The Born Rule from Configurational Stability: A Timeless Derivation

We derive the Born rule $P \propto |\psi|^2$ as a structural consequence of configurational stability within Lambda Convergence Universal Field Theory (LUFT). This paper constitutes Layer-3 of the LUFT program: having established the stability functional $I[\Phi]$ on configuration space (Layer-0), light propagation via the pre-metric Fresnel route (Layer-1), and fermion generations from shape tensor geometry (Layer-2), we now address quantum probability. The derivation is purely static: configuration space $\mathcal{C}$ is partitioned into stability basins weighted by $S[\Phi] = \exp(-I[\Phi]/\hbar_{eff})$, and consistency requirements on probability assignments uniquely select the quadratic map. No temporal concepts enter the fundamental formalism. Measurement corresponds to a topological boundary in $\mathcal{C}$ separating multi-basin (quantum) from single-basin (classical) regions. The quadratic probability map emerges from requiring projective invariance, factorizability, and classical additivity under phase degradation---only the bilinear form $|\psi|^2$ satisfies these constraints without violating associative composition. We express experimental discriminants as coherence structure discontinuities that observers parametrizing $\mathcal{C}$ with clocks interpret as temporal phenomena. The framework predicts non-analytic signatures in coherence ratios distinguishable from smooth environmental scaling, testable via pure dephasing without energy injection. Unlike collapse models requiring stochastic dynamics, this mechanism is purely geometric. Version note (v1.2.0, July 2026): A/B-sync with the spine v2.13.0 retraction: all c2 = A/B statements are replaced — A/B is a quadrature ratio with no kinematic content; the propagation cone is carried by the dispersion route (c2 = alpha*kappa at tree level, conditional on OS reconstruction). The h_eff = f(A, B, Delta I_max) scope item is annotated accordingly. Derivation content unchanged.