CF04: Complete Formalism — Telegraph-Fisher Causality (Finite-Speed Transport)

Parabolic diffusion models imply instantaneous propagation: any localized perturbationproduces nonzero tails everywhere for all t > 0. In the Void Dynamics Model (VDM) thisviolates the axiom-level locality/causality requirement (VDM-A-2). This CF derives afinite-speed closure by combining a continuity law with a flux relaxation (Cattaneo–Vernotte)constitutive relation. The resulting telegrapher equation is hyperbolic with characteristicspeed c =√D/τ , recovering diffusion in the limit τ → 0 while enforcing a sharp domain ofdependence for compactly supported initial data. We extend the closure to reaction–transportby introducing a logistic source (telegraph–Fisher/KPP), summarize the known minimumfront-speed law and its diffusive limit, and specify decisive falsifiers as VDM validation gates(support growth, dispersion fit, and front-speed scaling across a τ sweep). Finally, we discussan epistemic causality interpretation: bounded Fisher information limits resolvable gradientsand motivates finite-speed transport as a measurable information-flow constraint.