validation.py

#!/usr/bin/env python3
"""
GEOMETRIC STANDARD MODEL – NUMERICAL VALIDATION

Author: Timothy McGirl
Email: grapheneaffiliates@gmail.com

Verifies that closed-form geometric formulas reproduce
experimental values within stated uncertainties.

All constants derived from:
- Exceptional Lie algebras (G₂, F₄, E₆, E₇, E₈)
- Golden ratio powers (φ, φ², φ³, φ⁻¹)
- No continuous free parameters are fitted
"""

import math

# ==============================================================================
# MATHEMATICAL CONSTANTS
# ==============================================================================

PHI = (1 + math.sqrt(5.0)) / 2.0  # Golden ratio

# ==============================================================================
# LIE ALGEBRA DATA
# ==============================================================================

# G₂: Automorphism group of octonions
DIM_G2, RANK_G2, ROOTS_G2 = 14, 2, 12

# F₄: Isometry group of octonionic projective plane  
DIM_F4, RANK_F4, ROOTS_F4 = 52, 4, 48

# E₆, E₇, E₈: Exceptional Lie groups
DIM_E6, RANK_E6, ROOTS_E6 = 78, 6, 72
DIM_E7, RANK_E7, ROOTS_E7 = 133, 7, 126
DIM_E8, RANK_E8, ROOTS_E8 = 248, 8, 240

# ==============================================================================
# EXPERIMENTAL VALUES (CODATA 2022 / PDG)
# ==============================================================================

ALPHA_INV_EXP = 137.035999177      # Fine structure constant inverse
SIGMA_ALPHA_INV = 2.1e-8           # Uncertainty

MU_EXP = 1836.152673426            # Proton/electron mass ratio
SIGMA_MU = 3.2e-8                  # From 1836.152673426(32)

MTAU_ME_EXP = 3477.23              # Tau/electron mass ratio
SIGMA_MTAU = 0.23                  # From 3477.23(23)

MMU_ME_EXP = 206.7682827           # Muon/electron mass ratio
SIGMA_MMU = 4.6e-6                 # From 206.7682827(46)

ZETA_G1_EXP = 84e-6                # Vacuum coupling (Tate 1989)
SIGMA_ZETA_G1 = 12e-6              # 84 ± 12 ppm

# ==============================================================================
# GEOMETRIC MODEL FORMULAS
# ==============================================================================

def solve_alpha_inv(max_iter: int = 20) -> float:
    """
    Self-consistent solution of:
        α⁻¹ = 137 + φ/45 + α/170 - α²/895
    
    Denominators:
        45  = roots(F₄) - 3
        170 = (rank(G₂) + rank(E₈)) × (dim(G₂) + 3)
        895 = dim(E₇) × rank(E₇) - 3 × roots(G₂)
    """
    denom_1 = ROOTS_F4 - 3                              # 45
    denom_2 = (RANK_G2 + RANK_E8) * (DIM_G2 + 3)       # 170
    denom_3 = DIM_E7 * RANK_E7 - 3 * ROOTS_G2          # 895

    x = 137.0
    for _ in range(max_iter):
        a = 1.0 / x
        x = 137.0 + PHI / denom_1 + a / denom_2 - a * a / denom_3
    return x


def mu_pred(alpha: float) -> float:
    """
    Proton/electron mass ratio:
        μ = 1836 + φ²/17 - φ²/1970 + α/19344
    
    Denominators:
        17    = dim(G₂) + 3
        1970  = dim(E₈) × rank(E₈) - dim(G₂)
        19344 = dim(E₈) × dim(E₆)
    """
    phi2 = PHI * PHI
    denom_1 = DIM_G2 + 3                               # 17
    denom_2 = DIM_E8 * RANK_E8 - DIM_G2                # 1970
    denom_3 = DIM_E8 * DIM_E6                          # 19344
    
    return 1836.0 + phi2 / denom_1 - phi2 / denom_2 + alpha / denom_3


def m_tau_over_me_pred() -> float:
    """
    Tau/electron mass ratio:
        mτ/me = 3472 + 2φ²
    
    Uses identity φ³ + 1 = 2φ², where 2 = rank(G₂)
    """
    return 3472.0 + RANK_G2 * (PHI * PHI)


def m_mu_over_me_pred() -> float:
    """
    Muon/electron mass ratio:
        mμ/me = 211 - φ³ + φ⁻¹/142
    
    Denominator:
        142 = roots(E₇) + dim(G₂) + rank(G₂)
    """
    phi3 = PHI ** 3
    phi_inv = 1.0 / PHI
    denom = ROOTS_E7 + DIM_G2 + RANK_G2                # 142
    
    return 211.0 - phi3 + phi_inv / denom


def zeta_pred(alpha: float, g: int) -> float:
    """
    Vacuum coupling constant with genus scaling:
        ζ = φ × α²  (base value, corresponds to g=1 torus)
        ζ(g) = ζ₀ × (φ³)^(g-1)  for g ≥ 1
    
    g=1 (torus): ζ = φα² ≈ 86 ppm
    g=2 (figure-8): ζ = φα² × φ³ ≈ 365 ppm
    """
    zeta_base = PHI * alpha * alpha  # ~86 ppm
    return zeta_base * (PHI ** (3 * (g - 1)))


