Introducing the Curvature Field Function: Toward a Geometric Formulation of Wavefunction Collapse

Benchmarking the Sorkin Parameter κ in the Triple-Slit Experiment

Abstract

We introduce a curvature-phase field that encodes geometry-driven suppression in quantum interference and frames wavefunction collapse as the consumption of a finite curvature budget. The model couples a static curvature field Phi to the wave amplitude via “A squared equals one over one plus the squared gradient magnitude of Phi,” and links dynamics to a Lagrangian term, separating scale from shape. For a scale-free test, we benchmark the Sorkin parameter kappa(theta) from the triple-slit experiment of Sinha et al., comparing model kappa_PhiPsi to the experimental series kappa_exp using a gain-invariant Version-2 full-profile metric with a single global prefit. Using the reported photon parameters (lambda = 810 nm, w = 30 um, d = 100 um, L ~ 18–20 cm) and a fixed random seed, the model reproduces the analytic shape and attains about 96.4% concordance on kappa, while Gaussian and Bohmian baselines reach about 74.6% and 76.0%. Sensitivity sweeps (+/-10% in {w, d, L}) preserve shape correlation, and ablations (removing the curvature envelope or residual phase) systematically reduce agreement, consistent with a curvature-gradient mechanism. Central-intensity (CI) metrics are reported separately and are not mixed with kappa. These results support a geometric formulation of wavefunction collapse without ad hoc scale tuning.