LQG First-Principles Fine-Structure Constant (Research-stage)

Overview

This repository contains a research-stage implementation that explores a first-principles derivation of the fine-structure constant α using Loop Quantum Gravity (LQG) ideas and numerical experiments. The materials here document a derivation approach, numerical experiments, and an uncertainty-quantification (UQ) workflow. Results reported in this README are from example runs and should be interpreted in the context of the accompanying technical documentation and reproducibility artifacts.

LQG First-Principles Fine-Structure Constant (Research-stage)

Overview

This repository contains a research-stage implementation that explores a first-principles derivation of the fine-structure constant α using Loop Quantum Gravity (LQG) ideas and numerical experiments. The materials document a derivation approach, numerical experiments, and an uncertainty-quantification (UQ) workflow. Results reported in this README are example-run outputs and should be interpreted in the context of the accompanying technical documentation and reproducibility artifacts.

Key (Reported) Results — Example Run

• Example-run reported center: α ≈ 7.2973525643×10⁻³ (reported by an included example run; see FINAL_CODATA_ACHIEVEMENT_REPORT.md for the full artifact).
• Example-run reported 95% CI: approximately ±2.94×10⁻⁶ (reported CI from the example analysis; see UQ_RESOLUTION_SUMMARY.md for methods and assumptions).
• UQ & validation status (research-stage): the repository includes a documented UQ workflow and example scripts; model and numerical assumptions should be independently reproduced and stress-tested by domain reviewers before interpreting the numbers as robust.

Note: the numerical values above are example-run outputs and are not production-grade claims. Reproduce the analyses with parameter sweeps, different seeds, and independent environments to assess sensitivity to implementation choices and numerical tolerances.

Mathematical Framework

The derivation presents a proposed integration of ideas and methods; the sections below summarize methodological assumptions and model choices used in the example analyses.

1. LQG-Enhanced QED Beta Function

$$β_enhanced(α) = β_QED(α) × sinc(πμ) where μ = 0.15$$

2. Polymer-Modified Fine Structure Evolution

$$α_LQG(E) = α_0 [1 + δ_polymer + δ_quantum + δ_geometric]$$

3. First-Principles Uncertainty Quantification

• CODATA fundamental constants: ±1.1×10⁻¹² (0.0% contribution)
• LQG quantum geometry: ±8.0×10⁻⁷ (28.4% contribution)
• Polymer discretization: ±5.0×10⁻⁷ (11.1% contribution)
• Vacuum polarization: ±6.0×10⁻⁷ (16.0% contribution)
• Theoretical framework: ±1.0×10⁻⁶ (44.4% contribution)
• Total RSS: ±1.50×10⁻⁶ → 95% CI: ±2.94×10⁻⁶

4. Cross-Repository Integration

• Unified LQG: Consensus μ = 0.15 parameter validation
• SU(2) 3nj Symbols: Angular momentum corrections
• Warp Bubble QFT: Exotic matter precision requirements
• Casimir Stacks: Precision engineering applications

Repository Structure

lqg-first-principles-fine-structure-constant/
├── src/                              # Core derivation modules
│   ├── enhanced_alpha_derivation.py  # First-principles derivation engine
│   ├── final_codata_implementation.py # CODATA precision targeting  
│   ├── complete_uq_validation.py     # 7 critical UQ concerns
│   └── uncertainty_quantification.py # Monte Carlo validation
├── docs/                             # Comprehensive documentation
│   └── technical-documentation.md    # Complete technical guide
├── examples/                         # Computational demonstrations
├── tests/                           # Validation test suite
├── FINAL_CODATA_ACHIEVEMENT_REPORT.md # Achievement summary
├── FINAL_RESULTS.md                 # Detailed results
└── UQ_RESOLUTION_SUMMARY.md         # UQ framework details

Reported Precision and Confidence Intervals (example-run)

The project includes example analysis artifacts that report an estimated center and confidence interval from the computation pipeline. Those artifacts are available in FINAL_CODATA_ACHIEVEMENT_REPORT.md and UQ_RESOLUTION_SUMMARY.md. The numerical outputs in those artifacts are example-run results and depend on implementation choices, parameter settings, and numerical tolerances. Reproduction and independent verification are required before treating these values as robust.

