z",
  "venue": "Zenodo",
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}