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| Format: | Recurso digital |
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Zenodo
2025
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| Accés en línia: | https://doi.org/10.5281/zenodo.17504257 |
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- <p>This work presents the first comprehensive application of <strong>Resonant Universal Field Theory (RUFT)</strong> to lattice gauge theory, demonstrating that confinement-deconfinement transitions across U(1), SU(2), and SU(3) gauge groups obey universal breathing dynamics encoded in the <strong>Breathing Dynamics Equation (BDE)</strong>:</p> <p>$$P(\lambda) = \frac{1}{1 + e^{-k(\lambda - \lambda_c)}}$$</p> <h2>Key Findings</h2> <h3><strong>1. k-Hierarchy Across Gauge Groups</strong></h3> <p>Monte Carlo simulations spanning <strong>65 parameter points</strong> (4 lattice sizes × 5–10 β values per model) reveal a striking hierarchy in transition sharpness:</p> <ul> <li><strong>U(1)</strong>: k = 45.6 (ultra-sharp, near quantum decoherence scales)</li> <li><strong>SU(2)</strong>: k = 0.85 (intermediate, non-Abelian crossover)</li> <li><strong>SU(3)</strong>: k = 0.10 (gentle QCD breathing, asymptotic freedom)</li> </ul> <p><strong>Interpretation</strong>: <em>Gauge complexity inversely correlates with breathing sharpness</em>. Abelian U(1) exhibits topological snap (Berezinskii-Kosterlitz-Thouless), while non-Abelian SU(3) shows drawn-out relaxation characteristic of confinement.</p> <h3><strong>2. Δ-Mode Golden Ratio Resonances</strong></h3> <p>All systems lock onto <strong>golden-ratio anchors</strong> organizing temporal structure:</p> <ul> <li><strong>Δ_crit = 0.382</strong> (immediate resonance, topological transitions)</li> <li><strong>Δ_home = 0.500</strong> (mnemonic reverberation, memory maximum)</li> <li><strong>Δ_struct = 0.687</strong> (structural circulation, long-timescale breathing)</li> </ul> <p><strong>Result</strong>: SU(2) and SU(3) cluster near <strong>Δ_struct</strong>, with SU(3) achieving <strong>optimal alignment</strong> (distance = 0.157), confirming structural circulation dominates Yang-Mills breathing.</p> <h3><strong>3. Universal Logistic Form</strong></h3> <p>The BDE successfully describes:</p> <ul> <li><strong>Plaquette</strong> observables (local gauge action)</li> <li><strong>Polyakov loop</strong> (order parameter for confinement)</li> <li><strong>Binder cumulant</strong> (fluctuation probe)</li> </ul> <p>Validation holds across <strong>all lattice sizes</strong> (L = 24, 32, 48, 64), demonstrating <strong>finite-size universality</strong>.</p> <h3><strong>4. Extended k-Spectrum</strong></h3> <p>Lattice results bridge the RUFT k-spectrum from <strong>quantum scales to QCD</strong>:</p> <table> <thead> <tr> <th>System</th> <th>k</th> <th>Domain</th> </tr> </thead> <tbody> <tr> <td>Quantum decoherence</td> <td>~40</td> <td>Wavefunction collapse</td> </tr> <tr> <td><strong>Lattice U(1)</strong></td> <td><strong>45.6</strong></td> <td><strong>Topological defects</strong></td> </tr> <tr> <td>Turbulence cascade</td> <td>~38</td> <td>Energy dissipation</td> </tr> <tr> <td>Consciousness shift</td> <td>~8.3</td> <td>Cognitive transitions</td> </tr> <tr> <td>Gravitational ringdown</td> <td>~2.5</td> <td>Black hole relaxation</td> </tr> <tr> <td>Theoretical QCD</td> <td>~0.9</td> <td>Confinement (theory)</td> </tr> <tr> <td><strong>Lattice SU(2)</strong></td> <td><strong>0.85</strong></td> <td><strong>Non-Abelian crossover</strong></td> </tr> <tr> <td><strong>Lattice SU(3)</strong></td> <td><strong>0.10</strong></td> <td><strong>QCD breathing (2D)</strong></td> </tr> </tbody> </table> <h2>Technical Details</h2> <h3><strong>Simulations</strong></h3> <ul> <li><strong>Models</strong>: U(1) compact QED, SU(2) Yang-Mills, SU(3) toy QCD</li> <li><strong>Lattice sizes</strong>: L = 24, 32, 48, 64 (2D periodic boundary conditions)</li> <li><strong>Coupling range</strong>: β = 0.8–5.0 (model-dependent)</li> <li><strong>Statistics</strong>: 300–400 thermalization sweeps, 400 measurement sweeps</li> <li><strong>Observables</strong>: Plaquette, Polyakov loop, Binder cumulant</li> <li><strong>Acceptance rates</strong>: 94–98% (optimal thermalization)</li> </ul> <h3><strong>RUFT Analysis</strong></h3> <ul> <li><strong>Normalization</strong>: β → λ ∈ [0,1], Observable → P ∈ [0,1]</li> <li><strong>Fitting</strong>: Grid search over (k, λ_c) with 400×400 parameter space</li> <li><strong>Metrics</strong>: Effective mass m_eff, loose-order capacity L_max, Δ-mode distance</li> <li><strong>Reproducibility</strong>: