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

This paper reformulates coherence “membranes” in Holosphere Theory as curvature-regulated shells generated by angular diffusion from a localized source. The model is anchored by the coherence triad: the geometric strain bound smax⁡=πs_{\max} = \pismax=π, the healing constant γ=α/2π\gamma = \alpha / 2\piγ=α/2π, and the global dropout threshold θbreak\theta_{\mathrm{break}}θbreak associated with close-packed percolation geometry. We show that membrane thickness follows a robust diffusion law, ΔR(t)∝Dt\Delta R(t) \propto \sqrt{D t}ΔR(t)∝Dt, while weak directional anisotropy deforms shell shape without altering the square-root growth exponent. A clear separation emerges between two threshold mechanisms: local transport freezing at λstability=π/3\lambda_{\mathrm{stability}} = \pi/3λstability=π/3, and global coherence failure determined by the fraction of sites that ever exceed the cutoff ϵc=2α\epsilon_c = 2\alphaϵc=2α. Network-level failure occurs only when this ever-exceeded fraction enters a close-packed percolation band, demonstrating that local freezing does not immediately imply global dropout. Ray-based iso-crossing diagnostics eliminate band-counting artifacts and provide geometry-robust measurements of radius, thickness, and eccentricity. Mapping thickness to delay via Δt≈ΔR/vϕ\Delta t \approx \Delta R / v_\phiΔt≈ΔR/vϕ yields a falsifiable prediction: observable delay envelopes scale as t1/2t^{1/2}t1/2 in the pre-onset regime. Taken together, the results provide a triad-consistent, classical diffusion framework for curvature-regulated shell growth and percolation-controlled coherence failure in the Holosphere lattice.