Paper: Main Framework

Geometric Information Field Theory: Topological Derivation of Standard Model Parameters from G₂ Holonomy Manifolds

Brieuc de La Fournière (2026)

PDF (main, 44 pp.) DOI: 10.5281/zenodo.20070101 Markdown

Companion papers (Zenodo): A: certified G₂ · B: spectral · C: K3 NK · D: Donaldson analytic · v3.3 archive

Abstract

Framework proposing that Standard Model dimensionless parameters emerge as topological invariants of a 7D G₂ holonomy manifold K₇ with Betti numbers (b₂=21, b₃=77) coupled to E₈×E₈ gauge structure. v3.4 catalogues 95 observables (35 Type I exact-target relations) with 0.39% mean deviation on Type I from experiment (PDG 2024 / NuFIT 6.0); 213 conjuncts certified in Lean 4 with 4 main-chain axioms. DUNE will test δ_CP = 197° falsification criterion.

Key Results

Observable GIFT Formula Value Exp. Dev.
sin²θ_W b₂/(b₃+dim(G₂)) 3/13 0.2312 0.19%
N_gen rank(E₈)−Weyl 3 3 exact
Q_Koide dim(G₂)/b₂ 2/3 0.6667 0.001%
α_s(M_Z) √2/12 0.1179 0.1179 0.04%
δ_CP 7×14+99 197° 177°±20° 1σ
m_τ/m_e 7+10×248+10×99 3477 3477.2 0.004%
n_s ζ(11)/ζ(5) 0.9649 0.9649 0.004%

Global (v3.4): 95 observables in 4 types (33 Type I + 19 II + 21 III + 22 IV); 66 with experimental comparison; mean deviations 0.73% (Type I), 0.17% (Type II), 3.4% (Type III); 11 exact matches (<0.01%), 53 within 1%

Section Structure

  1. Introduction: Parameter problem, contemporary context, framework overview
  2. Mathematical Framework: Octonions, E₈×E₈, K₇ hypothesis, G₂ structure
  3. Methodology & Epistemic Status: Derivation principle, claims vs non-claims
  4. Derivation of 33 Predictions: Gauge, lepton, quark, neutrino, Higgs, cosmological sectors
  5. Formal Verification & Statistics: Lean 4 (290+ theorems), uniqueness among 192,349 alternatives
  6. G₂ Metric Program: PINN atlas construction, metric quality results
  7. Falsifiable Predictions, δ_CP via DUNE, fourth generation bounds
  8. Discussion: M-theory connections, comparison with other approaches, limitations
  9. Conclusion

Statistical Validation