Paper 27B: Curvature-Regulated Coherence Membranes: Classical Emergence of Causal Structure and Entropy Clocks in the Holosphere Lattice

Paper 27B reformulates Holosphere coherence membranes as curvature-regulated shells governed by classical overdamped diffusion with explicit admissibility thresholds. Membrane growth is characterized using two independent power-law exponents: one for front propagation (β_R) and one for membrane thickness (β_ΔR), extracted from raywise iso-crossing diagnostics. In unconstrained control runs (local freezing disabled), membrane thickness approaches classical diffusive scaling at late times (β_ΔR ≈ 1/2), while the median isoradius follows a stable propagation law (β_R ≈ 0.315). When admissibility constraints are enabled (local freezing at λ_stability = π/3 and global threshold tracking), both exponents are suppressed. Propagation becomes nearly pinned (β_R ≈ 10⁻²), and thickness remains strongly subdiffusive (β_ΔR ≪ 1/2). A diffusion sweep shows that increasing D accelerates threshold activation (growth of Θ(t)) and further reduces both exponents. Mapping thickness to a timing residual yields a falsifier-ready delay channel Δt ∝ t^{β_ΔR}. The model therefore predicts regime-dependent delay scaling: √t behavior appears only in diffusion-dominated regimes, while subdiffusive envelopes arise when admissibility is active. The results demonstrate that classical curvature-regulated diffusion plus thresholded admissibility is sufficient to generate finite membranes, exponent suppression, and a quantitative delay channel.