GL‑5.2: CF‑Modified Time Delays with Distance Scaling and β Offset (ψ Fixed)

This simulation tests the impact of the Curvature Factor (CF) on gravitational lensing time delays when applied to both distance geometry and a synthetic β offset (introducing nonzero Δθ). The Fermat potential remains fixed under an SIS profile (ψ(θ) = θ_E·θ), isolating CF geometry from lensing mass effects.Δt values were computed for three CF gradients (1.0, 2.0, 2.999) across three clusters (Abell 1689, MACS J1149, Bullet Cluster).All outputs were validated using Kolmogorov–Smirnov, Anderson–Darling (Rayleigh), and Chi-Square tests. Each statistical test returned p ≪ 0.05 and strong effect sizes, indicating significant deviation from GR baseline behavior.This run helps delineate which lensing discrepancies can be explained purely by CF geometry and angle offsets — and which require a new Fermat potential.