Phase 5: Falsifiable Galactic Weak-Field Predictions from Entropic Gravity

This dataset and notebook accompany Phase 5 of the Entropic Gravity project. Phase 5 extends the previously developed conserved total entropy S_tot framework to weak-field, linearized relativistic regimes, producing testable predictions for galaxies without invoking full General Relativity or dark matter.Contents:Python Notebook (Phase5_Figure1.ipynb)Computes the entropic acceleration fraction f_ent for different galaxy types: dwarf, Milky Way bulge, and large spiral.Computes corresponding PPN gamma values:gamma_PPN = 1 - 0.5 * f_ent (weak-field linearized metric)Figure 1 (Figure1_gent_fraction_final.png) for inclusion in publications.Figure 1Bar chart of f_ent per galaxyLine overlay of gamma_PPNVisualizes contribution of entropic gravity to galactic rotation curves.MethodologyLinearized expansion of the entropic scalar action:ln(1 - g / a0) ≈ -g / a0 - 0.5 * (g / a0)^2 + higher order termsFirst-order entropic acceleration:g_ent ≈ - (a0 / rho_Q) * gradient(rho_Q)Weak-field Einstein equations extended with entropic energy-momentum tensor:box(h_bar_mu_nu) = -16 * pi * G * (T_mu_nu_matter + tau_mu_nu_ent),with tau_mu_nu_ent ~ rho_Q * g / a0.Falsifiability and LimitsLinear approximation valid for galactic accelerations g