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.

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)