GIFT: Geometric Information Field Theory
A zero-parameter framework deriving Standard Model constants from G₂ holonomy geometry.
At a Glance
| Property | Value |
|---|---|
| Predictions | 95 observables (35 Type I + 19 Type II + 21 Type III + 22 Type IV) |
| Mean deviation | 0.39% on 35 Type I (exact-target) relations (PDG 2024 / NuFIT 6.0) |
| Free parameters | 0 (3 integer primitives: N=3, r₈=8, r₂=2) |
| Lean 4 verification | 144 files, 8392 build jobs, 0 sorry, 4 main-chain axioms (core v3.4.20) |
| Statistical significance | p < 2×10⁻⁵ (σ > 4.2), unique among 3M+ configurations |
| Monte Carlo null model | P(algebraic) = 10⁻¹³⁸ over 3M+ formulas |
Quick Links
| New here? | Getting Started: Pick your path |
| Read papers | Paper Main Framework (Paper Explicit G2 Metric) Paper Spectral Geometry |
| Browse predictions | Observable Reference, 95 observables with formulas |
| Check proofs | Lean Formalization, 213-conjunct certificate |
Key Results
| Observable | GIFT Formula | Value | Exp. | Dev. |
|---|---|---|---|---|
| sin²θ_W | b₂/(b₃+dim(G₂)) = 21/91 | 3/13 | 0.2312 | 0.19% |
| N_gen | rank(E₈) − Weyl | 3 | 3 | exact |
| Q_Koide | dim(G₂)/b₂ = 14/21 | 2/3 | 0.6667 | 0.001% |
| α_s(M_Z) | √2/(dim(G₂)−p₂) | √2/12 | 0.1179 | 0.04% |
| δ_CP | dim(K₇)×dim(G₂)+H* | 197° | 177°±20° | 1.0σ |
| m_τ/m_e | 7+10×248+10×99 | 3477 | 3477.2 | 0.004% |
| Ω_DE | ln(2)×98/99 | 0.686 | 0.685 | 0.21% |
Exact Algebraic Relations
All predictions derive from topological constants of a compact G₂ manifold K₇ with Betti numbers b₂ = 21, b₃ = 77, coupled to E₈×E₈ gauge structure (dim = 496):
sin²θ_W = b₂ / (b₃ + dim(G₂)) = 21/91 = 3/13
Q_Koide = dim(G₂) / b₂ = 14/21 = 2/3
N_gen = |PSL(2,7)| / fund(E₇) = 168/56 = 3
κ_T = 1/(b₃ − dim(G₂) − p₂) = 1/61
α = e^K (geometric coupling, zero free params)
Falsification Tests
| Prediction | Experiment | Timeline | Status |
|---|---|---|---|
| δ_CP = 197° ± 5° | DUNE | 2028–2039 | Awaiting |
| sin²θ_W = 3/13 | FCC-ee | 2040s | Awaiting |
| N_gen = 3 (no 4th gen) | LHC/FCC | Ongoing | Consistent |
| m_s/m_d = 20 | Lattice QCD | ~2030 | Consistent |
Outreach
Accessible writing on the ideas behind GIFT lives on the Substack blog; see the Site Map blog index for the full list. Latest: Episode 1: The day Newton lost control, Fall Guys and the myth of predictable physics.
Structure
This wiki consolidates GIFT documentation across three repositories:
- gift-framework/GIFT: Theoretical documentation, papers, outreach
- gift-framework/core: Lean 4 proofs, Python package, blueprint
- Zenodo deposits: Archived data with DOIs
Browse the sidebar for full navigation, or see the Site Map for a complete index.
| *GIFT Framework v3.4 | GitHub | Core | Blueprint | Zenodo (Paper A) · Paper B · Paper C | MIT License* |