Show HN: G=(hbar*c*2*(1+alpha/3)^2)/(m_p^2*4^64) ≈ 6.6742439706e-11 (8 ppm)

#!/usr/bin/env python3 """ GEOMETRIC DERIVATION OF G & VALIDATION WITH GR This script tests the hypothesis that G is a derivative artifact of the proton's holographic scaling (i=32). Reference Paper: https://doi.org/10.5281/zenodo.17847770 """ import math # 1. CONSTANTS (CODATA 2022) c = 299792458.0 # m/s hbar = 1.054571817e-34 # J s alpha = 7.2973525643e-3 # Fine-structure mp_kg = 1.67262192595e-27 # Proton mass me_kg = 9.1093837139e-31 # Electron mass G_codata = 6.67430e-11 # Empirical G (for validation) # Derived Planck Mass (Standard) for consistency check mP_std = math.sqrt(hbar * c / G_codata) def compute_acceleration(name, mass, topo_n, radius): # PHASE 1: DYNAMIC VALIDATION # Goal: Recover Schwarzschild metric using geometric projections. w = 2.0 # Structural limit # Linear Mass projection (Source) L_src = (mass * hbar) / (c * mP_std**2) # Structural Limit (Horizon) - Equivalent to Schwarzschild radius L_lim = w * L_src # Electrostatic projection if topo_n != 0: lambda_e = hbar / (me_kg * c) Le = alpha * abs(topo_n) * lambda_e L_src += Le # The Unified Geometric Metric if radius <= L_lim: return {"name": name, "stat": "HORIZON", "val": 0, "gr": 0} # Hypotenuse form: ai = c^2 * L / (r^2 * sqrt(1 - 2L/r)) metric_factor = math.sqrt(1.0 - L_lim / radius) ai_unified = (c**2 * L_src) / (radius**2 * metric_factor) # GR Benchmark (Schwarzschild) rs = 2 * G_codata * mass / c**2 acc_newton = (G_codata * mass) / (radius**2) acc_coulomb = 0.0 if topo_n != 0: acc_coulomb = (8.98755e9 * 1.60217e-19**2) / (radius**2 * me_kg) if radius <= rs: ai_gr = float('inf') else: ai_gr = (acc_newton / math.sqrt(1.0 - rs/radius)) + acc_coulomb return {"name": name, "stat": "OK", "val": ai_unified, "gr": ai_gr} def derive_closed_G(): # PHASE 2: HOLOGRAPHIC DERIVATION # Hypothesis: mp scales from mP at i=32 (4^32 surface scaling) # mp = (sqrt(2) * mP / 4^32) * (1 + alpha/3) geometry = math.sqrt(2) * (1 + alpha/3) mP_geo = (mp_kg * 4**32) / geometry # G = hbar * c / mP^2 return (hbar * c) / (mP_geo**2) # EXECUTION objects = [ {"n": "Electron", "m": me_kg, "q": 1, "r": 1e-10}, {"n": "Proton", "m": mp_kg, "q": 1, "r": 1e-10}, {"n": "Earth", "m": 5.972e24, "q": 0, "r": 6.371e6}, {"n": "Sun", "m": 1.989e30, "q": 0, "r": 6.963e8}, {"n": "Neutron Star", "m": 4.14e30, "q": 0, "r": 12000}, {"n": "Sgr A* (Lim)", "m": 8.26e36, "q": 0, "r": 1.23e10} ] print(f"{'OBJECT':<12}| {'UNIFIED':<18}| {'GR':<18}| {'DIFF %'}") print("-" * 65) for obj in objects: res = compute_acceleration(obj['n'], obj['m'], obj['q'], obj['r']) if res['stat'] == 'HORIZON': print(f"{res['name']:<12}| {'SATURATION':<18}| {'HORIZON':<18}| {'MATCH'}") else: diff = abs(res['val'] - res['gr']) / res['gr'] * 100 if diff < 1e-9: diff = 0.0 # Formatting with .5e to verify consistency print(f"{res['name']:<12}| {res['val']:<18.5e}| {res['gr']:<18.5e}| {diff:.8f}") print("-" * 65) print("\nPHASE 2: G DERIVATION") G_calc = derive_closed_G() disc = abs(G_calc - G_codata) / G_codata * 1e6 print(f"Formula: G = (hbar * c * 2 * (1 + alpha/3)^2) / (mp^2 * 4^64)") print(f"Derived G: {G_calc:.11e}") print(f"CODATA G: {G_codata:.11e}") print(f"Diff: {disc:.2f} ppm (within 22 ppm uncertainty)")