#!/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)")