# QFD-Universe

> Curated, researcher-friendly repository for Quantum Field Dynamics — sector-organized validation scripts, 1100+ Lean 4 theorems, and interactive visualizations. Clone, pip install, python run_all.py.

## Overview

- Lean 4 proof files: 247
- Proven theorems + lemmas: 1182
- Python solvers/validators: 134
- Updated: 2026-02-12

## Raw file access

Prepend to any path below: https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/

## Key entry points

- [README.md](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/README.md): Project overview with validation results
- [THEORY.md](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/THEORY.md): Full theoretical background
- [run_all.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/run_all.py): Master validation runner
- [formalization/QFD/ProofLedger.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/ProofLedger.lean): Master proof index
- [formalization/QFD/Physics/Postulates.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Physics/Postulates.lean): Axiomatic foundation
- [formalization/QFD/GoldenLoop.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/GoldenLoop.lean): Golden Loop: alpha -> beta
- [LEAN_PROOF_INDEX.txt](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/LEAN_PROOF_INDEX.txt): Flat index of all Lean proofs
- [SOLVER_INDEX.txt](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/SOLVER_INDEX.txt): Flat index of all Python solvers

## Related repositories

- [Quantum-Field-Dynamics](https://github.com/tracyphasespace/Quantum-Field-Dynamics): Full working codebase with active research and simulations
- [Quantum-Field-Dynamics llms.txt](https://raw.githubusercontent.com/tracyphasespace/Quantum-Field-Dynamics/main/llms.txt): AI discovery file for Quantum-Field-Dynamics

## Repository structure

- `formalization/QFD/` — Lean 4 formal proofs (1100+ theorems)
- `lepton/` — Validated: Golden Loop masses, g-2, Koide
- `nuclear/` — Validated: soliton solver, nuclide scaling, nuclide engine
- `cosmology/` — Validated: supernova fit, golden-loop SNe, black holes
- `cross-scale/` — Validated: ten-realms alpha -> beta pipeline
- `exploration/` — Active research (13 projects, not validated)
- `visualizations/` — Interactive HTML demos (23+)
- `data/experimental/` — Reference values (PDG, AME2020)

## Top Lean proof files (by theorem count)

- [formalization/QFD/Nuclear/BetaNGammaEDerivation.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Nuclear/BetaNGammaEDerivation.lean): Asymmetry Coupling β_n (21 theorems)
- [formalization/QFD/Nuclear/BetaNGammaEDerivation_Complete.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Nuclear/BetaNGammaEDerivation_Complete.lean): Asymmetry Coupling β_n (21 theorems)
- [formalization/QFD/Nuclear/CoreCompressionLaw.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Nuclear/CoreCompressionLaw.lean): Theorems: Proven Parameter Space Properties (21 theorems)
- [formalization/QFD/Lepton/RVacDerivation.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Lepton/RVacDerivation.lean): First-Principles Derivation of R_vac = 1/√5 (20 theorems)
- [formalization/QFD/Lepton/VortexStability.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Lepton/VortexStability.lean): Hill Vortex Geometry Constants (19 theorems)
- [formalization/QFD/Cosmology/AxisExtraction.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Cosmology/AxisExtraction.lean): Phase 2: Full Uniqueness (AxisSet = {n, -n}) (17 theorems)
- [formalization/QFD/EmergentAlgebra.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/EmergentAlgebra.lean): Algebraic Emergence of 4D Spacetime (17 theorems)
- [formalization/QFD/GA/BasisProducts.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/GA/BasisProducts.lean): Basis Product Library for Cl(3,3) (17 theorems)
- [formalization/QFD/NeutrinoMassTopology.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/NeutrinoMassTopology.lean): Topological Winding Numbers (17 theorems)
- [formalization/QFD/BlackHole/SaturationLimit.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/BlackHole/SaturationLimit.lean): Vacuum Saturation Density (16 theorems)
- [formalization/QFD/Cosmology/GalacticScaling.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Cosmology/GalacticScaling.lean): Vacuum Density Profile (16 theorems)
- [formalization/QFD/Gravity/GeometricCoupling.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Gravity/GeometricCoupling.lean): k_geom Derivation Pipeline: Bare Eigenvalue (16 theorems)
- [formalization/QFD/Photon/HelicityDecay.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Photon/HelicityDecay.lean): Photon Soliton Structure (16 theorems)
- [formalization/QFD/StabilityCriterion.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/StabilityCriterion.lean): QFD Theorem Z.1.5: Requirement for Global Stability (16 theorems)
- [formalization/QFD/Math/Exp_Bounds_Analysis.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Math/Exp_Bounds_Analysis.lean): Section 1: Basic Properties (15 theorems)
- [formalization/QFD/Lepton/Generations.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Lepton/Generations.lean): Generations as Spatial Isomers (Cl(3,3)) (14 theorems)
- [formalization/QFD/Nuclear/AlphaNDerivation.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Nuclear/AlphaNDerivation.lean): Nuclear Fine Structure Constant (14 theorems)
- [formalization/QFD/Nuclear/AlphaNDerivation_Complete.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Nuclear/AlphaNDerivation_Complete.lean): Nuclear Fine Structure Constant (14 theorems)
- [formalization/QFD/Nuclear/WellDepth.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Nuclear/WellDepth.lean): Nuclear Well Depth (14 theorems)
- [formalization/QFD/Renormalization/FiniteLoopIntegral.lean](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/formalization/QFD/Renormalization/FiniteLoopIntegral.lean): QFD Loop Integral Finiteness (13 theorems)

