TFP Updated Zoo
By John Gavel
==================================================================================================================================== TEMPORAL FLOW PHYSICS — PARTICLE ZOO (v12.10) Single empirical anchor: proton mass = 938.272 MeV Zero free parameters beyond K=12 icosahedral geometry ==================================================================================================================================== ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── LEPTON SECTOR ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── Particle Content Charge Spin TFP Pred Measured Unit % Error Accuracy % ────────── ────── ─────── ───── ────────────── ────────────── ───── ────────── ─────────── Electron -1.00 0.5 0.5108 0.5110 MeV -0.0390 99.961% Muon -1.00 0.5 105.7072 105.6600 MeV +0.0446 99.955% Tau -1.00 0.5 1780.4978 1776.8600 MeV +0.2047 99.795% nu_e 0.00 0.5 0.1110 0.1100 eV +0.9501 99.050% ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── BARYON SECTOR ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── Particle Content Charge Spin TFP Pred Measured Unit % Error Accuracy % ────────── ────── ─────── ───── ────────────── ────────────── ───── ────────── ─────────── Proton uud 1.00 0.5 938.2720 938.2720 MeV +0.0000 100.000% Neutron udd 0.00 0.5 940.6354 939.5650 MeV +0.1139 99.886% Lambda uds 0.00 0.5 1115.1993 1115.6830 MeV -0.0434 99.957% Xi0 uss 0.00 0.5 1317.7001 1314.8600 MeV +0.2160 99.784% Omega- sss -1.00 0.5 1671.9427 1672.4500 MeV -0.0303 99.970% ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── MESON SECTOR ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── Particle Content Charge Spin TFP Pred Measured Unit % Error Accuracy % ────────── ────── ─────── ───── ────────────── ────────────── ───── ────────── ─────────── pi+ ud̄ 1.00 0.0 139.8693 139.5700 MeV +0.2145 99.786% K+ us̄ 1.00 0.0 495.8487 493.6770 MeV +0.4399 99.560% rho+ ud̄ 1.00 1.0 759.0780 775.1100 MeV -2.0684 97.932% K*+ us̄ 1.00 1.0 896.9987 891.6700 MeV +0.5976 99.402% ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── BOSON SECTOR ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── Particle Content Charge Spin TFP Pred Measured Unit % Error Accuracy % ────────── ────── ─────── ───── ────────────── ────────────── ───── ────────── ─────────── W+ 1.00 1.0 80.6633 80.3770 GeV +0.3562 99.644% Z0 0.00 1.0 91.4753 91.1880 GeV +0.3150 99.685% H0 0.00 0.0 125.3963 125.2000 GeV +0.1568 99.843% ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── SUMMARY STATISTICS ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── Particles predicted: 16 Mean accuracy: 99.638% Predictions >= 99.0%: 15 / 16 Best prediction: Proton 100.0000% Worst prediction: rho+ 97.9316% ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── DERIVED GEOMETRIC CONSTANTS (all from K=12, zero free parameters) ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── K (coordination number) 12 H (handshake budget K(K-1)) 132 F (icosahedral faces) 20 Psi_sph (isoperimetric closure) 0.939326 delta (non-spatializable fraction) 0.060674 SIMPLEX (F/V x D/pi3) 1.250000 phi_1 (golden ratio) 1.618034 phi_3 = phi_1/2 0.809017 mu_2 = sqrt(5) (T1 adj. eigenval) 2.236068 pi_eff(12) = 3(sqrt6 - sqrt2) 3.105829 Delta_pi = pi_eff(12) - pi2 0.105829 BOSON_SCALE = H x Psi x phi1 200.621630 OMEGA_OBJ (p/e mass ratio) 1836.0422 (measured 1836.153, acc 99.994%) omega_routing = H*Psi/(K*SIMPLEX) 8.266066 route_p = 2u + d 3.0075758 route_e = (1+2/H)/620 0.0016373 Lepton denominator 4x155 620 E_total (lepton ladder) 17.0 delta(e->mu) +0.081292 delta(mu->tau) -0.131533 E_mu exponent 11.081292 E_step exponent 5.868467 tau_W = phi1^2/2 1.309017 tau_Z = pi2+(K-1)/H+Dpi/phi1^2 3.123756 sin^2(theta_W) = phi1^(-tau_Z) 0.222420 (measured 0.22306, acc 99.713%) D_seq (Higgs base) 1.615052 D_H (Higgs denominator) 1.599901 ====================================================================================================================================
Python Code
import numpy as np
import pandas as pd
# ============================================================
# TEMPORAL FLOW PHYSICS — PARTICLE ZOO SIMULATION
# Version: v12.10 (corrected Psi_sph, corrected boson chain)
#
# Single empirical anchor: proton mass = 938.272 MeV
# Zero free parameters beyond substrate geometry
#
# Key correction vs earlier versions:
# Psi_sph = 0.93933 (reduced isoperimetric formula, §3.5.4)
# Previous versions used Psi_sph ~ 0.93647 (wrong formula)
# This shifts M_W: 80.418 -> 80.663 GeV
# M_Z: 91.196 -> 91.475 GeV
#
# Boson derivation chain (§4.10):
# tau_W -> M_W directly (base 2, two-level count)
# tau_Z -> sin2_thetaW -> M_Z from M_W via mixing
# tau_Z does NOT give M_Z directly from BOSON_SCALE
# ============================================================
# ============================================================
# SECTION 1: SUBSTRATE CONSTANTS (§3.3, §3.5, §3.6, §3.9)
# ============================================================
K = 12.0 # coordination number
V = K # icosahedral vertices = K
H = K * (K - 1) # handshake budget = 132
F = 20.0 # icosahedral faces
E = 30.0 # icosahedral edges
D = 3.0 # spatial dimensions
pi2 = 3.0 # 2D simplex closure constant
pi3 = 4.0 # 3D simplex closure constant
Phi = (1.0 + np.sqrt(5)) / 2.0 # golden ratio phi_1 = 1.618034
phi3 = Phi / 2.0 # 3D coupling phi_3 = phi_1/2 = 0.809017
mu2 = np.sqrt(5.0) # T1 adjacency eigenvalue (§3.5.1)
# Laplacian eigenvalues (§3.5.2)
lambda1 = 5.0 - np.sqrt(5.0) # T1 gravity = 2.7639
lambda2 = 6.0 # H electromagnetism
lambda3 = 5.0 + np.sqrt(5.0) # T2 strong/weak = 7.2361
# Icosahedral isoperimetric ratio Psi_sph (§3.5.4)
# Reduced formula: pi^(1/3) * (6V)^(2/3) / A
# Uses unit-edge icosahedral volume and surface area
VOL_ICO = (5.0/12.0) * (3.0 + np.sqrt(5.0)) # unit-edge volume
AREA_ICO = 5.0 * np.sqrt(3.0) # unit-edge surface area
PSI = (np.pi**(1.0/3.0) * (6.0 * VOL_ICO)**(2.0/3.0)) / AREA_ICO
delta = 1.0 - PSI # non-spatializable fraction
# SIMPLEX = (F/V) x (D/pi3) = (20/12) x (3/4) = 5/4 (§3.9)
SIMPLEX = (F / V) * (D / pi3)
# Shell closure constant pi_eff(12) = 3(sqrt(6) - sqrt(2)) (§3.7)
pi_eff_12 = 3.0 * (np.sqrt(6.0) - np.sqrt(2.0))
Delta_pi = pi_eff_12 - pi2 # = 0.105829
# Routing phase parameter omega (§4.7)
omega_routing = H * PSI / (K * SIMPLEX) # = 8.26607
# Proton-electron mass ratio OMEGA_OBJ (§4.7, §5.2.3)
# Derived from H, K, F, Psi_sph alone — zero free parameters
OMEGA_OBJ = (H**2 * K**2) / (F * omega_routing**2) # = 1836.04
# Boson scale (§4.10)
BOSON_SCALE = H * PSI * Phi # = 200.622
# ============================================================
# SECTION 2: EMPIRICAL ANCHOR
# ============================================================
M_P = 938.272 # MeV — proton mass, single empirical input (§5.2.2)
# ============================================================
# SECTION 3: ROUTING COSTS (§4.5, §4.7)
# ============================================================
U_COST = 1.0 # CW helix, direct adjacency
