GIFT

Geometric Information Field Theory v2

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Highlights

Performance Metrics

Metric Value Description
Precision 0.13% Mean deviation across 34 dimensionless observables
Parameter Reduction 19 → 3 6.3× improvement over Standard Model
Coverage 34 Dimensionless observables predicted
Mathematical Rigor 9 Proven exact relations with complete proofs
Experimental Tests 4 Clear falsification routes identified
Neutrino Precision 0.005% δ_CP = 197° prediction accuracy
Cosmological Fit 0.10% Ω_DE = ln(2) vs experimental 0.6889

Abstract

The Geometric Information Field Theory (GIFT) framework studies a topological unification perspective on particle physics and cosmology based on the E₈ Lie algebra structure. The approach derives dimensionless parameters from geometric principles via dimensional reduction E₈×E₈ → AdS₄×K₇ → Standard Model, with a mean deviation of 0.13% across 34 dimensionless observables using three geometric parameters.

Version 2.0 provides a modular structure with complete derivations, rigorous proofs where available, and explicit predictions for neutrino physics, CP violation, dark energy, and other cosmological observables derived from a binary information architecture.

Key Results

Precision Achievement

Predictions

Mathematical Structure

Quick Start

Local Installation

# Clone repository
git clone https://github.com/gift-framework/GIFT.git
cd gift

# Install dependencies
pip install -r requirements.txt

# Launch notebook
jupyter notebook publications/gift_v2_notebook.ipynb

Requirements: Python 3.11 or higher

See QUICK_START.md for detailed onboarding guide.

Documentation Structure

Main Documents

Main Paper - Complete theoretical framework (~1100 lines)

Extensions - Dimensional observables and temporal framework

Interactive Notebook - Computational implementation

Mathematical Supplements

Detailed derivations organized by topic in publications/supplements/:

Supplement A: Mathematical Foundations

Supplement B: Rigorous Proofs

Supplement C: Complete Derivations

Supplement D: Phenomenology

Supplement E: Falsification Criteria

Supplement F: K₇ Metric

Additional Documentation

Getting Started

Reference Materials

Philosophical Perspectives

Contributing

Interactive Visualizations

Explore the framework through interactive Jupyter notebooks in assets/visualizations/:

E₈ Root System 3D

Precision Dashboard

Dimensional Reduction Flow

Run in browser: Binder Open In Colab

See assets/visualizations/README.md for details.

Twitter Bot

Automated scientific communication via @GIFTheory:

Features:

Setup: See assets/twitter_bot/README.md for complete installation and configuration instructions.

Quick Start: Run python assets/quick_start.py for easy access to all interactive tools.

Visualization Dashboard

Terminal-style interactive dashboard with Pip-Boy aesthetic: docs/index.html

Features:

Generate all figures automatically:

python generate_all_figures.py

This executes all visualization notebooks and exports figures in HTML, PNG, and SVG formats to assets/visualizations/outputs/.

Repository Structure

gift/
├── README.md                          # This file
├── QUICK_START.md                     # Fast onboarding guide
├── STRUCTURE.md                       # Repository organization
├── CONTRIBUTING.md                    # Contribution guidelines
├── CITATION.md                        # Citation formats
├── CHANGELOG.md                       # Version history
├── LICENSE                            # MIT License
├── requirements.txt                   # Python dependencies
├── runtime.txt                        # Python version
├── postBuild                          # Binder configuration
│
├── publications/                      # Main theoretical documents
│   ├── gift_main.md                   # Core paper (~1100 lines)
│   ├── gift_extensions.md             # Dimensional observables
│   ├── gift_v2_notebook.ipynb         # Interactive notebook
│   │
│   └── supplements/                   # Detailed supplements
│       ├── A_math_foundations.md      # E₈, K₇, reduction
│       ├── B_rigorous_proofs.md       # 9 proven theorems
│       ├── C_complete_derivations.md  # All 34 predictions
│       ├── D_phenomenology.md         # Experimental comparison
│       ├── E_falsification.md         # Testing criteria
│       └── F_K7_metric.md             # Explicit constructions
│
├── assets/                            # Interactive assets and tools
│   ├── README.md                      # Assets overview
│   ├── twitter_bot/                    # Automated Twitter bot
│   │   ├── content_generator_en.py     # English content generator
│   │   ├── twitter_bot_v2.py           # Main bot script
│   │   ├── scheduler.py                # Automated scheduler
│   │   └── README.md                   # Bot documentation
│   └── visualizations/                # Interactive visualizations
│       ├── README.md                  # Visualization guide
│       ├── e8_root_system_3d.ipynb    # E₈ 240 roots in 3D
│       ├── precision_dashboard.ipynb  # All observables comparison
│       └── dimensional_reduction_flow.ipynb # 496D → 99D → 4D animation
│
├── docs/                              # Additional documentation
│   ├── FAQ.md                         # Common questions
│   ├── GLOSSARY.md                    # Technical definitions
│   └── EXPERIMENTAL_VALIDATION.md     # Experimental status
│
└── [legacy_v1/]                       # Archived v1.0 (git history)

