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
Abstract
Published October 20, 2026 | Version v1
Relational Horizon Dynamics (RHD):
Seam Fusion: Complete Mathematical Research Dossier to-date:
Formal Seam Fusion, Marked Unfusion, and q-Scaled Emergent Kernel Geometry: 10/20/2026 v-1.0
Sole Author/Creator: TODD M. SISCA
Description:
Relational Horizon Dynamics | Complete Mathematical Research Dossier | Formal Seam Fusion, Marked Unfusion, and q-Scaled Emergent Kernel Geometry, v-1.0, 10/20/2026
Todd M. Sisca
This 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.
The 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.
Its 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.
The 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.
The 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.
The 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.
...supersedes "Complete dossier" of 105 pages, which had previously been published in chronological order while having the same date of 10/20/2026.
The author of the framework has TBIs, double vision, and trigemial neuralgia; and directs all research with AI reading and collaborative-assist.
The research is directed by Todd M. Sisca with AI-assisted mathematical development, computation, technical drafting, and adversarial checking.
Research 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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BibTeX
@misc{sisca2026relational,
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}},
author = {TODD SISCA},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23535687},
url = {https://zenodo.org/records/23535687},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - 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
AU - TODD SISCA
PY - 2026
DA - 2026/10/21
PB - Zenodo
DO - 10.5281/zenodo.23535687
UR - https://zenodo.org/records/23535687
AB - Published October 20, 2026 | Version v1 Relational Horizon Dynamics (RHD): Seam Fusion: Complete Mathematical Research Dossier to-date: Formal Seam Fusion, Marked Unfusion, and q-Scaled Emergent Kernel Geometry: 10/20/2026 v-1.0 Sole Author/Creator: TODD M. SISCA Description: Relational Horizon Dynamics | Complete Mathematical Research Dossier | Formal Seam Fusion, Marked Unfusion, and q-Scaled Emergent Kernel Geometry, v-1.0, 10/20/2026 Todd M. Sisca This 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. The 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. Its 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. The 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. The 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. The 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. ...supersedes "Complete dossier" of 105 pages, which had previously been published in chronological order while having the same date of 10/20/2026. The author of the framework has TBIs, double vision, and trigemial neuralgia; and directs all research with AI reading and collaborative-assist. The research is directed by Todd M. Sisca with AI-assisted mathematical development, computation, technical drafting, and adversarial checking. Research status: Mathematical working research requiring independent specialist examination. Physical spacetime emergence, a physical DSSYK regulator identification, and the broader physical interpretations remain unproved.
ER -