Numerical Validation of the ESMA Framework: Benchmark Against the Bialynicki-Birula–Mycielski Gausson, Convergence Analysis, and Quantified Nonlocal Coupling

Editorial note: This file was uploaded here by mistake as a new version of "Variational Formulation and Effective Nonlinear Self-Confinement in the ESMA Framework." Its content is independent numerical-validation work and is unrelated to that paper's v1. The same material is also published under the correct record, "Numerical Validation of the ESMA Framework" (concept DOI: 10.5281/zenodo.19110504). We benchmark the split-step Fourier (SSFM) implementation of the ESMA framework's logarithmic term against the exact "gausson" soliton solution of Bialynicki-Birula & Mycielski (1976), obtaining a fidelity of 1.000000000 and norm conservation to 3×10⁻¹³ for both a stationary and a Galilean-boosted soliton. A self-convergence study shows the numerical scheme converges at empirical order p ≈ 2.25 in the time step, consistent with the second-order Strang splitting used. We quantify the nonlocal coupling artifact identified in the original variance operator: two wave packets separated by 30 length units, with zero density overlap, show a spurious relative width shift ranging from the numerical noise floor (~10⁻⁹) at locality scale l ≤ 3 up to 7×10⁻² at l = 20, while the local gradient-based extension (β term) remains at the noise floor independent of separation.