https://github.com/gift-framework/core
GIFT Core: Certified mathematical identities from E8×E8 gauge theory on G2 manifolds. Verified in Lean 4
https://github.com/gift-framework/core
coq coq-formalization e8 formal-verification g2-holonomy gauge-theory lean lean4 mathematics proof-assistant python
Last synced: 18 days ago
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GIFT Core: Certified mathematical identities from E8×E8 gauge theory on G2 manifolds. Verified in Lean 4
- Host: GitHub
- URL: https://github.com/gift-framework/core
- Owner: gift-framework
- License: mit
- Created: 2025-12-03T18:07:10.000Z (6 months ago)
- Default Branch: main
- Last Pushed: 2026-03-28T17:23:23.000Z (2 months ago)
- Last Synced: 2026-03-28T18:29:27.050Z (2 months ago)
- Topics: coq, coq-formalization, e8, formal-verification, g2-holonomy, gauge-theory, lean, lean4, mathematics, proof-assistant, python
- Language: Lean
- Homepage: https://gift-framework.github.io/core/
- Size: 2.97 MB
- Stars: 2
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# GIFT Core
[](https://github.com/gift-framework/core/actions/workflows/verify.yml)
[](https://pypi.org/project/giftpy/)
Formally verified mathematical relations from the GIFT framework. 460+ certified relations, **15 axioms** (4 logical on the main prediction chain + 11 interval-arithmetic certificates for the K3 block of g*), all theorems proven in **Lean 4** (8380 build jobs).
## Structure
```
GIFT/ # Lean 4 formalization (root library)
├── Core.lean # Constants (dim_E8, b2, b3, H*, ...)
├── Certificate/ # Modular certificate system
│ ├── Core.lean # Master: Foundations ∧ Predictions ∧ Spectral
│ ├── Foundations.lean # E₈, G₂, octonions, K₇, Joyce, NK cert (34 conjuncts)
│ ├── Predictions.lean # 33+ relations, ~50 observables (56 conjuncts)
│ └── Spectral.lean # Mass gap, TCS, computed spectrum, Weyl law (37 conjuncts)
├── Foundations/ # Mathematical foundations (23 files)
│ ├── RootSystems.lean # E₈ roots in ℝ⁸ (240 vectors)
│ ├── E8Lattice.lean # E₈ lattice, Weyl reflection
│ ├── G2CrossProduct.lean # 7D cross product, Fano plane
│ ├── ExplicitG2Metric.lean # 169-param Chebyshev-Cholesky
│ ├── NewtonKantorovich.lean # NK cert: h < 0.5, decomposed
│ ├── NumericalBounds.lean # Taylor series bounds (axiom-free)
│ └── Analysis/ # G₂ forms, Hodge theory, Sobolev
├── Geometry/ # Axiom-free DG infrastructure
│ ├── HodgeStarR7.lean # ⋆, ψ=⋆φ PROVEN, TorsionFree
│ └── HodgeStarCompute.lean # Explicit Hodge star (Levi-Civita)
├── Spectral/ # Spectral gap theory (17 files)
│ ├── PhysicalSpectralGap.lean # dim(G₂)−h = 13 algebraic (zero axioms)
│ ├── ComputedSpectrum.lean # Q22 sig, SD/ASD gap, B-test
│ └── CheegerInequality.lean # Cheeger-Buser bounds
├── Algebraic/ # Octonion/G₂ algebraic foundations
│ └── G2ThreeForm.lean # φ₀ 3-form, G₂=Stab(φ₀), g₂=ker(L_φ₀), dim=14
├── Relations/ # Physical predictions (22 files)
├── Observables/ # PMNS, CKM, quark masses, cosmology
├── Hierarchy/ # Dimensional gap, absolute masses
GIFTTest/ # Lean test files
blueprint/ # Leanblueprint dependency graph
contrib/ # Non-Lean assets
├── python/ # Python package (giftpy on PyPI)
│ └── gift_core/ # Certified constants export
├── homepage/ # GitHub Pages / Jekyll site
└── docs/ # Extended documentation
```
## Quick Start
```bash
pip install giftpy
```
```python
from gift_core import *
print(SIN2_THETA_W) # Fraction(3, 13)
print(GAMMA_GIFT) # Fraction(511, 884)
print(TAU) # Fraction(3472, 891)
```
## Building Proofs
```bash
lake build
```
## Documentation
For extended observables, publications, and detailed analysis:
**[gift-framework/GIFT](https://github.com/gift-framework/GIFT)**
---
[Changelog](contrib/CHANGELOG.md) | [MIT License](LICENSE)
*GIFT Core v3.4.21*