Mathematical Verification

Machine-verified proofs with live CI status

Proof CI Status

Live Verification

3

Claims Verified

5

Tools Available

📁 Source Code

Overview

RFT 15.5 demonstrates through exhaustive computer algebra that the embedding E₈ → E₆ × SU(3) is the unique way to achieve three-generation phenomenology in 4D spacetime. This page provides machine-verified proofs and downloadable evidence.

All calculations are reproducible via Docker containers and run automatically in our CI/CD pipeline, ensuring mathematical rigor and transparency.

Disclaimer: "Proven" status indicates mathematical/computational verification only. Physical validity requires independent experimental confirmation.

🚀 Launch Live Verification

Run Notebooks Interactively

Experience the unification math yourself! Launch any notebook in a live Jupyter environment. Tweak parameters, modify calculations, see the proofs execute in real-time.

💡 Tip: Try changing c₂ from 3 to 4 in Three_Generation_Index and see how it breaks the 3-family result!

🔧 Verification Tools

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GAP Subgroup Scanner

Exhaustive E₈ → E₆×SU(3) uniqueness verification

📓 Download Notebook 📊 Download Results CSV
📐

Index Theorem Calculator

Hirzebruch-Riemann-Roch χ = -3 verification

📓 Download Calculator 📓 Monad Construction
🧮

Bundle Decomposer

SU(4) → SM group breaking analysis

📓 Download Decomposer 📓 Cohomology Tools

✅ Latest Verification Results

Real-time mathematical proof status

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E₈ Uniqueness

✓ PROVEN

1/453,060 embeddings valid

Three Families

χ = -3

Index theorem verified

SU(4) Breaking

9 → 8+1

Generators preserved

🔄 Continuous Integration

All calculations run automatically on every code change. GAP scans complete in ~5min, Sage calculations in ~2min.

📈 View CI Runs 💻 Source Code

📄 RFT 15.6: Reproducibility & Web-Integration Toolkit

Complete documentation for reproducing all mathematical proofs, including Docker containers, CI/CD workflows, and web integration specifications.

📥 Download PDF 📥 RFT 15.5: Exhaustive Scan

📄 Supporting Papers

Traditional academic papers (optional reading)

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RFT 15.5 - Computational Proof

Exhaustive Subgroup Scan & Instanton Bound Theorem

PDF DOCX

RFT 15.4 - Uniqueness Theory

Mathematical foundations for embedding uniqueness

PDF DOCX

RFT 15.3 - Phenomenology

First-Principles Phenomenology & RG Lock-In

PDF DOCX

All 15.x Series

Complete paper collection

Browse All

Note: Papers provide traditional academic context. For hands-on verification, use the computational tools above.

📊 Live Prediction Comparator

Compare RFT vs PDG Data

Test RFT predictions against experimental measurements. Select a prediction type and see how our theoretical values compare to PDG 2024 data.

Enter energy scale in GeV

RFT Prediction

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±— uncertainty

PDG 2024 Data

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±— experimental

Agreement

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σ from PDG

🔗 Related Resources