Dist Babble: Particle Zoo Updated.

TFP Unified Derivation

By John Gavel

Icosahedral Efficiency (Ψ): 0.939326
Fine Structure (α⁻¹): 137.0990
S_SCALE (Derived): 6.5691
Weak Mixing Angle (sin²θ_W): 0.231246

Mass Predictions

Name	Predicted	Actual	Unit	Accuracy
Electron	0.510998	0.511	MeV	99.999609%
Muon	103.850862	105.660	MeV	98.287774%
Tau	1716.076040	1776.800	MeV	96.582398%
ν_e	0.111088	0.110	eV	99.010848%
Proton	938.213872	938.270	MeV	99.994018%
Neutron	940.577131	939.560	MeV	99.891744%
Lambda	1129.097785	1115.600	MeV	98.790087%
Xi⁰	1401.994880	1314.860	MeV	93.373068%
Omega⁻	1670.818597	1672.400	MeV	99.905441%
Proton (flow law)	943.512262	938.270	MeV	99.441284%
W Boson	80.970044	80.380	GeV	99.265932%
Z Boson	95.185995	91.190	GeV	95.617946%

Bell Violation (CHSH, Pentagonal TFP)

Photon: 2.8240
Electron: 2.8240
Muon: 2.6780
Tau: 2.4488

Flavor Mixing (Cabibbo)

Predicted θ_C: 13.28°
Experimental: 13.04°
Accuracy: 98.14%

CKM Matrix Elements (TFP)

V_ud: 0.9732 (Exp: 0.973)
V_us: 0.2298 (Exp: 0.224)
V_ub: 0.0039 (Exp: 0.0036)

Python Code


import numpy as np
import pandas as pd

# ==========================================================
# HARDWARE: 132-geometry, golden ratio, icosahedral efficiency
# ==========================================================
M0  = 0.510998                 # electron mass (MeV)
K   = 12.0                     # coordination
H   = K * (K - 1)              # handshake budget = 132
F   = 20.0                     # faces
V   = 12.0                     # vertices
Phi = (1 + np.sqrt(5)) / 2     # golden ratio

# Icosahedral efficiency Psi
V_ICO = (5/12) * (3 + np.sqrt(5))
A_ICO = 5 * np.sqrt(3)
PSI   = (np.pi**(1/3) * (6 * V_ICO)**(2/3)) / A_ICO

# Simplex, parity, substrate tension
SIMPLEX = (F / V) * (3/4)
PARITY  = 1.0 - 1.0 / (2.0 * H)
OMEGA   = (H / K) * PSI / SIMPLEX

# ==========================================================
# UNIVERSAL FLOW / SCALING LAWS
# ==========================================================
# Fine structure constant
EFF_CAPACITY = (H * (K - 1)) / (K * PSI)
HOLONOMY     = (2 * np.pi) + Phi + Phi**-2
ALPHA_INV    = EFF_CAPACITY + HOLONOMY

# Lepton ladder parameters
S_SCALE = (H / F) * (1.0 - 1.0 / (H * Phi))

def lepton_mass(gen: int) -> float:
    """Lepton masses from M0 via geometric expansion/interference."""
    if gen == 1:
        return M0
    d = gen - 1
    expansion    = S_SCALE * d
    interference = (SIMPLEX / PARITY) * (d**2)
    return M0 * np.exp(expansion - interference)

def neutrino_mass_eV() -> float:
    """Electron neutrino mass scale (eV)."""
    return M0 * (1 / H)**2 * (1 / (2 * H)) * 1e6

# Weak mixing angle via pentagonal series
S_unstable = 2 + 2 * Phi
S_stable   = 2 / Phi
R          = S_unstable / S_stable
w          = np.sqrt(Phi)

def series_sum(H_val, S_u):
    total = 0.0
    for j in range(1, 100):
        phi_j = Phi**(-j)
        if phi_j < 1e-12:
            break
        total += phi_j / (1 + phi_j * H_val / S_u)
    return total

S_sum   = series_sum(H, S_unstable)
c_eff   = 2 * (R * w * S_sum)
sin2_W  = Phi**-3 * (1 - c_eff / H)

# ==========================================================
# BARYONS: geometric proton ratio + strange topology + tau tax
# ==========================================================
# Geometric proton-to-electron mass ratio (no empirical input)
XI_PROTON    = (H**2) * (K**2) / (F * (OMEGA**2))
PROTON_RATIO = XI_PROTON

def baryon_mass(n_u: int, n_d: int, n_s: int) -> float:
    """
    Baryon masses from:
      - route backbone (u,d,s costs)
      - geometric proton ratio
      - topology-aware strange cost
      - tau-mode recursion tax for s-s conflicts
    """
    u_cost = 1.0
    d_cost = 1.0 + 1.0 / H