D_COST = 1.0 + 1.0/H # CCW helix, parity residual +1/H
S_COST = Phi * (1.0 - 1.0/(2.0*H)) # strange quark, phi1 routing level
route_p = 2.0*U_COST + D_COST # proton route = 3 + 1/H
# Parity correction factor
PARITY = 1.0 - 1.0/(2.0*H) # = 1 - 1/264
# Shared-edge parity correction for Lambda (§4.7)
EPSILON_LAMBDA = 1.0 / (pi2 * K) # = 1/36
# ============================================================
# SECTION 4: LEPTON MASSES (§4L)
# ============================================================
# --- Electron ---
# Extended-shell four-orbit formula (§4L.3, §4L.4)
# Denominator = pi3 x (K(K+1) - 1) = 4 x 155 = 620
# Derivation: 2-tick winding period requires central-site engagement
# K(K+1)-1 = H + (2K-1) = 132 + 23 = 155 per orbit
# pi3 = 4 orbits from relay residue closure (§4L.3)
extended_shell_pairs = K * (K + 1.0) - 1.0 # = 155
lepton_denom = pi3 * extended_shell_pairs # = 620
route_e = (1.0 + 2.0/H) / lepton_denom # = 0.0016373
M_E = route_e * M_P / route_p
# --- Generation ladder exponents (§4L.5) ---
# e->mu: K-1 = 11 (T2 axial, self-exclusion count)
# mu->tau: K/2 = 6 (H EM Laplacian eigenvalue)
E_total = (K - 1.0) + K/2.0 # = 17
# Routing hierarchy corrections (§3.11.3, §4L.6)
# delta(e->mu): site B, DIFFER condition, phi1-suppressed
# delta(mu->tau): terminal C, AGREE condition, full magnitude
# Correction magnitude = mu2 = sqrt(5) (T1 adjacency eigenvalue, §3.5.1)
delta_emu = +mu2 / (Phi * E_total) # = +sqrt(5)/(phi1 x 17) = +0.081293
delta_mutau = -mu2 / E_total # = -sqrt(5)/17 = -0.131533
E_mu_exp = (K - 1.0) + delta_emu # = 11.081293
E_step_exp = (K/2.0) + delta_mutau # = 5.868467
M_MU = M_E * Phi**E_mu_exp
M_TAU = M_MU * Phi**E_step_exp
# --- Neutrino mass scale (§4L.7) ---
M_NUE_EV = M_E * (1.0/H)**2 * (1.0/(2.0*H)) * 1.0e6 # eV
# ============================================================
# SECTION 5: BARYON MASSES (§4.7)
# ============================================================
def baryon_mass(n_u, n_d, n_s):
"""
Baryon mass (MeV) from routing costs and proton anchor.
M = M_p x route / route_p
"""
if (n_u, n_d, n_s) == (2, 1, 0): # Proton (uud)
route = 2.0*U_COST + D_COST
elif (n_u, n_d, n_s) == (1, 2, 0): # Neutron (udd)
route = U_COST + 2.0*D_COST
elif (n_u, n_d, n_s) == (1, 1, 1): # Lambda (uds)
s_eff = S_COST * (1.0 - EPSILON_LAMBDA)
route = U_COST + D_COST + s_eff
elif (n_u, n_d, n_s) == (1, 0, 2): # Xi0 (uss)
route = U_COST + 2.0*S_COST
elif (n_u, n_d, n_s) == (0, 0, 3): # Omega- (sss)
spin_align = 2.0*np.pi / K # spin-3/2 alignment cost (§4.6.3)
route = 3.0*S_COST + spin_align
else:
raise ValueError(f"Unsupported quark content (u={n_u}, d={n_d}, s={n_s})")
return M_P * route / route_p
# ============================================================
# SECTION 6: MESON MASSES (§4.8)
# ============================================================
# Pion: dual suppression by pi2 and mu2 (§4.8.2)
# M_pi = M_p / (pi2 x mu2)
M_PI = M_P / (pi2 * mu2)
# Kaon: strange quark extension with phi3 = phi1/2 (§4.8.3)
# M_K = M_pi x phi1 x (pi2 - phi3)
M_K = M_PI * Phi * (pi2 - phi3)
# Vector mesons: phi3 alignment factor (§4.8.4)
# rho: M_rho = M_p x phi3
# K*: M_K* = M_K x (1 + phi3)
M_RHO = M_P * phi3
M_KST = M_K * (1.0 + phi3)
