Geometric Information Field Theory

What if physics isn't fine-tuned, just well-shaped?

GIFT derives Standard Model parameters from the geometry of a single 7-dimensional manifold. No free parameters. No fitting. Every prediction is a consequence of shape.

Start Here

Whether you're curious, a physicist, a mathematician, or a formalization enthusiast — there's a door for you.

From the Blog

Accessible writing on the ideas behind GIFT. All posts on giftheory.substack.com.

Key Results

Every value below is derived from topology — the shape of a single G₂-holonomy manifold K₇. Nothing is fitted.

Exact Relations (Lean 4 Verified)

Relation Value Topological origin
sin²θW 3/13 b₂/(b₃ + dim G₂)
κT 1/61 1/(b₃ − dim G₂ − p₂)
τ 3472/891 (496 × 21)/(27 × 99)
det(g) 65/32 G₂ metric determinant
δCP 197° 7 × dim G₂ + H*
QKoide 2/3 dim G₂ / b₂

Precision by Sector

Sector Predictions Mean deviation Highlight
Electroweak 3 0.12% sin²θW = 3/13
Lepton 3 0.04% QKoide = 2/3 (0.0009%)
Neutrino 3+1 0.25% θ₁₂ = arctan(2/3)
Cosmology 3 0.07% ns = ζ(11)/ζ(5)
Structural 4 exact Ngen = 3

Statistical Uniqueness

Test Result
Configurations tested 3,000,000+
GIFT rank #1
Better alternatives found 0
Null model p-value < 2×10⁻⁵ (σ > 4.2)
Bayes factor 304–4,738 (decisive)

Papers & Proofs

Main Paper (v3.4)

Complete theoretical framework: E₈×E₈ compactification, K₇ construction, all derivations. 44 pp.

S1: Foundations (v3.4)

E₈, G₂, K₇ mathematical construction. Lattice theory, holonomy, TCS gluing. 27 pp.

S2: Derivations (v3.4)

All 33 Type I derivations with full computation. 0.39% mean deviation (PDG 2024 / NuFIT 6.0). 42 pp.

S3: Observables (v3.4)

95-observable catalog with type breakdown (35 Type I + 19 II + 21 III + 22 IV). 10 pp.

Paper A — Certified G₂ Structure

First computer-assisted existence proof for a metric with special holonomy. Zenodo 19892350.

Paper B — Spectral Geometry

Laplacian spectrum, harmonic forms, λ₁ ≈ 6π²/475. Zenodo 19893371.

Paper C — K3 Newton-Kantorovich

NK diagnostics on a Donaldson K3 metric (CI(2,2,2)). Zenodo 19708916.

Paper D — Donaldson Analytic Note

Explicit closed-form G₂ ansatz on a K3-coassociative neck with 5-layer Wirtinger certificate. Zenodo 20039066.

Lean 4 Proofs

144 files, 4 main-chain axioms, zero sorry. Formally verified in Lean 4 (core v3.4.20).

Workshops

Invited remote participant, "DANGER: Data, Numbers, and Geometry" workshop, Banff International Research Station (BIRS), April 5–10, 2026.

Falsification Tests

GIFT makes concrete predictions that can be tested by running or planned experiments.

Prediction Experiment Timeline Falsification criterion
δCP = 197° DUNE 2027–2030 Outside [187°, 207°]
sin²θW = 3/13 FCC-ee 2040s Outside [0.2295, 0.2320]
ms/md = 20 Lattice QCD 2030 Converges outside [19, 21]
Ngen = 3 LHC Ongoing 4th generation discovery