    # Strange cost + conflict count by topology
    if (n_u, n_d, n_s) == (1, 1, 1):      # Lambda: isolated s
        s_cost    = Phi * (1 - 1/(2*H))
        conflicts = 0
    elif (n_u, n_d, n_s) == (1, 0, 2):    # Xi0: one s-s pair
        s_cost    = Phi + (K / H)
        conflicts = 1
    elif (n_u, n_d, n_s) == (0, 0, 3):    # Omega-: s-triangle
        s_cost    = Phi + (K / H)
        conflicts = 3
    else:
        s_cost    = 0.0
        conflicts = 0

    current_route = n_u * u_cost + n_d * d_cost + n_s * s_cost
    proton_route  = 2 * u_cost + 1 * d_cost

    base = M0 * PROTON_RATIO * (current_route / proton_route)

    if conflicts > 0:
        m_tau = lepton_mass(3)
        base += conflicts * (1.0 / (6.0 * K)) * m_tau

    return base

# ==========================================================
# CHSH / Bell violation (pentagonal TFP)
# ==========================================================
def chsh_tfp(gen: int) -> float:
    base = 2.0
    chi  = 2.0
    gap  = (F - K) / (K * Phi) * chi

    if gen == 0:  # photon
        return base + gap
    d = gen - 1
    interference   = (SIMPLEX / PARITY) * (d**2)
    generation_cost = interference / S_SCALE
    pent_factor     = 1 / (1 + d * (c_eff / H))
    available       = pent_factor / (1 + generation_cost)
    return base + gap * available

# ==========================================================
# W/Z FLOW LAW FROM SAME HARDWARE
# ==========================================================
BOSON_SCALE   = H * PSI * Phi
POWER_EXPONENT = (Phi**2) / 2.0

def flow_mass_N(N: float) -> float:
    """Mass in GeV from 132-flow squeezed through N active nodes."""
    return BOSON_SCALE / (N**POWER_EXPONENT)

def W_mass_GeV() -> float:
    return flow_mass_N(2.0)

def Z_mass_GeV() -> float:
    #return W_mass_GeV() * np.sqrt(1 + Phi**-2)
    # Synchronizes the Flow Law with the Pentagonal Series (sin2_W)
    return W_mass_GeV() / np.sqrt(1 - sin2_W)

def proton_flow_MeV() -> float:
    return flow_mass_N(60.0) * 1000.0

# ==========================================================
# CABIBBO, CKM
# ==========================================================
theta_c_rad = np.arctan(Phi**-3)
theta_c_deg = np.degrees(theta_c_rad)

Vud = np.cos(theta_c_rad)
Vus = np.sin(theta_c_rad)
Vub = (Phi**-12) * SIMPLEX

# ==========================================================
# RESULTS
# ==========================================================
rows = [
    ("Electron",      lepton_mass(1),        0.511,    "MeV"),
    ("Muon",          lepton_mass(2),      105.66,    "MeV"),
    ("Tau",           lepton_mass(3),     1776.80,    "MeV"),
    ("nu_e (eV)",     neutrino_mass_eV(),    0.11,    "eV"),
    ("Proton",        baryon_mass(2,1,0), 938.27,    "MeV"),
    ("Neutron",       baryon_mass(1,2,0), 939.56,    "MeV"),
    ("Lambda",        baryon_mass(1,1,1),1115.60,    "MeV"),
    ("Xi0",           baryon_mass(1,0,2),1314.86,    "MeV"),
    ("Omega-",        baryon_mass(0,0,3),1672.40,    "MeV"),
    ("Proton(flow)",  proton_flow_MeV(),   938.27,    "MeV"),
    ("W-Boson",       W_mass_GeV(),         80.38,    "GeV"),
    ("Z-Boson",       Z_mass_GeV(),         91.19,    "GeV"),
]

data = []
for name, pred, actual, unit in rows:
    acc = (1 - abs(pred - actual) / actual) * 100
    data.append((name, pred, actual, unit, acc))

df = pd.DataFrame(data, columns=["Name", "Pred", "Actual", "Unit", "Accuracy"])

print("=== TFP UNIFIED DERIVATION (SIMPLIFIED) ===")
print(f"Icosahedral Efficiency (Psi): {PSI:.6f}")
print(f"Fine Structure (alpha^-1):    {ALPHA_INV:.4f}")
print(f"S_SCALE (Derived):           {S_SCALE:.4f}")
print(f"Weak Mixing Angle (sin²θ_W): {sin2_W:.6f}")
print("-" * 65)
print(df.to_string(index=False))

print("\n=== BELL VIOLATION (CHSH, pentagonal TFP) ===")
for gen, name in enumerate(["Photon", "Electron", "Muon", "Tau"]):
    print(f"{name:8}: {chsh_tfp(gen):.4f}")

print(f"\n=== FLAVOR MIXING (CABIBBO) ===")
print(f"Predicted θ_C: {theta_c_deg:.2f}°  (Exp: 13.04°)")

print(f"\n=== CKM MATRIX ELEMENTS (TFP) ===")
print(f"Vud (Up-Down):    {Vud:.4f}  (Exp: 0.973)")
print(f"Vus (Up-Strange): {Vus:.4f}  (Exp: 0.224)")
print(f"Vub (Up-Bottom):  {Vub:.4f} (Exp: 0.0036)")

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Particle Zoo Updated.