Relativity and Cosmology

Causal Topology Vacuum Model: A Statistics Resolved, Matroidal, and Horizon Regulated Framework

Authors: Russell S. Clark II, Brian L. Swift

This integrated draft is a research-program white paper that harmonizes three strands of the Causal Topology Vacuum Model (CTVM): the broad v7 dark-sector program, the shorter v8 corrective scaffold, and the Volovik/statistical-sector revision. The central claim is no longer that CTVM has been derived as a theorem of algebraic quantum field theory (AQFT). The corrected claim is more precise: CTVM is a layered, testable framework in which regulated vacuum correlations are separated into operational response sectors, encoded by response-weighted representable matroids, and conditionally related to gravitational sourcing through a separate semiclassical or holographic dictionary. Version 15.5 retains the referee-facing viability improvements and critical-path improvements: a tighter dependency schema, a modular-compatibility status note, a compact SK-versus-CPTP worked example, an explicit matroid falsifier, clearer Volovik analogy boundaries, and more visible falsifier/non-claim summaries. First, the transport—teleportation diagnostic is rewritten as operational prose rather than as a numbered pseudo-equation, while preserving the distinction between path-dependent geometric response and resource-mediated algebraic relabeling. Second, the near-degenerate horizon-edge assumption is strengthened into a spectral-shell hypothesis with an explicit expansion parameter for the approximation γ+ ≃ γ−. These are deliberately clarifying revisions; they sharpen presentation, operational falsifiability, and horizon-edge kinetics without adding new load-bearing claims. Version 15.5 further tightens the architectural-tradeoff statement and quarantines the conditional residual-sector construction: a thresholded binary reduction of the residual response block, a matroid-to-CSS code ansatz, a quantified addressability/leakage trade-off, a small three-detector CSS illustration, and an analytic longitudinal-mode asymptotic in Appendix H.12. These additions are framed as construction targets and calculable hypotheses, not as completed proofs of residual gravitational inertness. Version 15.5 also retains a modular-equivalence consistency check motivated by the companion Entropic Inertia analysis: if inertia is a Rindler modular work response, then any sector excluded from gravitational sourcing must also be absent from the inertial modular-work functional, or else the Einstein equivalence principle would be violated. This is stated as a conditional sector-matching principle, not as a proof of the equivalence principle.

Comments: 84 Pages. This paper is intended to describe a research program and causal topology framework toward an improved formulation of the cosmological constant problem.

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[v1] 2026-06-10 20:36:58

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