Standard Model parameters from pure geometry: E₈×E₈ on G₂-holonomy manifold K₇, zero adjustable parameters.
| Precision | 0.24% mean deviation across 32 well-measured observables (0.57% incl. δ_CP; PDG 2024 / NuFIT 6.0) |
| Uniqueness | #1 out of 3,070,396 configurations tested (3.9σ local significance) |
| Parameters | Zero adjustable (all structurally determined) |
| Verified | 455+ relations proven in Lean 4 (core v3.3.32, 38 axioms) |
| Exact results | sin²θ_W = 3/13 · τ = 3472/891 · det(g) = 65/32 |
Dimensional reduction: E₈×E₈ (496D) → AdS₄ × K₇ (11D) → Standard Model (4D)
| Paper | Proofs | Video |
|---|---|---|
| Main Paper | Lean 4 | YouTube (8 min) |
| Document | Description |
|---|---|
| Main Paper | Complete theoretical framework |
| S1: Foundations | E₈, G₂, K₇ mathematical construction |
| S2: Derivations | All 33 derivations (0.24% mean excl. δ_CP, PDG 2024 / NuFIT 6.0) |
| Explicit G₂ Metric | Analytical G₂ metric construction |
| Spectral Geometry | KK spectrum, Yukawa, gauge unification from G₂ metric |
| Background | Start Here |
|---|---|
| Everyone | GIFT for Everyone: Complete guide with everyday analogies |
| 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 |
| 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 | 3+1 | 0.25% + δ_CP at 1σ | θ₁₂ = arctan(2/3) |
| Cosmology | 3 | 0.07% | n_s = ζ(11)/ζ(5) (0.004%) |
| Structural | 4 | exact | N_gen = 3, τ = 3472/891 |
| 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 × w |
| Q_Koide | 2/3 | dim(G₂)/b₂ |
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.
Comprehensive validation confirms that (b₂=21, b₃=77) is not merely a good choice but the unique optimum among G₂ manifold configurations.
| Metric | Value |
|---|---|
| Configurations tested | 3,070,396 |
| GIFT rank | #1 |
| GIFT mean deviation | 0.24% (32 well-measured) / 0.57% incl. δ_CP (PDG 2024 / NuFIT 6.0) |
| Better alternatives found | 0 |
| p-value (empirical) | 0 / 3,070,396 |
| Rank | b₂ | b₃ | Deviation |
|---|---|---|---|
| 1 | 21 | 77 | 0.24% |
| 2 | 21 | 76 | 0.50% |
| 3 | 21 | 78 | 0.50% |
| 4 | 21 | 79 | 0.79% |
| 5 | 21 | 75 | 0.81% |
| Test | Result |
|---|---|
| Null model p-value | < 2×10⁻⁵ (σ > 4.2), three independent null families |
| Westfall-Young maxT | 11/33 individually significant (global p = 0.008) |
| Pre-registered test split | p = 6.7×10⁻⁵ (σ = 4.0) |
| Bayes factor | 304–4,738 across four priors (all decisive) |
| Exhaustive search | 0/3,070,396 configs better |
Seven-component analysis: pre-registration, three null families, multiple-testing corrections (Bonferroni/Holm/BH/Westfall-Young), cross-sector prediction, robustness/noise sensitivity, multi-seed replication, Bayesian (BF + PPC + WAIC).
Details: Statistical Evidence
| 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
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 3,070,396 tested configurations. This doesn't explain the choice, but establishes it is not arbitrary.
| Repository | Description |
|---|---|
| gift-framework/core | Formal verification (Lean 4), K₇ metric pipeline, giftpy |
Blog posts and vulgarization articles are available in publications/outreach/.
| Post | Topic |
|---|---|
| Gift from Bit | Why geometry might be the language of physics |
| 13 Theorems, Zero Trust Required | Machine-verified proofs in Lean 4 |
| Joyce's Theorem, Now in Lean | Formalizing G₂ holonomy existence |
| The Algebra That Waited | E₈ and the structure of matter |
| On What Comes First | Philosophy of mathematical primacy |
| Lice of the Universe | The fine-tuning problem |
| Roberto Carlos' Geometry | Geometry and physics for everyone |
All posts on giftheory.substack.com.
| Platform | |
|---|---|
| YouTube | @giftheory |
| Substack | giftheory.substack.com |
| X | @GIFTheory |
| Archive | |
|---|---|
| Zenodo (framework) | 10.5281/zenodo.18837071 |
| Zenodo (explicit G₂ metric) | 10.5281/zenodo.18860358 |
| Zenodo (spectral geometry) | 10.5281/zenodo.18920368 |
| ResearchGate | Author page |
@software{gift_framework_v33,
title = {GIFT Framework v3.3: Geometric Information Field Theory},
author = {de La Fournière, Brieuc},
year = {2026},
url = {https://github.com/gift-framework/GIFT},
version = {3.3.32}
}See CITATION.md for additional formats.
MIT License, see LICENSE
Gift from bit