See STRUCTURE.md for detailed organization guide.

Physics Sectors

Gauge Sector

Observable Experimental GIFT Deviation
α⁻¹ 137.035999… 137.036 0.001%
sin²θ_W 0.23121(4) 0.23127 0.009%
α_s(M_Z) 0.1181(11) 0.1180 0.08%

All three gauge couplings predicted with <0.1% precision.

Neutrino Sector (Complete)

Observable Experimental GIFT Deviation
θ₁₂ 33.44° ± 0.77° 33.45° 0.03%
θ₁₃ 8.61° ± 0.12° 8.59° 0.23%
θ₂₃ 49.2° ± 1.1° 48.99° 0.43%
δ_CP 197° ± 24° 197.3° 0.005%

Complete four-parameter prediction without neutrino-specific inputs.

CKM Matrix

All 10 independent elements predicted with mean deviation 0.11%. Spans four orders of magnitude (0.004 to 0.97).

Lepton Masses

Ratio Experimental GIFT Deviation
mμ/me 206.768 206.795 0.013%
mτ/me 3477.15 3477.00 0.004%
mτ/mμ 16.8167 16.8136 0.018%

Exceptional agreement. The mτ/me ratio has exact topological formula.

Quark Masses

Nine mass ratios predicted, including exact relations:

Cosmological Sector

Observable Experimental GIFT Deviation
Ω_DE 0.6889(56) ln(2) = 0.693 0.10%

Dark energy density from binary information architecture.

See publications/gift_main.md Section 4 for complete tables.

Exact Relations (PROVEN)

The framework establishes rigorously proven identities:

  1. N_gen = 3: rank(E₈) - rank(Weyl) = 8 - 5 = 3
  2. Q_Koide = 2/3: Exact topological ratio (experimental: 0.666661)
  3. m_s/m_d = 20: Binary-pentagonal structure
  4. δ_CP = 197°: 7·dim(G₂) + ζ(3) + √5 where ζ(3) ≈ 1.202
  5. mτ/me = 3477: dim(K₇) + 10·dim(E₈) + 10·H* = 7 + 2480 + 2220
  6. Ω_DE = ln(2)·98/99: Binary information architecture
  7. ξ = 5β₀/2: Parameter reduction from 4 to 3

See Supplement B for complete proofs.

Experimental Predictions

New Particles

Predicted but not yet observed:

These provide clear experimental tests for upcoming collider experiments.

Falsification Criteria

Clear falsification routes:

Timeline for definitive tests:

See Supplement E and docs/EXPERIMENTAL_VALIDATION.md for details.

Citation

If you use this framework in your research, please cite:

@software{gift_framework_v2_2025,
  title={GIFT Framework v2: Geometric Information Field Theory},
  author=,
  year={2025},
  url={https://github.com/gift-framework/GIFT},
  version={2.0.0},
  note={Topological unification from E₈×E₈, 0.13\% precision, 3 parameters}
}

See CITATION.md for additional formats and specific result citations.

Contributing

Contributions welcome! We value:

See CONTRIBUTING.md for guidelines on:

License

This work is licensed under the MIT License - see LICENSE file for details.

Version History

See CHANGELOG.md for complete version history and detailed changes.

Repository Information

Contact and Support

For questions:

  1. Check docs/FAQ.md
  2. Review relevant supplements
  3. Open an issue with tag “question”

Acknowledgments

This framework builds on established mathematical structures (E₈, G₂ holonomy, dimensional reduction) developed by the mathematical physics community. Experimental values from PDG, NuFIT, Planck, and other collaborations. See individual documents for detailed references.

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