This repository contains the theoretical documentation for GIFT v3.4.
Directory Layout
GIFT/
├── publications/ # Published content & validation
│ ├── papers/ # Scientific articles
│ │ ├── markdown/ # Core documents (v3.4 — canonical sources)
│ │ │ ├── GIFT_v3.4_main.md # Main paper
│ │ │ ├── GIFT_v3.4_S1_foundations.md # E₈, G₂, K₇ foundations
│ │ │ ├── GIFT_v3.4_S2_derivations.md # 33 Type I derivations
│ │ │ ├── GIFT_v3.4_S3_observables.md # 95-observable catalog
│ │ │ ├── g2_certified_neck.md # Paper A — certified G₂ structure
│ │ │ └── g2_spectral.md # Paper B — spectral geometry
│ │ ├── tex/ # LaTeX sources (v3.4)
│ │ ├── pdf/ # Compiled PDFs (all published)
│ │ │ ├── gift_3.4_main.pdf # Framework (Zenodo 20070101)
│ │ │ ├── g2_certified_neck.pdf # Paper A (Zenodo 19892350)
│ │ │ ├── g2_spectral.pdf # Paper B (Zenodo 19893371)
│ │ │ ├── K3_NK_Certificate.pdf # Paper C (Zenodo 19708916)
│ │ │ └── donaldson_analytic.pdf # Paper D (Zenodo 20039066)
│ │ ├── legacy/v3.3/ # v3.3 framework PDFs + markdown (archived)
│ │ ├── figures/ # Publication figures (PDF + PNG)
│ │ └── notebooks/ # Companion Jupyter notebooks
│ │ ├── g2_certified_neck_companion.ipynb
│ │ └── g2_spectral_companion.ipynb
│ ├── outreach/ # Vulgarization & blog posts
│ ├── references/ # Data & reference catalogs
│ │ ├── GIFT_ATLAS.json # Canonical structured atlas
│ │ ├── observables.csv # Machine-readable observables
│ │ ├── OBSERVABLE_REFERENCE.md # Complete observable catalog
│ │ ├── STATISTICAL_EVIDENCE.md # Rigorous statistical analysis
│ │ ├── INDEPENDENT_VALIDATIONS.md # External research converging with GIFT
│ │ └── Bibliography.md # References
│ └── validation/ # Monte Carlo validation
│ └── legacy/v3.3/ # v3.3 validation scripts (archived;
│ # v3.4 stats refresh in core/private)
│
├── docs/ # User-facing documentation + Jekyll site
│ ├── index.html # Landing page (gift-framework.github.io)
│ ├── _config.yml # Jekyll config
│ ├── GIFT_FOR_EVERYONE.md # Complete guide with everyday analogies
│ ├── FAQ.md # Common questions
│ ├── GLOSSARY.md # Technical terms
│ ├── GIFTPY_FOR_GEOMETERS.md # Guide for geometers
│ ├── INFO_GEO_FOR_PHYSICISTS.md # Guide for physicists
│ ├── LEAN_FOR_PHYSICS.md # Guide for formalization
│ ├── wiki/ # GitHub Wiki mirror (EN + FR)
│ └── figures/ # Lean blueprints, diagrams
│
├── README.md # Main repository overview
├── CHANGELOG.md # Version history
├── CITATION.md # How to cite
├── STRUCTURE.md # This file
└── LICENSE # MIT License
Quick Navigation
| Looking for… | Go to |
|---|---|
| Framework overview | README.md |
| Beginner-friendly guide | docs/GIFT_FOR_EVERYONE.md |
| Complete theory | publications/papers/markdown/GIFT_v3.4_main.md |
| All derivations | publications/papers/markdown/GIFT_v3.4_S2_derivations.md |
| Observable catalog | publications/papers/markdown/GIFT_v3.4_S3_observables.md |
| Paper A (certified G₂) | publications/papers/pdf/g2_certified_neck.pdf |
| Paper B (spectral geometry) | publications/papers/pdf/g2_spectral.pdf |
| Companion notebooks | publications/papers/notebooks/ |
| Observables data | publications/references/observables.csv |
| Blog posts & outreach | publications/outreach/ |
| Formal verification | gift-framework/core |
| v3.3 archive | publications/papers/legacy/v3.3/ |
| Technical definitions | docs/GLOSSARY.md |
Core Documents (v3.4)
| Document | Content |
|---|---|
| GIFT_v3.4_main.md | Complete theoretical framework |
| GIFT_v3.4_S1_foundations.md | E₈, G₂, K₇ mathematical construction |
| GIFT_v3.4_S2_derivations.md | 33 Type I derivations with proofs |
| GIFT_v3.4_S3_observables.md | 95-observable catalog (35 I + 19 II + 21 III + 22 IV) |
| g2_certified_neck.md (Paper A) | Computer-assisted G₂ existence proof |
| g2_spectral.md (Paper B) | Laplacian spectrum, harmonic forms |
Wiki
The GitHub Wiki provides a navigable multi-audience hub consolidating all documentation, paper summaries, reference data, blog posts, and project meta.
Related Repositories
| Repository | Content |
|---|---|
| gift-framework/core | Formal proofs (Lean 4), K₇ metric pipeline, giftpy |
Version
Current: v3.4.20 (2026-05-10) Relations: 213 conjuncts certified (core v3.4.20, 4 main-chain axioms + 11 interval-arith certificates) Predictions: 95 observables (35 Type I, exact targets, 0.39% mean deviation; PDG 2024 / NuFIT 6.0) Validation: 3M+ configs exhaustive (log₁₀ p_algebraic = −138) Papers: Framework v3.4 (Zenodo 20070101) + A (19892350) + B (19893371) + C (19708916) + D (20039066)