GIFT 3.2 : Geometric Information Field Theory

The Geometric Information Field Theory (GIFT) framework proposes a topological origin for the 19 free parameters of the Standard Model, deriving 18 dimensionless quantities from invariants of a compact seven-dimensional G₂-holonomy manifold K₇, constructed via twisted connected sum. Drawing from octonionic algebra and E₈×E₈ gauge structure, GIFT contains no continuous adjustable parameters, achieving a mean deviation of 0.24% from experimental values (PDG 2024), including exact matches for the number of generations (3), Koide parameter (2/3), and strange-to-down quark mass ratio (20).

The main document provides an overview, cataloging predictions such as sin²θ_W = 3/13 ≈ 0.2308 (0.20% deviation) and δ_CP = 197° (within current experimental range). Supplement S1 details mathematical foundations, including E₈ root systems, G₂ holonomy conditions, and K₇ topology (b₂=21, b₃=77), with metric determinant det(g)=65/32 verified analytically and in Lean 4. S2 presents complete derivations of the 18 relations, emphasizing their independence from torsion and statistical uniqueness: exhaustive search over 19,100 configurations confirms (21,77) as the unique optimum (p<10⁻⁴, >4σ after look-elsewhere correction). S3 explores theoretical extensions including scale bridge, torsional dynamics, and cosmological predictions such as Ω_DE ≈ 0.686.

While these agreements suggest a geometric underpinning, they await rigorous scrutiny; the prediction δ_CP = 197° offers falsifiability through DUNE (2034–2039). The framework invites further exploration of whether such topological patterns reflect fundamental structure or numerical coincidence.