Primordial Particle Formation and Standard Model Parameters from 8-Dimensional Lattice Geometry

Let me review the current formulas and update with the new mass derivations and correct 480 formula:

Now I have all the updated information. Here's the consolidated, corrected Zenodo description:

Updated Paper 61 Zenodo Description (v3.0)

We address two fundamental questions: (1) how do particles come to exist, and (2) why do they have the masses they have?

Particle Formation from Cosmological Cooling

Particles emerge as frozen fluctuations during cosmological cooling: when χ₀(t) increases (Big Bang cooling), random energy fluctuations become trapped in χ-wells as confining walls form around them. Numerical simulations confirm this mechanism: 4 of 5 tests produced 3–72 stable particles from random initial conditions.

The χ₀ = 19 Discovery (First Principles)

UPDATE v3.0: χ₀ = 19 is now derived from first principles via computational degrees of freedom counting—not CMB fitting.

For GOV-01 + GOV-02 to compute the next state of each lattice point:

The CMB spectral index n_s = 0.9649 ± 0.0042 now validates this derivation (prediction: 0.9667, 0.18% error).

Key Results: Particle Masses from Angular Momentum

BREAKTHROUGH (v3.0): All particle masses derive from 4D angular momentum quantization:

The l(l+1) factor emerges directly from GOV-01's Laplacian in spherical coordinates.

Offset formulas (all derived from χ₀):

• Leptons: (gen−1)(6gen−17) where 6 = (χ₀−1)/3, 17 = χ₀−2
• Proton: +4 = D = spacetime dimensions = (χ₀−11)/2

Key Results: Coupling Constants

The 480 is derived: 480 = D! × (χ₀+1) = 4! × 20 = 24 × 20, where D = (χ₀−11)/2 = 4.

Higgs Self-Coupling λ (Falsifiable)

Standard Model value: 0.1291 | Error: 0.03%

HL-LHC Falsification Criterion (2028–2030): If measured λ differs from 0.129 by more than ±10%, LFM is falsified.

CP Violation (Complete)

CKM Phase (quarks):
$$\delta_{\text{CKM}} = 3(\chi_0 + 3) = 66° \quad \text{(Measured: 65.8° ± 3.0°, Error: 0.30%)}$$

PMNS Phase (neutrinos):

Complete Mixing Matrices

PMNS (Neutrino Mixing):

CKM (Quark Mixing):

Physical Interpretation

Every integer derives from χ₀ = 19:

Statistics

Conclusion

Particles are not fundamental entities but emergent structures: they form through cosmological cooling and their properties derive from the single integer χ₀ = 19, which represents the minimum degrees of freedom required to compute lattice field dynamics.

Supplementary Materials: DEFINITIVE_FORMULA_CATALOG.md contains the complete master table.

Errata

ERRATUM (v3.0, February 2026): Major update: (1) χ₀ = 19 now derived from first-principles DOF counting, not CMB fitting. (2) Particle masses now derive from angular momentum: m/m_e = l(l+1) where l = τχ₀ + offset. Proton: l=42 → 1806 (1.6%), muon: l=14 → 210 (1.6%), tau: l=59 → 3540 (1.8%). (3) Fine structure derivation complete: 480 = D!×(χ₀+1) = 4!×20. All integers now trace to χ₀. Total: 41 predictions, 36 within 2% (88%), 15 EXACT.

ERRATUM (v2.1, February 2026): Added CKM CP phase δ_CKM = 3(χ₀+3) = 66° (0.30% error) and Higgs λ = 4/(χ₀+12) = 4/31 = 0.12903 (0.03% error). HL-LHC falsification criterion established.

ERRATUM (v2.0, February 2026): Added neutrino CP phase δ_CP = 180° + (χ₀−4) = 195°, matching NOvA measurement exactly.