# ============================================================
# SECTION 7: BOSON MASSES (§4.10)
# ============================================================
# --- W boson (§4.10.1) ---
# tau_W = phi1^2/2 (two levels compound via Fibonacci identity phi1^2=phi1+1)
# Base = 2 (two-level count, NOT phi1 which is the per-level suppression ratio)
# Correction: global parity factor x(1-1/(2H)) — W holds definite winding
tau_W = Phi**2 / 2.0 # = 1.309017
M_W = (BOSON_SCALE / (2.0**tau_W)) * PARITY # GeV
# --- Z boson (§4.10.1a, §4.10.1c) ---
# Three-layer tau_Z = pi2 + (K-1)/H + Delta_pi/phi1^2 = 3.123756
# tau_Z gives sin^2(theta_W), NOT M_Z directly
# M_Z = M_W / sqrt(1 - sin^2(theta_W)) [electroweak mass relation]
tau_Z = pi2 + (K - 1.0)/H + Delta_pi/Phi**2 # = 3.123756
sin2_thetaW = Phi**(-tau_Z) # = 0.22242
M_Z = M_W / np.sqrt(1.0 - sin2_thetaW) # GeV
# --- Higgs boson (§4.10.2) ---
# Spin-0: isotropic routing across all pi2=3 helix positions
# D_seq = pi2^(phi1^2/(2*pi2))
# D_H = D_seq - 2/H (C->A non-adjacent correction, AGREE case)
# M_H = BOSON_SCALE / D_H
D_seq = pi2**(Phi**2 / (2.0*pi2)) # = 1.615052
D_H = D_seq - 2.0/H # = 1.599901
M_H = BOSON_SCALE / D_H # GeV
# ============================================================
# SECTION 8: QUANTUM NUMBERS (§4.6)
# ============================================================
def quark_charge(winding):
"""Charge from spinor/winding period ratio (§4.6.1)"""
if winding == "CW":
return +2.0/3.0 # up-type
elif winding == "CCW":
return -1.0/3.0 # down-type
return 0.0
def particle_charge(name):
table = {
"Electron": -1.0, "Muon": -1.0, "Tau": -1.0,
"nu_e": 0.0,
"pi+": +1.0, "K+": +1.0,
"rho+": +1.0, "K*+": +1.0,
"W+": +1.0, "Z0": 0.0, "H0": 0.0,
}
if name in table:
return table[name]
quark_map = {
"Proton": (2,1,0), "Neutron": (1,2,0),
"Lambda": (1,1,1), "Xi0": (1,0,2),
"Omega-": (0,0,3),
}
if name in quark_map:
n_u, n_d, n_s = quark_map[name]
return (n_u * quark_charge("CW")
+ (n_d + n_s) * quark_charge("CCW"))
return 0.0
def particle_spin(name):
if name in ["W+", "Z0"]:
return 1.0
if name in ["H0", "pi+", "K+"]:
return 0.0
if name in ["rho+", "K*+"]:
return 1.0
return 0.5 # leptons and baryons
# ============================================================
# SANITY CHECKS
# ============================================================
assert abs(particle_charge("Proton") - (+1.0)) < 1e-12
assert abs(particle_charge("Neutron") - ( 0.0)) < 1e-12
assert abs(particle_charge("Lambda") - ( 0.0)) < 1e-12
assert abs(particle_charge("Xi0") - ( 0.0)) < 1e-12
assert abs(particle_charge("Omega-") - (-1.0)) < 1e-12
# ============================================================
# SECTION 9: RESULTS TABLE
# ============================================================
# (name, sector, predicted_MeV_or_GeV, measured, unit, quark_content)
particles = [
# LEPTONS
("Electron", "Lepton", M_E, 0.51100, "MeV", ""),
("Muon", "Lepton", M_MU, 105.66000, "MeV", ""),
("Tau", "Lepton", M_TAU, 1776.86000, "MeV", ""),
("nu_e", "Lepton", M_NUE_EV, 0.11000, "eV", ""),
# BARYONS
("Proton", "Baryon", baryon_mass(2,1,0), 938.272, "MeV", "uud"),
("Neutron", "Baryon", baryon_mass(1,2,0), 939.565, "MeV", "udd"),
("Lambda", "Baryon", baryon_mass(1,1,1), 1115.683, "MeV", "uds"),
("Xi0", "Baryon", baryon_mass(1,0,2), 1314.860, "MeV", "uss"),
("Omega-", "Baryon", baryon_mass(0,0,3), 1672.450, "MeV", "sss"),
# MESONS
("pi+", "Meson", M_PI, 139.570, "MeV", "ud̄"),
("K+", "Meson", M_K, 493.677, "MeV", "us̄"),
("rho+", "Meson", M_RHO, 775.110, "MeV", "ud̄"),
("K*+", "Meson", M_KST, 891.670, "MeV", "us̄"),
# BOSONS
("W+", "Boson", M_W, 80.377, "GeV", ""),
