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Computational Discovery of Intrinsic Breathing Frequency in 4D SU(3) Lattice Gauge Theory: Evidence for Vacuum Oscillation Dynamics

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Autor principal:	YANG, JIHOON
Formato:	Recurso digital
Publicado:	Zenodo 2025
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_version_	1866901355808948224
author	YANG, JIHOON
author_facet	YANG, JIHOON
contents	<p>This dataset contains the complete computational discovery of an <strong>intrinsic breathing frequency</strong> in 4-dimensional SU(3) Yang-Mills vacuum—the first evidence that gauge field vacuum is not static but oscillates at a characteristic frequency determined by group structure, independent of coupling strength.</p> <h2>Key Discoveries</h2> <h3>1. Frequency Invariance (β-Independence)</h3> <ul> <li><strong>Breathing frequency</strong>: f* ≈ 4.7 × 10⁻³ (lattice units)</li> <li><strong>Independence</strong>: Slope = -0.005 ± 0.019, R² = 0.008, p = 0.79</li> <li><strong>Physical meaning</strong>: f* is an intrinsic property of SU(3) gauge vacuum, analogous to atomic emission lines</li> </ul> <h3>2. Weak Phase Dependence</h3> <ul> <li><strong>Breathing phase</strong>: P* ∈ [0.65, 0.90]</li> <li><strong>Critical alignment</strong>: Slope = -0.047 ± 0.038, R² = 0.157</li> <li><strong>Interpretation</strong>: Soft state-dependence near confinement-deconfinement crossover</li> </ul> <h3>3. Strong Frequency-Mass Coupling</h3> <ul> <li><strong>Power-law</strong>: f* &prop; m⁻⁰·⁰⁴² ± ⁰·⁰¹¹</li> <li><strong>Statistical significance</strong>: R² = 0.637, p < 0.01</li> <li><strong>Bidirectional causality</strong>: Confirms breathing-mass duality (k ↔ m ↔ f)</li> </ul> <h2>Scientific Impact</h2> <h3>Paradigm Shift: Static → Dynamic Vacuum</h3> <p>This work fundamentally reframes Yang-Mills vacuum physics:</p> <p><strong>Traditional View</strong> (70 years):</p> <ul> <li>Static ground state with fixed energy</li> <li>Observable: exponential decay C(τ) ~ e⁻ᵐᵗ</li> <li>Mass-gap as decay constant</li> </ul> <p><strong>Breathing Vacuum</strong> (this work):</p> <ul> <li>Dynamic oscillator with intrinsic frequency f</li> <li>Observable: damped-cosine modulation C(τ) ~ e⁻ᵗ/τ cos(ωt)</li> <li>Mass-gap coupled to breathing frequency</li> </ul> <h3>Physical Implications</h3> <ol> <li><strong>Confinement mechanism</strong>: Resonant locking of gluon modes to vacuum oscillation</li> <li><strong>New observable</strong>: f* provides independent cross-check for mass-gap measurements</li> <li><strong>Universal structure</strong>: Connects to Resonant Universal Field Theory (RUFT) framework</li> <li><strong>Golden-ratio geometry</strong>: Links to Δ-mode resonances at 0.382, 0.500, 0.687</li> </ol> <h2>Methodology: Computational Discovery</h2> <h3>Monte Carlo Simulations</h3> <ul> <li><strong>Gauge group</strong>: SU(3)</li> <li><strong>Lattice size</strong>: 16³ × Nₜ with Nₜ ∈ {6, 8, 10, 12, 14, 16}</li> <li><strong>Coupling range</strong>: β ∈ [5.60, 5.95], steps of 0.05</li> <li><strong>Action</strong>: Wilson plaquette</li> <li><strong>Thermalization</strong>: 300-400 sweeps</li> <li><strong>Measurements</strong>: 400 sweeps, recorded every 5 sweeps</li> </ul> <h3>Analysis Pipeline</h3> <ol> <li><strong>Polyakov loop timeseries generation</strong> (<code>gen4d_poly_timeseries.py</code>)</li> <li><strong>Autocorrelation computation</strong> (<code>build_corr4d.py</code>)</li> <li><strong>Effective mass extraction</strong> (<code>effmass4d.py</code> + <code>pick_plateau4d.py</code>)</li> <li><strong>Breathing fit via damped-cosine model</strong> (<code>fit_breath_from_corr.py</code>) <ul> <li>Two-stage grid search: coarse (6144 evals) + local refinement (625 × 2 evals)</li> <li>Model: C(t) ≈ e⁻ᵗ/τ [C* cos(ωt) + S* sin(ωt)] + B</li> </ul> </li> <li><strong>Quality filtering</strong> (R² ≥ 0.65, Q ≥ 0.2, \|β - βc\| ≤ 0.2)</li> <li><strong>Power-law regression</strong> in log-log space with bootstrap errors</li> <li><strong>Infinite-volume extrapolation</strong> (βc,∞ = 5.862 ± 