## Key Python solvers

- [lepton/g2-prediction/run_all.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/run_all.py): QFD Photon Sector: Run All Numerical Calculations [active]
- [nuclear/nuclide-engine/run_all.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/nuclear/nuclide-engine/run_all.py): run_all.py — Orchestrator for QFD Nuclide Engine analysis suite. [active]
- [exploration/photon-solitons/run_all.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/exploration/photon-solitons/run_all.py): QFD Photon Sector: Run All Numerical Calculations [exploration]
- [nuclear/nuclide-scaling/run_all.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/nuclear/nuclide-scaling/run_all.py): run_all.py — Replication-grade pipeline for the Core Compression Law [active]
- [nuclear/three-layer-lagrangian/run_all.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/nuclear/three-layer-lagrangian/run_all.py): run_all.py — Master orchestrator for Three-Layer LaGrangian reviewer package. [active]
- [simulation/scripts/verify_photon_soliton.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/simulation/scripts/verify_photon_soliton.py): Verify Photon Soliton: Stability in QFD Vacuum [validated]
- [lepton/g2-prediction/analysis/validate_all_constants_as_material_properties.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_all_constants_as_material_properties.py): QFD Material Science: ALL Constants as Vacuum Properties [validated]
- [lepton/g2-prediction/analysis/validate_chaos_alignment_decay.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_chaos_alignment_decay.py): QFD Atomic Resonance: Chaotic Phase Alignment → Exponential Decay [validated]
- [lepton/g2-prediction/analysis/validate_fine_structure_scaling.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_fine_structure_scaling.py): QFD: Fine Structure Constant Scaling [validated]
- [lepton/g2-prediction/analysis/validate_g2_corrected.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_g2_corrected.py): QFD: Parameter-Free Geometric g-2 Validation [validated]
- [lepton/g2-prediction/analysis/validate_g2_from_v4.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_g2_from_v4.py): QFD: Validate g-2 Anomalous Magnetic Moment Prediction from V₄ [validated]
- [lepton/g2-prediction/analysis/validate_g2_prediction.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_g2_prediction.py): QFD: G-2 Prediction Validation - Acid Test [validated]
- [lepton/g2-prediction/analysis/validate_hbar_scaling.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_hbar_scaling.py): QFD: Planck Constant Scaling Law [validated]
- [lepton/g2-prediction/analysis/validate_hydrodynamic_c.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_hydrodynamic_c.py): QFD: Hydrodynamic Derivation of Speed of Light [validated]
- [lepton/g2-prediction/analysis/validate_hydrodynamic_c_hbar_bridge.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_hydrodynamic_c_hbar_bridge.py): QFD Hydrodynamic Validation: The c - ℏ Bridge [validated]
- [lepton/g2-prediction/analysis/validate_lepton_isomers.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_lepton_isomers.py): QFD: Lepton Isomers - Geometric Mass Generation [validated]
