GIFT

Quick Start Guide

Get up and running with the GIFT framework in minutes.

What is GIFT?

The Geometric Information Field Theory (GIFT) derives fundamental physics parameters from pure mathematics. Starting with E₈×E₈ exceptional Lie algebras and G₂ holonomy manifolds, the framework predicts 34 dimensionless observables with 0.13% mean precision using only 3 geometric parameters.

Key achievement: Reduces Standard Model’s 19 free parameters to 3 derived geometric quantities.

Installation

Option 1: Run in Browser (Recommended)

No installation needed. Click either link:

Binder (free, no account):

Google Colab (requires Google account):

Option 2: Local Installation

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

# Create virtual environment (optional but recommended)
python -m venv venv
source venv/bin/activate  # On Windows: venv\Scripts\activate

# Install dependencies
pip install -r requirements.txt

# Launch Jupyter
jupyter notebook publications/gift_v2_notebook.ipynb

Requirements: Python 3.11 or higher

5-Minute Tour

Step 1: Key Results

The framework makes exact predictions for several quantities:

Exact Relations (0% deviation by construction)

• Number of generations: N_gen = 3
• Koide relation parameter: Q = 2/3
• Strange/down quark mass ratio: m_s/m_d = 20

High-Precision Predictions (<0.01% deviation)

• Fine structure constant: α⁻¹ = 137.036 (0.001%)
• CP violation phase: δ_CP = 197° (0.005%)
• Koide formula: Q_measured = 0.666661 (0.005%)

Complete Neutrino Sector (all <0.5%)

• θ₁₂ = 33.45° (0.03% deviation)
• θ₁₃ = 8.59° (0.23% deviation)
• θ₂₃ = 48.99° (0.43% deviation)
• δ_CP = 197.3° (0.005% deviation)

Step 2: Understanding the Framework

The dimensional reduction proceeds:

E₈×E₈ (496-dimensional)
   ↓ compactification
AdS₄ × K₇
   ↓ G₂ holonomy breaking
Standard Model (SU(3)×SU(2)×U(1))

Key components:

1. E₈×E₈: Two copies of largest exceptional Lie algebra
2. K₇: 7-dimensional manifold with G₂ holonomy
3. Cohomology: H²(K₇)=ℝ²¹ → gauge bosons, H³(K₇)=ℝ⁷⁷ → fermions
4. Information: Binary architecture 496→99 → physical parameters

Step 3: Explore the Notebook

Open publications/gift_v2_notebook.ipynb and run cells sequentially:

Section 1: Three geometric parameters

β₀ = 1/(4π²)  # Base coupling
ξ = 5β₀/2     # Correlation parameter (derived!)
ε₀ = 1/8      # Symmetry breaking scale

Section 2: Derived quantities

• Fine structure constant
• Weak mixing angle
• Strong coupling
• Generation number

Section 3: Neutrino predictions

• Complete mixing matrix
• Mass hierarchy
• CP violation

Section 4: Comparison with experiment

• Tables of predictions vs measurements
• Statistical analysis
• Precision plots

Step 4: Read the Documentation

For Quick Overview → README.md

• Framework summary
• Key results at a glance
• Installation and usage

For Theoretical Details → publications/gift_main.md

• Complete framework (~1100 lines)
• Mathematical structure
• Experimental validation

For Mathematical Rigor → publications/supplements/B_rigorous_proofs.md

• Exact proofs of 9 key relations
• Step-by-step derivations
• Topological arguments

For Specific Topics → publications/supplements/

• A: Mathematical foundations (E₈, K₇, reduction)
• C: All 34 observable derivations
• E: Falsification criteria and experimental tests

Key Predictions by Physics Sector

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%

Source: Supplement C, Sections 4-6

Neutrino Sector

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%

Source: Supplement C, Section 8

CKM Matrix

All 10 elements predicted with mean deviation 0.11%.

