GIFT

GIFT Framework Interactive Visualizations

Interactive Jupyter notebooks visualizing the geometric and mathematical structures underlying the GIFT framework.

Overview

These visualizations provide interactive exploration of the dimensional reduction process, precision analysis, and mathematical structures that enable topological unification of Standard Model parameters.

Notebooks

1. E₈ Root System 3D (e8_root_system_3d.ipynb)

Description: Interactive 3D visualization of the complete E₈ root system (240 roots) projected from 8D to 3D using Principal Component Analysis.

Features:

• Complete 240-root structure with two root lengths (√2 and 2)
• Color-coded by root type (short vs long)
• Interactive rotation, zoom, and pan
• Statistical analysis of root geometry
• Connection to GIFT framework (Weyl group, N_gen = 3)

Key insights:

• E₈ provides the fundamental 248-dimensional structure
• Weyl group W(E₈) = 2¹⁴ × 3⁵ × 5² × 7 determines Weyl factor = 5
• N_gen = rank(E₈) - Weyl = 8 - 5 = 3 (three generations)

Runtime: ~5-10 seconds

2. Precision Dashboard (precision_dashboard.ipynb)

Description: Comprehensive comparison of all validated dimensionless observables against experimental measurements across all physics sectors.

Features:

• Sector-wise precision gauges (Gauge, Neutrino, Lepton, Quark, Higgs, Cosmology)
• Interactive heatmap of all 16 observables sorted by precision
• Statistical distributions (histogram and box plots)
• Detailed results table with deviations
• Mean deviation: ~0.15% across all observables

Sectors covered:

• Gauge couplings (3): α⁻¹(M_Z), sin²θ_W, α_s(M_Z)
• Neutrino mixing (4): θ₁₂, θ₁₃, θ₂₃, δ_CP
• Lepton masses (4): Q_Koide, m_μ/m_e, m_τ/m_e, m_τ/m_μ
• Quark ratios (1): m_s/m_d
• Higgs sector (1): λ_H
• Cosmology (3): Ω_DE, n_s, H₀

Key results:

• 4 exact predictions (0.000% deviation): δ_CP, m_s/m_d, m_τ/m_e, N_gen
• All observables < 0.5% deviation
• Most observables < 0.2% deviation

Runtime: ~2-3 seconds

3. Dimensional Reduction Flow (dimensional_reduction_flow.ipynb)

Description: Animated visualization of the dimensional reduction process from E₈×E₈ (496D) through K₇ (99D) to the Standard Model (4D).

Features:

• Animated bar chart showing progressive reduction
• Sankey diagram illustrating information flow
• Detailed breakdown of cohomology structure
• Information compression analysis (496 → 99 = 5:1 ratio)
• Connection to quantum error-correcting codes [[496, 99, 31]]

Reduction stages:

1. E₈×E₈ (496D): Two copies of exceptional Lie algebra
2. K₇ (99D): G₂ holonomy manifold with H*(K₇) = 1 + 21 + 77
3. SM (4D): Standard Model emerges from cohomological structure

Key insights:

• H²(K₇) = 21 provides gauge boson structure
• H³(K₇) = 77 provides chiral matter content
• Information preserved through cohomological mapping
• Physical parameters as topological invariants

Runtime: ~3-5 seconds

Installation

Local Setup

1. Ensure Python 3.11+ is installed
2. Install dependencies:

   pip install -r ../requirements.txt
   

3. Launch Jupyter:

   jupyter notebook
   

Cloud Execution (Binder)

Click the badge to run all notebooks in your browser without installation:

Dependencies

Core visualization libraries:

• plotly>=5.14.0 - Interactive 3D plots and animations
• numpy>=1.21.0 - Numerical computations
• pandas>=1.3.0 - Data handling
• scikit-learn>=1.0.0 - PCA projection
• matplotlib>=3.5.0 - Static plots
• seaborn>=0.11.0 - Statistical visualizations
• kaleido>=0.2.1 - Static image export (optional)
• networkx>=3.0 - Graph structures (optional)

Usage Tips

Interactive Features

All visualizations support:

• Hover: Detailed information on data points
• Zoom: Scroll or pinch to zoom in/out
• Pan: Click and drag to move view
• Rotate (3D plots): Click and drag to rotate camera
• Export: Download as PNG/HTML using Plotly controls

Performance

For best performance:

• Run notebooks in order (some may reuse computed data)
• Use JupyterLab for enhanced interactivity
• Export HTML for offline viewing with full interactivity

Customization

All notebooks are fully editable. Key parameters to modify:

• e8_root_system_3d.ipynb: PCA components, color schemes, plot angles
• precision_dashboard.ipynb: Deviation thresholds, sector groupings
• dimensional_reduction_flow.ipynb: Animation speed, color transitions

Export Options

Each notebook can export visualizations:

• HTML: Fully interactive, shareable (.write_html())
• PNG: Static images for papers (.write_image())
• CSV: Data tables for further analysis

Example:

fig.write_html('my_visualization.html')
fig.write_image('my_visualization.png', width=1200, height=900)

Scientific References

These visualizations implement mathematical structures from:

• Supplement A: E₈ Lie algebra, K₇ manifold, dimensional reduction
• Supplement B: Rigorous proofs of exact relations
• Supplement C: Complete observable derivations
• Main Paper: Framework overview and key results

Technical Notes

Color Schemes

All visualizations use colorblind-friendly palettes:

• E₈ roots: Red (short) vs Blue (long)
• Precision: Green (excellent) → Yellow (good) → Red (tension)
• Reduction stages: Purple (E₈×E₈) → Blue (K₇) → Green (SM)

Data Validation

All numerical values are validated against:

• publications/gift_v2_notebook.ipynb (computational validation)
• Experimental values from PDG, NuFIT, Planck collaborations
• Mathematical formulas from Supplements B and C

Reproducibility

To ensure reproducibility:

• Fixed random seeds where applicable
• Explicit formulas in code comments
• Data provenance documented in each cell
• Versions pinned in requirements.txt

Contributing

Improvements welcome! Potential enhancements:

• Additional physical sectors (CKM matrix details, quark masses)
• 3D animations of K₇ twisted connected sum construction
• Interactive parameter exploration widgets
• Comparative visualizations with other unification approaches

See CONTRIBUTING.md for guidelines.

License

These visualizations are part of the GIFT Framework and are licensed under the MIT License - see LICENSE.

Citation

If you use these visualizations in your research, please cite:

@software{gift_visualizations_2025,
  title={GIFT Framework Interactive Visualizations},
  author=,
  year={2025},
  url={https://github.com/gift-framework/GIFT/tree/main/visualizations},
  note={Interactive exploration of E₈×E₈ dimensional reduction}
}

Questions and Support

• Documentation: See main README.md
• FAQ: docs/FAQ.md
• Issues: https://github.com/gift-framework/GIFT/issues
• Discussions: Use “visualization” tag for visualization-specific questions

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Gift from bit: Physical law as information geometry.

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