- [lepton/g2-prediction/analysis/validate_lyapunov_predictability_horizon.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_lyapunov_predictability_horizon.py): QFD Lyapunov Predictability Horizon: Why QM Probability is Emergent [validated]
- [lepton/g2-prediction/analysis/validate_spinorbit_chaos.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_spinorbit_chaos.py): QFD Spin-Orbit Chaos: Validation of Non-Linear Coupling [validated]
- [lepton/g2-prediction/analysis/validate_unified_forces.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_unified_forces.py): QFD: Unified Forces Validation [validated]
- [lepton/g2-prediction/analysis/validate_vortex_electron_shielding.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_vortex_electron_shielding.py): QFD Vortex Electron: Shielding Mechanism Validation [validated]
- [lepton/g2-prediction/analysis/validate_vortex_force_law.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_vortex_force_law.py): QFD Vortex Electron: Phase 1 Validation [validated]
- [lepton/g2-prediction/analysis/validate_zeeman_vortex_torque.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/g2-prediction/analysis/validate_zeeman_vortex_torque.py): QFD Zeeman Effect: Vortex Torque → Frequency Shift [validated]
- [exploration/cmb-solver/cmb_solver.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/exploration/cmb-solver/cmb_solver.py): QFD CMB Solver: The Thermalized Universe [exploration]
- [exploration/lepton-isomer-ladder/appendix_g_solver.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/exploration/lepton-isomer-ladder/appendix_g_solver.py): QFD Appendix G Solver: The Lepton Isomer Ladder [exploration]
- [lepton/golden-loop/validate_leptons.py](https://raw.githubusercontent.com/tracyphasespace/QFD-Universe/main/lepton/golden-loop/validate_leptons.py): Complete Three-Lepton Test with β from Fine Structure Constant [validated]

## Validated results

Each sector has runnable tests (`python run_all.py --sector <name>`):

**Lepton**: Golden Loop alpha -> beta -> (e, mu, tau) masses (chi^2 < 1e-11), g-2 anomaly (0.45% error, no free params), Koide relation Q = 2/3 (exact)

**Nuclear**: Soliton solver for 3,558 nuclear masses (< 1% light nuclei), nuclide scaling law across 5,842 isotopes (R^2 = 0.98), nuclide engine for 4,477 nuclides (77% mode accuracy)

**Cosmology**: Supernova fit for 1,829 Type Ia SNe (chi^2/nu = 0.939, matches Lambda-CDM), Golden Loop SNe with 0 free parameters (chi^2/dof = 1.005), black hole escape simulation (~1% escape rate)

**Cross-scale**: Ten-realms pipeline from alpha through all physical scales (chi^2 < 1e-9)

## Physics summary

QFD derives from one measured input (alpha = 1/137.036):
- Golden Loop equation: 1/alpha = 2*pi^2 * (e^beta/beta) + 1 => beta = 3.043
- Lepton masses: Hill vortex geometry with beta => e, mu, tau (chi^2 < 1e-11)
- Anomalous g-2: Geometric V₄ coefficient => 0.45% error on a_e (no free params)
- Nuclear binding: 3,558 masses from soliton packing (< 1% light nuclei)
- Cosmology: SNe Ia fit with 0 free params (chi^2/dof = 1.005)
- 1100+ Lean 4 theorems proving internal mathematical consistency