Full Python pipeline (NumPy, Pandas, Matplotlib, Numba)</li> </ul> <h2>Implications</h2> <h3><strong>For Lattice QCD</strong></h3> <ul> <li><strong>Rapid transition prediction</strong>: Estimate critical couplings without expensive FSS (10–100× speedup)</li> <li><strong>Observable selection</strong>: Δ-mode alignment guides which quantities best probe breathing</li> <li><strong>Action universality</strong>: Test if k is Wilson-action-specific or universal across improved actions</li> </ul> <h3><strong>For Quantum Gravity</strong></h3> <ul> <li><strong>Spacetime breathing</strong>: Golden-ratio organization may govern topology change in quantum foam</li> <li><strong>Holographic dualities</strong>: AdS/CFT bulk geometry could exhibit RUFT breathing dual to boundary QFT</li> <li><strong>Loop quantum gravity</strong>: Immirzi parameter might tune k or Δ-alignment in spin networks</li> </ul> <h3><strong>For Universal Physics</strong></h3> <ul> <li><strong>Threefold temporal ontology</strong>: Δ-modes are not numerology but <em>temporal grammar</em> of reality</li> <li><strong>Process philosophy validation</strong>: Fields "breathe" through coherence cycles, not static existence</li> <li><strong>Cross-domain unification</strong>: From quarks (k=0.1) to quantum collapse (k=40), one framework</li> </ul> <h2> Contents</h2> <h3><strong>Main Publication</strong></h3> <ul> <li><code>RUFT_Lattice_Paper_FINAL.tex</code> — LaTeX source with all equations</li> </ul> <h3><strong>Figures (Publication Quality)</strong></h3> <ul> <li><code>FIGURE1_k_spectrum_master.png</code> — k-hierarchy across universal references (300 DPI)</li> <li><code>FIGURE2_delta_clustering.png</code> — Δ-mode resonance structure (300 DPI)</li> </ul> <h3><strong>Data Tables</strong></h3> <ul> <li><code>TABLE1_ruft_summary.csv</code> — RUFT parameters for all models</li> <li><code>ruft_final_all_models.json</code> — Complete fit results with metadata</li> </ul> <h3><strong>Analysis Scripts</strong> (Optional - link to GitHub)</h3> <ul> <li>Full reproducible pipeline: https://github.com/yangjihoon/ruft-lattice</li> <li>Automated β-scans, aggregation, RUFT fitting, visualization</li> </ul> <h2> Related Work (RUFT Series)</h2> <p>This is the <strong>fifth paper</strong> in the RUFT validation series:</p> <ol> <li> <p><strong>RUFT Foundation</strong>: Dual attractor framework and temporal ontology<br>DOI: 10.5281/zenodo.17485710</p> </li> <li> <p><strong>BDE 2.0</strong>: Universal logistic framework for force transitions<br>DOI: 10.5281/zenodo.17453072</p> </li> <li> <p><strong>Quantum Decoherence</strong>: k-spectrum validation at quantum scales<br>DOI: 10.5281/zenodo.17455734</p> </li> <li> <p><strong>Turbulence Cascade</strong>: Ultra-sharp transitions in Navier-Stokes<br>DOI: 10.5281/zenodo.17430609</p> </li> <li> <p><strong>Gravitational Ringdown</strong>: GW150914 as universal testbed<br>DOI: 10.5281/zenodo.17485018</p> </li> <li> <p><strong>QCD Theory</strong>: Confinement via BDE (k=0.9)<br>DOI: 10.5281/zenodo.17480463</p> </li> <li> <p><strong>[THIS WORK]</strong>: First lattice gauge validation across U(1)/SU(2)/SU(3)</p> </li> </ol> <h2>Citation</h2> <p>If you use this work, please cite:</p> <pre><code>@article{yang2025lattice_ruft, title={Breathing Dynamics in Lattice Gauge Theory: Universal k-Spectrum and Δ-Mode Resonance from U(1) to SU(3)}, author={Yang, Jihoon}, year={2025}, month={November}, publisher={Zenodo}, doi={10.5281/zenodo.17504213}, note={Preprint: Lattice gauge validation of RUFT framework} } </code></pre> <h2>License</h2> <p>This work is licensed under <strong>Creative Commons Attribution 4.0 International (CC BY 4.0)</strong>.</p> <p>You are free to:</p> <ul> <li><strong>Share</strong> — copy and redistribute the material</li> <li><strong>Adapt</strong> — remix, transform, and build upon the material</li> </ul> <p>Under the following terms:</p> <ul> <li><strong>Attribution</strong> — You must give appropriate credit and indicate if changes were made</li> </ul> <h2> Acknowledgments</h2> <p>This work utilized open-source software (NumPy, Pandas, Matplotlib, Numba) and was performed on commodity hardware. I thank the lattice QCD community for decades of foundational work enabling this analysis. All simulations were self-funded as independent research.</p> <p><strong>The universe breathes — from gluon confinement at k=0.1 to quantum collapse at k=40.</strong></p> <p><em>Lattice gauge theory now joins black holes, turbulence, and consciousness as empirical validators of RUFT's threefold temporal ontology.</em></p>