Paper Main Framework

Paper: Main Framework

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

Brieuc de La Fournière (2026) Full text (markdown) | Zenodo DOI: 10.5281/zenodo.18837071

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Abstract

Framework proposing that 19 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. Derives 33 dimensionless predictions with mean deviation 0.24% from experiment. 18 core relations formally verified in Lean 4. DUNE will test δ_CP = 197° falsification criterion.

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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: 33 predictions, 0.24% mean deviation (32 well-measured), 4 exact, 28/33 sub-1%

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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

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Statistical Validation

• (21,77) unique optimal among 192,349 configurations (p < 5×10⁻⁶)
• E₈×E₈ achieves 12.8× better agreement than next best gauge group
• G₂ holonomy achieves 13× better than Calabi-Yau (SU(3))
• Lean 4 verification: 290+ theorems, 0 sorry, 0 domain-specific axioms

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Related

• Paper S1 Foundations — Mathematical foundations
• Paper S2 Derivations — Complete derivations
• Paper Explicit G2 Metric — Numerical G₂ metric
• Paper Spectral Geometry — KK spectrum
• Observable Reference — Full prediction catalog
• Statistical Evidence — 7-component validation