("Z0", "Boson", M_Z, 91.188, "GeV", ""),
("H0", "Boson", M_H, 125.200, "GeV", ""),
]
rows = []
for name, sector, pred, meas, unit, content in particles:
pct_error = (pred - meas) / meas * 100.0
accuracy = 100.0 - abs(pct_error)
charge = particle_charge(name)
spin = particle_spin(name)
rows.append((
name, sector, content,
charge, spin,
pred, meas, unit,
pct_error, accuracy
))
df = pd.DataFrame(rows, columns=[
"Particle", "Sector", "Content",
"Charge", "Spin",
"TFP Pred", "Measured", "Unit",
"% Error", "Accuracy %"
])
# ============================================================
# SECTION 10: FORMATTED OUTPUT
# ============================================================
W = 132 # print width
print()
print("=" * W)
print(" TEMPORAL FLOW PHYSICS — PARTICLE ZOO (v12.10)")
print(" Single empirical anchor: proton mass = 938.272 MeV")
print(" Zero free parameters beyond K=12 icosahedral geometry")
print("=" * W)
for sector in ["Lepton", "Baryon", "Meson", "Boson"]:
sub = df[df["Sector"] == sector].copy()
print(f"\n{'─'*W}")
print(f" {sector.upper()} SECTOR")
print(f"{'─'*W}")
print(f" {'Particle':<12 harge="" ontent="">7} {'Spin':>5} "
f"{'TFP Pred':>14} {'Measured':>14} {'Unit':<5 error="" f="">10} {'Accuracy %':>11}")
print(f" {'─'*10} {'─'*6} {'─'*7} {'─'*5} "
f"{'─'*14} {'─'*14} {'─'*5} "
f"{'─'*10} {'─'*11}")
for _, r in sub.iterrows():
print(f" {r['Particle']:<12 f="" harge="" ontent="" r="">7.2f} {r['Spin']:>5.1f} "
f"{r['TFP Pred']:>14.4f} {r['Measured']:>14.4f} "
f"{r['Unit']:<5 error="" f="" r="">+10.4f} {r['Accuracy %']:>10.3f}%")
# Summary statistics
print(f"\n{'─'*W}")
print(" SUMMARY STATISTICS")
print(f"{'─'*W}")
mean_acc = df["Accuracy %"].mean()
worst = df.loc[df["Accuracy %"].idxmin()]
best = df.loc[df["Accuracy %"].idxmax()]
above99 = (df["Accuracy %"] >= 99.0).sum()
print(f" Particles predicted: {len(df)}")
print(f" Mean accuracy: {mean_acc:.3f}%")
print(f" Predictions >= 99.0%: {above99} / {len(df)}")
print(f" Best prediction: {best['Particle']:<12 -="" 1836.153="" 3="" 4x155="" abs="" acc="" adj.="" all="" article="" best="" budget="" ccuracy="" closure="" constants="[" coordination="" d="" delta:.6f="" delta="" denominator="" derived="" e-="" e="" eigenval="" elta_pi:.6f="" elta_pi="pi_eff(12)" epton="" f="" faces="" fraction="" free="" from="" geometric="" golden="" h="" handshake="" hi:.6f="" icosahedral="" int="" isoperimetric="" k="" ladder="" lepton="" lepton_denom="" mass="" measured="" mu2:.6f="" mu_2="sqrt(5)" n="" non-spatializable="" number="" omega_routing:.6f="" omega_routing="H*Psi/(K*SIMPLEX)" p="" parameters="" phi1="" phi3:.6f="" phi_1="" phi_3="phi_1/2" pi2="" pi3="" pi_eff="" pi_eff_12:.6f="" prediction:="" print="" psi="" ratio="" route_e:.7f="" route_e="(1+2/H)/620" route_p:.7f="" route_p="2u" si_sph="" sqrt2="" sqrt6="" total:.1f="" total="" worst="" x="" zero="">mu)", f"{delta_emu:+.6f}"),
("delta(mu->tau)", f"{delta_mutau:+.6f}"),
("E_mu exponent", f"{E_mu_exp:.6f}"),
("E_step exponent", f"{E_step_exp:.6f}"),
("tau_W = phi1^2/2", f"{tau_W:.6f}"),
("tau_Z = pi2+(K-1)/H+Dpi/phi1^2", f"{tau_Z:.6f}"),
("sin^2(theta_W) = phi1^(-tau_Z)",
f"{sin2_thetaW:.6f} (measured 0.22306, "
f"acc {100*(1-abs(sin2_thetaW-0.22306)/0.22306):.3f}%)"),
("D_seq (Higgs base)", f"{D_seq:.6f}"),
("D_H (Higgs denominator)", f"{D_H:.6f}"),
]
for label, value in constants:
print(f" {label:<42 code="" print="" value="" w="">
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