# ==============================================================================
# VALIDATION
# ==============================================================================

def sigma_deviation(pred: float, exp: float, sigma: float) -> float:
    """Calculate σ-deviation between prediction and experiment."""
    return abs(pred - exp) / sigma


def main():
    # Solve for α (self-consistent)
    alpha_inv_model = solve_alpha_inv()
    alpha_model = 1.0 / alpha_inv_model

    print("=" * 72)
    print("GEOMETRIC STANDARD MODEL – NUMERICAL VALIDATION")
    print("=" * 72)
    print()
    
    # Fine structure constant
    print("FINE STRUCTURE CONSTANT (α⁻¹)")
    print(f"  Formula: 137 + φ/45 + α/170 - α²/895")
    print(f"  Model:   {alpha_inv_model:.12f}")
    print(f"  CODATA:  {ALPHA_INV_EXP:.12f}")
    print(f"  Δ:       {alpha_inv_model - ALPHA_INV_EXP:+.3e}")
    print(f"  σ:       {sigma_deviation(alpha_inv_model, ALPHA_INV_EXP, SIGMA_ALPHA_INV):.4f}σ ✓")
    print()

    # Proton mass ratio
    mu_model = mu_pred(alpha_model)
    print("PROTON/ELECTRON MASS RATIO (μ)")
    print(f"  Formula: 1836 + φ²/17 - φ²/1970 + α/19344")
    print(f"  Model:   {mu_model:.12f}")
    print(f"  CODATA:  {MU_EXP:.12f}")
    print(f"  Δ:       {mu_model - MU_EXP:+.3e}")
    print(f"  σ:       {sigma_deviation(mu_model, MU_EXP, SIGMA_MU):.4f}σ ✓")
    print()

    # Tau mass ratio
    mtau_model = m_tau_over_me_pred()
    print("TAU/ELECTRON MASS RATIO (mτ/me)")
    print(f"  Formula: 3472 + 2φ²")
    print(f"  Model:   {mtau_model:.9f}")
    print(f"  CODATA:  {MTAU_ME_EXP:.9f}")
    print(f"  Δ:       {mtau_model - MTAU_ME_EXP:+.3e}")
    print(f"  σ:       {sigma_deviation(mtau_model, MTAU_ME_EXP, SIGMA_MTAU):.4f}σ ✓")
    print()

    # Muon mass ratio
    mmu_model = m_mu_over_me_pred()
    print("MUON/ELECTRON MASS RATIO (mμ/me)")
    print(f"  Formula: 211 - φ³ + φ⁻¹/142")
    print(f"  Model:   {mmu_model:.9f}")
    print(f"  CODATA:  {MMU_ME_EXP:.9f}")
    print(f"  Δ:       {mmu_model - MMU_ME_EXP:+.3e}")
    print(f"  σ:       {sigma_deviation(mmu_model, MMU_ME_EXP, SIGMA_MMU):.4f}σ ✓")
    print()

    # Vacuum coupling
    zeta_g1_model = zeta_pred(alpha_model, g=1)
    zeta_g2_model = zeta_pred(alpha_model, g=2)
    
    print("VACUUM COUPLING (ζ)")
    print(f"  Formula: ζ = φα², ζ(g) = ζ₀ × (φ³)^(g-1)")
    print(f"  ζ(g=1):  {zeta_g1_model*1e6:.2f} ppm")
    print(f"  Tate:    {ZETA_G1_EXP*1e6:.2f} ppm")
    print(f"  σ:       {sigma_deviation(zeta_g1_model, ZETA_G1_EXP, SIGMA_ZETA_G1):.4f}σ ✓")
    print()
    print(f"  ζ(g=2):  {zeta_g2_model*1e6:.2f} ppm  ← DECISIVE TEST PENDING")
    print()

    # Summary
    print("=" * 72)
    print("SUMMARY: Five measured constants within experimental uncertainty")
    print("         Sixth prediction ζ(g=2) awaits experimental test")
    print("=" * 72)
    print()
    print("  Constant   Prediction          Measured             σ-dev")
    print("  ────────   ──────────          ────────             ─────")
    print(f"  α⁻¹       {alpha_inv_model:.9f}      {ALPHA_INV_EXP:.9f}      {sigma_deviation(alpha_inv_model, ALPHA_INV_EXP, SIGMA_ALPHA_INV):.2f}σ ✓")
    print(f"  μ          {mu_model:.9f}     {MU_EXP:.9f}     {sigma_deviation(mu_model, MU_EXP, SIGMA_MU):.2f}σ ✓")
    print(f"  mτ/me      {mtau_model:.6f}         {MTAU_ME_EXP:.6f}         {sigma_deviation(mtau_model, MTAU_ME_EXP, SIGMA_MTAU):.2f}σ ✓")
    print(f"  mμ/me      {mmu_model:.7f}        {MMU_ME_EXP:.7f}        {sigma_deviation(mmu_model, MMU_ME_EXP, SIGMA_MMU):.2f}σ ✓")
    print(f"  ζ(g=1)     {zeta_g1_model*1e6:.1f} ppm            {ZETA_G1_EXP*1e6:.1f} ppm            {sigma_deviation(zeta_g1_model, ZETA_G1_EXP, SIGMA_ZETA_G1):.2f}σ ✓")
    print(f"  ζ(g=2)     {zeta_g2_model*1e6:.1f} ppm            ???                 PENDING")
    print()
    print("=" * 72)


if __name__ == "__main__":
    main()