Gauge Structure and the Standard Model
MEG derives the Standard Model gauge group and matter content from the Spin(8) internal symmetry of the vacuum kernel, broken to SU(3) × SU(2) × U(1) by the Z₃ triality vacuum selection.
| Quantity | MEG | Observed | Accuracy |
|---|---|---|---|
| Gauge group | SU(3) × SU(2) × U(1) | SU(3) × SU(2) × U(1) | exact |
| Generations | 3 | 3 | exact |
| Fermions per generation | 16 Weyl | 16 Weyl | exact |
| Higgs representation | (1, 2)−1/2 | (1, 2)−1/2 | exact |
The gauge group is derived through the DHR superselection structure of the noiseless 8_s fibre; the generation count from the Z₃ triality; the Higgs from the SO(8)/G_SM coset, where Z₃ breaking is identified with electroweak symmetry breaking.
Coupling Constants
| Quantity | MEG | Observed | Accuracy |
|---|---|---|---|
| Base coupling α₁ | 1/10 | — | derived |
| Electroweak VEV vEW | 246.8 GeV | 246.2 GeV | 0.2% |
| Instanton scale ρ_c | 0.10–0.16 fm | ρ̄ ≈ 0.33 fm | factor 2–3 |
| GUT coupling g² | 5/16 | — | derived |
The base coupling α₁ = 1/10 is derived from the Z₃ closure fixed-point condition. The electroweak hierarchy v_EW/μ_GUT is derived from the SO(8) Landau pole with no free parameters. The strong coupling α₃ = 0.324 at the instanton scale is derived from the one-loop instanton prefactor with the projected instanton measure, predicting an instanton size ρ_c = 0.10–0.16 fm — within a factor of 2–3 of the phenomenological instanton-liquid value, stable across loop order and scheme.
Fermion Masses and Mixing
| Quantity | MEG | Observed | Accuracy |
|---|---|---|---|
| CKM matrix (3 angles + phase) | derived | observed | within 0.12° |
| PMNS matrix | derived (0 params) | observed | within 4.5% |
| Σmν | ~73 meV | < 120 meV | testable |
| Higgs mass | 124.9–128 GeV | 125.25 GeV | 0.3–2% |
The CKM matrix is derived from the information-geometric structure of the three-generation kernel. The PMNS matrix is a zero-parameter prediction. The neutrino mass sum Σm_ν ≈ 73 meV is a testable prediction within reach of current and near-future cosmological surveys.
Gravity and Cosmology
| Quantity | MEG | Observed | Accuracy |
|---|---|---|---|
| Newton's constant G | 6.2 × 10⁻¹¹ | 6.674 × 10⁻¹¹ | 7% |
| Coherence length ℓ₀ | ~11 kpc | ~9–11 kpc (SPARC) | fitted |
| Galaxy rotation curves | 55+ galaxies | SPARC data | median χ² ≈ 0.5 |
Gravity emerges from the faithful part of the kernel-to-spacetime projection. The entropy field S(x) satisfies the PLES variational principle, producing the gravitational field equations. The acceleration law a = c²∇S reproduces galactic rotation curves across 55+ SPARC galaxies with a single parameter (the coherence length ℓ₀). Newton's constant is derived from G = c²α₁⁶/(4πρ₀ℓ₀²).
The Mass Gap and Confinement
| Quantity | MEG | Lattice/Obs | Accuracy |
|---|---|---|---|
| Instanton size ρ_c | 0.10–0.16 fm | ρ̄ ≈ 0.33 fm | factor 2–3 |
| Coupling α₃ at instanton scale | 0.324 | — | predicted |
| Topological charge Q | 1 | 1 (standard QCD) | exact |
MEG derives confinement in three layers: structurally (the derived SU(3) is unbroken and asymptotically free), quantitatively (the tunnelling fugacity with the projected instanton measure gives α₃ = 0.324 at the instanton scale, predicting ρ_c = 0.10–0.16 fm, within a factor of 2–3 of the instanton-liquid value), and topologically (the adjoint hedgehog mechanism gives Q = 1 from the directional noiseless condition, verified numerically to machine precision).