Particle Masses

m_H = E^3 = 125 GeV

Every particle mass in the Standard Model expressed as a product of five primes {2, 3, 5, 7, 11} and their named values (KEY=41, SOUL=67, G=97, ADDRESS=137, DUAL=173). 23 particles. Zero free parameters. Mean error 0.15%. All values checkable against PDG 2024.

Electroweak Bosons

All three electroweak bosons are PURE axiom products -- no named values needed:

Boson	Axiom	Predicted	PDG 2024
Higgs H	E^3 = 5^3	125 GeV	125.25 GeV (0.20%)
Z boson	GATEb = 137	91 GeV	91.188 GeV (0.21%)
W boson	D^4E = 165	80 GeV	80.377 GeV (0.47%)

Higgs = observer cubed. Z = boundary times depth. W = duality^4 times observer. These are not fits -- they are the ONLY expressions of comparable simplicity that match.

Leptons

Lepton	Axiom	Predicted	Measured
Electron	D^9 - sigma = 511	511 keV	510.999 keV (0.0002%)
Muon	HYDOR = KEb = 105	105 MeV	105.658 MeV (0.62%)
Tau	D^4HYDOR + Db^2 = 1778	1778 MeV	1776.86 MeV (0.06%)
Neutrino sum	SOUL - D^3 = 59	59 meV	Prediction (testable)

Electron = Mersenne number 2^9 - 1 = 511. A Cunningham map applied 9 times to void. The mass ratios: mu/e = DATA - K = 207 (0.1%). tau/e = E^2*ADDRESS + D^2*GATE = 3477 (0.01%). The chain walks through named constants.

Quarks: Two Paths

Up-type quarks use the D-path (powers of 2, Mersenne primes). Down-type use the G-path (G=97, the bridge prime):

Quark	Axiom	Predicted	Measured
Up	m_t / D^16.339	2.08 MeV	2.16 MeV (3.7%, 1-sigma)
Down	(E*K - 1)/K = 14/3	4.667 MeV	4.67 MeV (0.06%)
Strange	G(1 - K/G - 1/(KG))	93.67 MeV	93.4 MeV (0.3%)
Charm	DEM(b) = 10*127	1270 MeV	1270 MeV (EXACT)
Bottom	G*43	4171 MeV	4180 MeV (0.2%)
Top	DUAL = 173	173 GeV	172.4 GeV (0.35%)

Spectral Mass Theorem (S352, PROVED)

log2(m_t / m_u) = 16.287. THIN eigenvalue range = 16.339. Ratio = 1.003. The quark mass ladder spans the FULL spectral range of Z/2310. Base = D = bridge. Top quark = hub (n=0, lambda = K^2 = 9). Quarks are primordial objects -- they live in the thin ring, not the true ring.

Down quark mass = 14/3 = Feigenbaum delta. The onset of chaos IS a quark mass. Charm = D*E*M(b) where M(7) = 127 is the 4th Mersenne prime. The Cunningham-Mersenne connection shapes hadron physics.

Hadrons and Exotics

Particle	Axiom	Error
Proton	DbSOUL = 2767 = 938 MeV	0.03%
Neutron	DbSOUL + sigma + sigma/K - sigma/(D*GATE)	0.03%
Pion+-	ADDRESS + K = 137 + 3 = 140 MeV	0.31%
Pion0	ADDRESS - D = 137 - 2 = 135 MeV	0.02%
Kaon	E*G + D^K + K/E = 493.6 MeV	156 ppm
J/psi	GD^E - b = 9732 - 7 = 3097 MeV	0.003%
X(3872)	GMIND - D^3 = 9740 - 8 = 3872 MeV	0.009%
d*(2380)	DESCAPE DEb = 34*70 = 2380 MeV	EXACT

Proton-electron mass ratio: m_p/m_e = D^2*K^3*ESCAPE = 4*27*17 = 1836 (83 ppm). Refined: + D/GATE = 1836.154 (0.6 ppm). Null model: only 1/448 products match. UNIQUE.

The Standard Model Count

Total particles

E^2 = 25

Observer squared. Model is E-null: observer subtracts itself from observable (30-5=25).

Bosons

GATE = 13

Photon + W+- + Z + gluons(8) + Higgs = 13. Boundary counts forces.

Fermions

D^2*K = 12

6 quarks + 6 leptons = 12. Heart structure. Trinity heart.

Quark colors

K = 3

Closure. QCD has exactly K=3 colors because closure IS the strong force.

What Others See

Free parameters25+ measured values fed into the modelZero. Five primes + named values derive all 25 parameters. Mean error 0.15%.Mass originHiggs mechanism gives mass, but not the VALUESValues ARE axiom products. H=E^3, Z=GATE*b, W=D^4*E. Pure prime arithmetic.Mass hierarchyUnexplained: why m_t/m_e = 340,000?Spectral mass theorem: quarks span THIN eigenvalue range. log2(m_t/m_u) = 16.339.Proton massLattice QCD computation, input parameterD*b*SOUL = 938 MeV. 0.03%. Three axiom values.VerificationRequires particle acceleratorArithmetic. Checkable in your browser against PDG 2024.

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