GIFT 3.4 : Geometric Information Field Theory

The Standard Model requires 19 experimentally determined parameters lacking theoretical explanation. We present a geometric framework in which physical observables emerge as topological invariants of a seven-dimensional G₂ holonomy manifold K₇ coupled to E₈×E₈ gauge structure, with the topological inputs treated as discrete and the metric determinant det(g) = 65/32 imposed as a normalization target (§2.3); no continuously adjustable physical parameter is introduced.

Building on a Newton–Kantorovich-certified neck/metric model ([A], [B]) and a Joyce–Karigiannis topological/lattice route realizing (b₂, b₃) = (21, 77) (while the full smooth analytic compact construction remains open) we derive **95 observables** from K₇ organized in four types: 33 direct algebraic (Type I, mean deviation 0.73%), 19 one-step physical extractions (Type II, 0.17%), 21 multi-step dynamical chains (Type III, 3.4%), and 22 structural diagnostics (Type IV). Of 66 experimentally comparable observables, 11 are exact matches (deviation < 0.01%) and 53 are within 1%.

The framework includes three new framework-level results beyond the original 33 predictions: (1) a proposed E₈ → Standard Model breaking chain with anomaly-cancellation checks and bundle-universality diagnostics, (2) a combined lepton mass hierarchy mechanism achieving sub-percent precision from two independent geometric sources with α = e^K (zero free parameters), and (3) a sensitivity analysis demonstrating 2.13× overdetermination with coincidence probability 10⁻³⁴⁶ under a uniform null and 10⁻¹³³ under an algebraic null model (4.2M random formulas from the same 20 constants). Of the 95 observables, 55 are formally verified in Lean 4 (213 certificate conjuncts, 4 axioms, 0 sorry); Lean certifies the algebraic relations and internal consistency, not the physical interpretation or the existence of the complete compact construction (§8.3).

DUNE (2028–2040) will test the topological prediction δ_CP = 197° with resolution of a few degrees to ~15°; measurement outside [182, 212]° would create serious tension. We present this as an exploratory investigation emphasizing falsifiability, not a claim of correctness.