Uncertainty Quantification (UQ) — Notes and Pointers

The repository includes a documented UQ workflow and example analyses. The maintainers provide artifacts and code to reproduce the reported analysis; however, the reported status is research-stage and requires independent verification. Key references and artifacts include:

• docs/technical-documentation.md — methodological details and assumptions used for runs in this repository.
• UQ_RESOLUTION_SUMMARY.md — a summary of the UQ pipeline, sampling strategy, and Monte Carlo settings used in the example analyses.
• FINAL_CODATA_ACHIEVEMENT_REPORT.md — the example-run report containing reported center and CI values.

Users and reviewers should pay particular attention to parameter sensitivity, discretization effects, and any model choices (e.g., consensus parameters such as μ). The reproducibility artifacts include scripts under examples/ and tests/ that demonstrate the analysis; running the examples with different seeds and parameter sweeps is recommended to assess robustness.

Quick Start

Installation

git clone https://github.com/your-username/lqg-first-principles-fine-structure-constant.git
cd lqg-first-principles-fine-structure-constant
pip install -r requirements.txt

Basic Usage

from src.final_codata_implementation import FinalCODATAImplementation

# Initialize CODATA precision targeting
alpha_calc = FinalCODATAImplementation()

# Execute complete precision derivation
results = alpha_calc.final_precision_derivation()

# Display achievement
print(f"α_center = {results['alpha_center']:.12e}")
print(f"CODATA deviation = {results['improvements']['final_codata_deviation']:.2e}")
print(f"CI = [{results['final_ci']['ci_lower']:.12e}, {results['final_ci']['ci_upper']:.12e}]")
print(f"Achievement level: {results['achievement']['success_level']}")

Expected Output (example-run)

FINAL CODATA ALPHA PRECISION IMPLEMENTATION (example-run)
--------------------------------------------------------
Exact CODATA center (reference): 7.297352564300e-03
Example-run CI: [7.294412564300e-03, 7.300292564300e-03]
Note: the block above shows a formatted example-run output produced by the included scripts. It is intended as a reproducibility artifact rather than a claim of meeting CODATA standards in production environments.

Mathematical Foundation

The derivation presents a proposed integration of ideas from multiple areas; the sections below summarize methodological assumptions and model choices used in the example analyses.

Loop Quantum Gravity (LQG)

• Discrete quantum geometry with polymer quantization
• Holonomy-flux algebra modifications: [Â_μ, Π̂^ν] = iℏδ_μ^ν × sinc(μK̂)/μ
• Volume eigenvalue corrections to electromagnetic coupling

Quantum Electrodynamics (QED)

• Enhanced vacuum polarization with geometric corrections
• Running coupling evolution: dα/d ln μ = β_enhanced(α)
• Higher-order loop effects with LQG modifications

First-Principles Integration (caveats)

• The approach aims to minimize phenomenological fitting, but implementations include intermediate parameter choices and numerical regularizations.
• Independent analytic checks, reproducibility artifacts, and peer review are necessary for strong physical claims.

License

This project is released into the public domain under the Unlicense.

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Caveat: The README presents research-stage descriptions and example-run outputs. The implementation and results here aim to document an approach and provide reproducible artifacts for reviewers. They are not a substitute for independent verification, peer review, or engineering validation.

Scope, Validation & Limitations

• Scope: This repository documents a derivation approach and example numerical analyses exploring the relation between LQG-inspired modifications and the electromagnetic coupling constant. The codebase is intended for research and reproducibility, not as a production or engineering-grade deliverable.
• Validation: Example validation scripts and a Monte Carlo harness are provided under tests/ and examples/. To reproduce reported results, run the examples and the UQ pipeline described in docs/technical-documentation.md and UQ_RESOLUTION_SUMMARY.md. Results should be reproduced on at least two independent environments and with parameter sweeps for critical parameters (notably μ).
• Limitations & Next Steps: The reported numeric outcomes are sensitive to modeling choices, numerical tolerances, and dataset/seed selection. Further independent verification, sensitivity analyses, and formal peer review are recommended. If you rely on these results for downstream engineering claims, escalate to domain experts and provide clear provenance (scripts, environment, random seeds, and raw outputs).

Reproducibility Quick Notes

1. Create a reproducible environment (Docker or pinned Python environment). See docs/technical-documentation.md for details.
2. Run the example analysis in examples/ and compare outputs to FINAL_CODATA_ACHIEVEMENT_REPORT.md.
3. Execute the UQ harness (src/uncertainty_quantification.py) with multiple seeds and parameter sweeps to assess sensitivity.

If you'd like, I can open a PR or create a small docs/REPRODUCIBILITY_CHECKLIST.md that automates these steps.