Relational Horizon Dynamics (RHD/FDD/FAP): Complete Research and FAP Audit Bound Volume

Relational Horizon Dynamics (RHD/FDD/FAP): Complete Research and FAP Audit Bound Volume Todd M. Sisca | Independent Research | October 31, 2026 | 521 pages This comprehensive bound research volume consolidates the Relational Horizon Dynamics (RHD) mathematical research program, its foundational Factorization-Disrupting Density (FDD) framework, and the Forcing Alignment Protocol (FAP), including source manuscripts, mathematical constructions, computational investigations, adversarial reviews, and documented limitations. Conceived and developed under Todd M. Sisca's research direction beginning in April 2026, the program investigates mathematical relationships among set-theoretic forcing, quantum entanglement, operator algebras, modular theory, singular measures, and emergent auxiliary geometry. The volume contains five principal components: Historical RHD/FDD/FAP master (494 pages): Cohen and random forcing constructions, operator-algebraic distinctions, an abstract ER = EPR dictionary ladder, quasi-free CAR modular seams, dyadic singular measures, positive seam fusion/unfusion, marked kernel geometry, metric rigidity, balanced swaps, resonance arithmetic, and historical FAP assessments. Atomic-Seam Dilaton Test (6 pages): Exact kernel curvature, an obstruction to direct vacuum Jackiw–Teitelboim isometry, reconstructed generalized dilaton potential, and q-scale redundancy. Resonance-Selected Geometric Modes (3 pages): Exact resonance selection at c = 6/25, a critical-tiling moment bound, central curvature obstruction, and conditional collective modes. Continuum and Entanglement Bridge (8 pages): Dyadic continuum limits, finite modular Hamiltonians, orientation-dependent entangling operations, kernel-overlap entropy constructions, resonance preservation, and convergence obstructions. New-Tier FAP Referee-Style Audit (9 pages): Claim-by-claim mathematical screening, adversarial tests, negative controls, publication-level proof obligations, and explicit unresolved dependencies. The complete bound volume preserves the historical source material and distinguishes mathematical results, computational corroboration, conditional constructions, conjectures, and outstanding physical correspondence problems. The work does not establish physical spacetime emergence, a universal quantum-entanglement theory, gravitational dynamics, or experimental confirmation. Research conception, original RHD program, and source corpus: Todd M. Sisca.The author of the frameowrk has traumatic brain injuries, double vision, and trigeminal neuralgia, and uses AI reading/collaborative: in this bound-volume case: GPT-6 [alongwith Opus 5.5 and Fable].