Phase 7: Directional Weak Lensing as a Falsifiable Test of Conserved Entropic Gravity

This upload presents Phase 7 of the emergent gravity framework based on a conserved total entropy action. Phase 7 proposes a decisive, falsifiable observational test that distinguishes the entropic gravity model from cold dark matter (CDM) and MOND-like theories.Key elements:The entropic component of gravity produces a directional stress tensor aligned with baryonic acceleration gradients:T_ent_ij ∝ (g_i g_j) / a0where g = -grad(Phi) is the baryonic acceleration and a0 is the entropic acceleration scale.This directional stress induces a quadrupolar modulation in weak lensing shear around low-surface-brightness dwarf galaxies:gamma(theta) = gamma_0(r) * [1 + epsilon * cos(2*theta)]with epsilon ≈ g_ent / g_tot ≈ 0.1 - 0.3.An observable anisotropy estimator is defined:A = / Predictions:Conserved entropic gravity: A ≈ 0.1 - 0.3CDM and MOND: A ≈ 0Falsification criteria:If observed anisotropy is absent or uncorrelated with baryonic acceleration direction, the theory is decisively ruled out.This test is feasible with existing survey data: Hyper Suprime-Cam (HSC), Dark Energy Survey (DES), CFHTLenS, and future Euclid releases.Phase 7 converts the previously phenomenological framework into a testable, predictive scientific theory, providing a clean observational path to verify or falsify entropic gravity at galactic scales.