GIFT
Geometric Information Field Theory v3.1
Standard Model parameters from pure geometry — E₈×E₈ on G₂-holonomy manifold K₇, zero adjustable parameters.
At a Glance
| Precision | 0.087% mean deviation across 18 dimensionless predictions |
| Uniqueness | #1 out of 19,100 configurations tested (>4σ significance) |
| Parameters | Zero adjustable (all structurally determined) |
| Verified | 180+ relations proven in Lean 4 + Coq (zero axioms) |
| Exact results | sin²θ_W = 3/13 · τ = 3472/891 · det(g) = 65/32 · Monster = 47×59×71 |
Dimensional reduction: E₈×E₈ (496D) → AdS₄ × K₇ (11D) → Standard Model (4D)
Quick Start
| Paper | Proofs | Video |
|---|---|---|
| Main Paper | Lean 4 + Coq | YouTube (8 min) |
Documentation
Core
| Document | Description |
|---|---|
| Main Paper | Complete theoretical framework |
| S1: Foundations | E₈, G₂, K₇ mathematical construction |
| S2: Derivations | All 18 dimensionless derivations (0.087% mean) |
| S3: Dynamics | RG flow, torsional dynamics |
For Specific Audiences
| Background | Start Here |
|---|---|
| Geometer | GiftPy for Geometers — G₂ metric construction pipeline |
| Physicist | Info Geo for Physicists — Topological approach to SM parameters |
| Formalization | Lean for Physics — Machine-verified physical relations |
| Philosophy | Philosophy — Foundational perspective |
Exploratory Extensions
| Document | Description |
|---|---|
| Speculative Physics | Scale bridge, Yukawa, M-theory, quantum gravity |
| Number-Theoretic Structures | Fibonacci, Prime Atlas, Monster, Moonshine |
| GIFT Atlas | Complete constant/relation database |
Key Results
Precision by Sector
| Sector | Predictions | Mean Deviation | Highlight |
|---|---|---|---|
| Electroweak | 3 | 0.12% | sin²θ_W = 3/13 |
| Lepton | 3 | 0.04% | Q_Koide = 2/3 (0.0009%) |
| Quark | 1 | 0.00% | m_s/m_d = 20 (exact) |
| Neutrino | 4 | 0.15% | δ_CP = 197° |
| Cosmology | 3 | 0.07% | n_s = ζ(11)/ζ(5) (0.004%) |
| Structural | 4 | exact | N_gen = 3, τ = 3472/891 |
Exact Relations (Lean 4 + Coq Verified)
| Relation | Value | Topological Origin |
|---|---|---|
| sin²θ_W | 3/13 | b₂/(b₃ + dim(G₂)) |
| κ_T | 1/61 | 1/(b₃ − dim(G₂) − p₂) |
| τ | 3472/891 | (496 × 21)/(27 × 99) |
| det(g) | 65/32 | Metric determinant from G₂ structure |
| δ_CP | 197° | 7 × dim(G₂) + H* |
| m_s/m_d | 20 | p₂² × Weyl |
| Q_Koide | 2/3 | dim(G₂)/b₂ |
| Monster | 196883 | L₈ × (b₃−18) × (b₃−6) = 47×59×71 |
Analytical G₂ Metric (v3.1)
The G₂ structure admits an exact closed form:
| Property | Value | Status |
|---|---|---|
| Associative 3-form | φ = (65/32)^{1/14} × φ₀ | EXACT |
| Metric | g = (65/32)^{1/7} × I₇ | EXACT |
| Torsion | T = 0 (constant form) | EXACT |
| det(g) | 65/32 | EXACT |
Joyce’s existence theorem is trivially satisfied — no numerical fitting required.
