Paper T14: Born Statistics from Angular Coherence Filtering: Quantum as an Emergent Continuum of a Classical SU(2) Lattice

This paper presents a classical, non-circular route to Born statistics inside Holosphere Theory. The mechanism layer is an admissibility filter: most kinematically possible micro-trajectories fail a link-level gate, and the surviving coherence-compatible trajectories induce a real density on S2S^2S2. The reporting layer is the classical configuration geometry S3≃SU(2)S^3 \simeq SU(2)S3≃SU(2) (Paper T33), where overlap depends on geodesic separation via C(Δ)=cos⁡(Δ/2)C(\Delta)=\cos(\Delta/2)C(Δ)=cos(Δ/2) and intensities follow ∣C∣2|C|^2∣C∣2, with 4π holonomy and dark nodes at Δ=π,3π\Delta=\pi,3\piΔ=π,3π. A central empirical contribution is an audit-grade numerical emergence check: using icosahedral refinements, a cotangent Laplace–Beltrami discretization, and lumped mass weighting, the lowest non-constant eigenmodes converge to the symmetry-selected rail ψcoh(θ,ϕ)=sin⁡θcos⁡ϕ\psi_{\text{coh}}(\theta,\phi)=\sin\theta\cos\phiψcoh(θ,ϕ)=sinθcosϕ, with orientation fixed only after solving the eigenproblem by selecting the rail-aligned combination within the near-degenerate ℓ≈1\ell\approx 1ℓ≈1 triplet. The resulting shape and Born-map errors obey clean refinement power laws and the first non-constant eigenvalue converges to λ→2\lambda\to 2λ→2, without using a spherical-harmonic basis or a quantum operator as input. The paper further supplies survivor-volume diagnostics (Appendix G) that compare empirical survivor-bin masses against exact bin-integral predictions for ρcoh=ψcoh2\rho_{\text{coh}}=\psi_{\text{coh}}^2ρcoh=ψcoh2 under declared masks, plus an S3S^3S3 validation that ∣C∣2|C|^2∣C∣2 matches the Beta(1/2,3/2)(1/2,3/2)(1/2,3/2) benchmark when applicable. Platform timing and device readout semantics are explicitly out of scope; the deliverable is a compact, falsifiable pipeline that separates calibration anchors from derivational inputs and exposes concrete audit hooks.