Source: Supplement C, Section 9

Cosmological Sector

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

Source: Main paper Section 4.7, Extensions document

Understanding the Mathematics

Three Geometric Parameters

β₀ = 1/(4π²): Base coupling strength

• Emerges from E₈ root system normalization
• Related to fine structure constant via β₀ = α·(geometric factors)

ξ = 5β₀/2: Correlation parameter

• Exactly derived: Not independent! Previously treated as free parameter
• Governs breaking patterns and mixing matrices

ε₀ = 1/8: Symmetry breaking scale

• From G₂ holonomy structure
• Controls mass hierarchies

Parameter count: 3 (down from Standard Model’s 19)

Example: Fine Structure Constant

Derivation chain:

1. Start with E₈ structure: dim(E₈) = 248
2. K₇ cohomology: b₂ = 21, b₃ = 77
3. Branching E₈ → SU(5)×SU(3) → SU(3)×SU(2)×U(1)
4. Normalize gauge couplings via β₀
5. Result: α⁻¹ = 137.036… (0.001% deviation)

See: Supplement C.4 for complete derivation

Example: Three Generations

Exact relation:

N_gen = rank(E₈) - rank(Weyl(E₇))
      = 8 - 5
      = 3

Status: PROVEN via index theorem See: Supplement B.4 for rigorous proof

Finding Specific Information

Want to understand a specific prediction? → Check Supplement C (Complete Derivations)

Need rigorous mathematical proof? → Check Supplement B (Rigorous Proofs)

Looking for experimental comparison? → Check Supplement D (Phenomenology)

Want to know if framework can be falsified? → Check Supplement E (Falsification Criteria)

Need definition of technical term? → Check docs/GLOSSARY.md

Have a question? → Check docs/FAQ.md or open issue on GitHub

Common First Questions

Q: Is this tested experimentally? A: Yes. 34 observables compared with experiment, mean deviation 0.13%. See Supplement D and docs/EXPERIMENTAL_VALIDATION.md.

Q: How many free parameters? A: 3 geometric parameters (β₀, ξ, ε₀), where ξ is derived from β₀ via exact relation. Standard Model has 19.

Q: Can this be falsified? A: Yes. Multiple clear tests outlined in Supplement E. Strongest: fourth generation discovery or δ_CP deviation from 197° at high precision.

Q: What about gravity? A: Framework derives low-energy parameters but doesn’t yet address quantum gravity directly. Connection to information theory suggests potential path forward.

Q: Why E₈×E₈? A: E₈ is largest exceptional Lie algebra with unique properties. Two copies provide sufficient structure for Standard Model content via dimensional reduction. Binary architecture (496→99) may encode optimal information compression.

Next Steps

For Theorists

1. Read main paper: publications/gift_main.md
2. Study mathematical foundations: publications/supplements/A_math_foundations.md
3. Examine proofs: publications/supplements/B_rigorous_proofs.md
4. Explore extensions and open questions

For Experimentalists

1. Review predictions: publications/gift_main.md Section 4
2. Check falsification criteria: publications/supplements/E_falsification.md
3. See experimental timeline: docs/EXPERIMENTAL_VALIDATION.md
4. Identify relevant experiments for your facility

For Students

1. Start with README.md overview
2. Run notebook: publications/gift_v2_notebook.ipynb
3. Read FAQ: docs/FAQ.md
4. Study glossary: docs/GLOSSARY.md
5. Work through main paper sections

For Contributors

1. Read CONTRIBUTING.md for guidelines
2. Check STRUCTURE.md for repository organization
3. Review open issues on GitHub
4. Propose improvements or extensions

Getting Help

Documentation: Most questions answered in:

• README.md (overview)
• docs/FAQ.md (common questions)
• docs/GLOSSARY.md (definitions)

Issues: For bugs, questions, or suggestions:

• https://github.com/gift-framework/GIFT/issues

Discussion: For broader topics:

• GitHub Discussions (coming soon)

Citation

If you use GIFT in your research:

@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.

Summary

In 5 minutes you can:

1. Run notebook in browser (Binder/Colab)
2. See 34 predictions vs experiment
3. Understand basic framework structure
4. Explore specific sectors of interest

In 30 minutes you can:

1. Read main paper introduction
2. Understand dimensional reduction chain
3. See derivation of key results
4. Check falsification criteria

In a few hours you can:

1. Study complete mathematical foundations
2. Verify numerical calculations
3. Examine all 34 predictions in detail
4. Understand connections to information theory

Welcome to the GIFT framework. The mathematics is rich, the predictions are precise, and the implications are profound.

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“From bit to GIFT”

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