Number-Theoretic Structures
| Structure | Result | Status |
|---|---|---|
| Fibonacci F₃–F₁₂ | Maps to GIFT constants (p₂, N_gen, Weyl, rank, α_B, b₂, …) | ✓ Proven |
| Prime Atlas | 100% coverage of primes < 200 | ✓ Proven |
| Monster dimension | 196883 = 47×59×71, arithmetic progression d=12 | ✓ Proven |
| j-invariant | 744 = 3 × 248 = N_gen × dim(E₈) | ✓ Proven |
| McKay correspondence | Coxeter(E₈) = 30 = icosahedron edges | ✓ Proven |
Statistical Uniqueness
Comprehensive validation confirms that (b₂=21, b₃=77) is not merely a good choice but the unique optimum among G₂ manifold configurations.
Exhaustive Search Results
| Metric | Value |
|---|---|
| Configurations tested | 19,100 |
| GIFT rank | #1 |
| GIFT mean deviation | 0.23% |
| Second-best deviation | 0.50% |
| Improvement factor | 2.2× |
Top 5 Configurations
| Rank | b₂ | b₃ | Deviation |
|---|---|---|---|
| 1 | 21 | 77 | 0.23% |
| 2 | 21 | 76 | 0.50% |
| 3 | 21 | 78 | 0.50% |
| 4 | 21 | 79 | 0.79% |
| 5 | 21 | 75 | 0.81% |
Statistical Significance
- LEE-corrected significance: >4σ
- p-value: < 5.2 × 10⁻⁵
- Bootstrap CI: 100% of alternatives perform worse
GIFT occupies a sharp minimum: moving one unit in any direction more than doubles the deviation.
Details: Uniqueness Test Report
Falsification Tests
| Prediction | Experiment | Timeline | Falsification Criterion |
|---|---|---|---|
| δ_CP = 197° | DUNE | 2027-2030 | Outside [187°, 207°] |
| sin²θ_W = 3/13 | FCC-ee | 2040s | Outside [0.2295, 0.2320] |
| m_s/m_d = 20 | Lattice QCD | 2030 | Converges outside [19, 21] |
| N_gen = 3 | LHC | Ongoing | Fourth generation discovery |
Details: S2 Section 10
Limitations
What “Zero-Parameter” Means
The framework contains no continuous adjustable parameters fitted to data. However, it makes discrete structural choices:
- E₈×E₈ as gauge group
- K₇ manifold with (b₂=21, b₃=77)
- TCS building blocks
These are mathematically motivated but constitute model selection. The framework predicts observables given these choices — it does not explain why nature chose this geometry.
However: Statistical validation shows (b₂=21, b₃=77) is the unique optimum among 19,100 tested configurations. This doesn’t explain the choice, but establishes it is not arbitrary.
Why Not Numerology?
The v3.0 structures (Fibonacci, Monster, McKay) have independent mathematical existence:
- Fibonacci appears in phyllotaxis, shell spirals, golden ratio
- Monster group is a theorem (Griess 1982)
- McKay correspondence is established mathematics (McKay 1980)
Their appearance suggests structural rather than coincidental relationships.
Interactive Visualizations
| Blueprint | Description |
|---|---|
| GIFT Lean Blueprint | Dependency graph |
| K7 Manifold Blueprint | K₇ construction |
Created with Lean Blueprint Copilot
Related Repositories
| Repository | Description |
|---|---|
| gift-framework/core | Formal verification (Lean 4 + Coq), K₇ metric pipeline |
Connect
| Platform | |
|---|---|
| YouTube | @giftheory |
| Substack | giftheory.substack.com |
| X | @GIFTheory |
| Archive | |
|---|---|
| Zenodo | 10.5281/zenodo.17979433 |
| ResearchGate | Author page |
Citation
@software{gift_framework_v31,
title = {GIFT Framework v3.1: Geometric Information Field Theory},
author = {de La Fournière, Brieuc},
year = {2025},
url = {https://github.com/gift-framework/GIFT},
version = {3.1.1}
}
See CITATION.md for additional formats.
License
MIT License — see LICENSE
Gift from bit