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Lean 4 formalization (root library)\n├── Core.lean                   # Constants (dim_E8, b2, b3, H*, ...)\n├── Certificate/                # Modular certificate system\n│   ├── Core.lean               # Master: Foundations ∧ Predictions ∧ Spectral\n│   ├── Foundations.lean        # E₈, G₂, octonions, K₇, Joyce, NK cert (34 conjuncts)\n│   ├── Predictions.lean        # 33+ relations, ~50 observables (56 conjuncts)\n│   └── Spectral.lean           # Mass gap, TCS, computed spectrum, Weyl law (37 conjuncts)\n├── Foundations/                 # Mathematical foundations (23 files)\n│   ├── RootSystems.lean        # E₈ roots in ℝ⁸ (240 vectors)\n│   ├── E8Lattice.lean          # E₈ lattice, Weyl reflection\n│   ├── G2CrossProduct.lean     # 7D cross product, Fano plane\n│   ├── ExplicitG2Metric.lean   # 169-param Chebyshev-Cholesky\n│   ├── NewtonKantorovich.lean  # NK cert: h \u003c 0.5, decomposed\n│   ├── NumericalBounds.lean    # Taylor series bounds (axiom-free)\n│   └── Analysis/               # G₂ forms, Hodge theory, Sobolev\n├── Geometry/                   # Axiom-free DG infrastructure\n│   ├── HodgeStarR7.lean        # ⋆, ψ=⋆φ PROVEN, TorsionFree\n│   └── HodgeStarCompute.lean   # Explicit Hodge star (Levi-Civita)\n├── Spectral/                   # Spectral gap theory (17 files)\n│   ├── PhysicalSpectralGap.lean # dim(G₂)−h = 13 algebraic (zero axioms)\n│   ├── ComputedSpectrum.lean   # Q22 sig, SD/ASD gap, B-test\n│   └── CheegerInequality.lean  # Cheeger-Buser bounds\n├── Algebraic/                  # Octonion/G₂ algebraic foundations\n│   └── G2ThreeForm.lean        # φ₀ 3-form, G₂=Stab(φ₀), g₂=ker(L_φ₀), dim=14\n├── Relations/                  # Physical predictions (22 files)\n├── Observables/                # PMNS, CKM, quark masses, cosmology\n├── Hierarchy/                  # Dimensional gap, absolute masses\n\nGIFTTest/                       # Lean test files\n\nblueprint/                      # Leanblueprint dependency graph\n\ncontrib/                        # Non-Lean assets\n├── python/                     # Python package (giftpy on PyPI)\n│   └── gift_core/              # Certified constants export\n├── homepage/                   # GitHub Pages / Jekyll site\n└── docs/                       # Extended documentation\n```\n\n## Quick Start\n\n```bash\npip install giftpy\n```\n\n```python\nfrom gift_core import *\n\nprint(SIN2_THETA_W)   # Fraction(3, 13)\nprint(GAMMA_GIFT)     # Fraction(511, 884)\nprint(TAU)            # Fraction(3472, 891)\n```\n\n## Building Proofs\n\n```bash\nlake build\n```\n\n## Documentation\n\nFor extended observables, publications, and detailed analysis:\n\n**[gift-framework/GIFT](https://github.com/gift-framework/GIFT)**\n\n---\n\n[Changelog](contrib/CHANGELOG.md) | [MIT License](LICENSE)\n\n*GIFT Core v3.4.21*\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fgift-framework%2Fcore","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fgift-framework%2Fcore","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fgift-framework%2Fcore/lists"}