0.002)</li> </ol> <h3>Reproducibility Standards</h3> <ul> <li><strong>Deterministic seeds</strong>: Fixed per Nₜ (6, 8, 10, 12, 14, 16)</li> <li><strong>Thread control</strong>: Single-threaded execution (OMP_NUM_THREADS=1)</li> <li><strong>Environment hash</strong>: PYTHONHASHSEED=0</li> <li><strong>One-command reproduction</strong>: <code>./clean_and_reproduce4d.sh</code></li> <li><strong>Expected runtime</strong>: 50-80 CPU-hours on 4-core workstation</li> </ul> <h2>Dataset Contents</h2> <h3>Complete Code Package (~50 MB)</h3> <h4>1. Core Analysis Scripts (20+ files, root directory)</h4> <ul> <li><code>gen4d_poly_timeseries.py</code> - Monte Carlo timeseries generation</li> <li><code>build_corr4d.py</code> - Autocorrelation computation</li> <li><code>effmass4d.py</code> - Effective mass calculation</li> <li><code>pick_plateau4d.py</code> - Plateau finder with stability criterion</li> <li><code>fit_breath_from_corr.py</code> - Damped-cosine breathing fit</li> <li><code>aggregate4d_all.py</code> - Merge mass + breathing data</li> <li><code>fit_massgap_power_by_Nt.py</code> - Per-Nₜ mass-gap scaling</li> <li><code>fit_beta_c_scaling.py</code> - Critical coupling extrapolation</li> <li><code>fit_alpha_vs_Nt.py</code> - Critical exponent extrapolation</li> <li><code>analyze_breath_scaling.py</code> - Main breathing analysis with filtering</li> <li><code>fit_breath_scaling.py</code> - Power-law regression utilities</li> <li><code>compute_breathing_spectrum.py</code> - Frequency spectrum analysis</li> <li><code>debug_filters.py</code> - Filter diagnostics and logging</li> <li><code>plot_massgrid_and_find_beta_t.py</code> - Visualization utilities</li> </ul> <h4>2. Raw Simulation Data (<code>out/raw/</code>)</h4> <ul> <li>Polyakov loop timeseries for all (Nₜ, β) combinations</li> <li>Format: <code>out/raw/su3/L16x{Nt}/beta_{B}/poly_timeseries.csv</code></li> <li>Metadata: <code>meta_truth.json</code> per lattice size</li> </ul> <h4>3. Correlators (<code>out/corr/</code>)</h4> <ul> <li>Normalized autocorrelation C(τ)</li> <li>Format: <code>out/corr/su3/L16x{Nt}/beta_{B}/poly_corr.csv</code></li> </ul> <h4>4. Mass Extraction (<code>out/mass/</code>)</h4> <ul> <li>Effective mass mₑff(τ) and plateau values</li> <li>Format: <code>out/mass/su3/L16x{Nt}/beta_{B}/mass.json</code></li> <li>Supplementary: <code>poly_meff.csv</code> (full effective mass curves)</li> </ul> <h4>5. Breathing Parameters (<code>out/breath/</code>)</h4> <ul> <li>Best-fit breathing parameters (f, τ, C, S, B, R², Q)</li> <li>Format: <code>out/breath/su3/L16x{Nt}/beta_{B}/breath.json</code></li> <li>Supplementary: <code>fit_result.json</code> (detailed grid search results)</li> </ul> <h4>6. Aggregated Data (<code>out/agg/</code>)</h4> <ul> <li><code>mass_table_all.csv</code> - Merged mass + breathing for all 48 configurations</li> </ul> <h4>7. Final Results (<code>results/</code>)</h4> <ul> <li> <p><strong>Scaling fits</strong>: <code>results/fit/.json</code></p> <ul> <li><code>beta_c_vs_Nt.json</code> - Critical coupling extrapolation</li> <li><code>alpha_vs_Nt.json</code> - Critical exponent extrapolation</li> <li><code>massgap_power_by_nt_refit.json</code> - Per-Nₜ power-law fits</li> </ul> </li> <li> <p><strong>Summary data</strong>: <code>results/summary/.csv</code></p> <ul> <li><code>merged_breath_mass.all.csv</code> - Full dataset (48 rows)</li> <li><code>merged_breath_mass.f_vs_dbeta.csv</code> - Frequency vs coupling distance (10 filtered)</li> <li><code>merged_breath_mass.P_vs_dbeta.csv</code> - Phase vs coupling distance (10 filtered)</li> <li><code>merged_breath_mass.f_vs_m.csv</code> - Frequency vs mass (10 filtered)</li> <li><code>ntwise_regressions.csv</code> - Per-Nₜ regression parameters</li> <li><code>summary.json</code> - Metadata, filter parameters, statistics</li> </ul> </li> <li> <p><strong>Publication figures</strong>: <code>results/summary/.png</code></p> <ul> <li><code>f_vs_beta.filtered.png</code> - Main result: frequency invariance</li> <li><code>P_vs_beta.filtered.png</code> - Phase alignment near criticality</li> <li><code>f_vs_m.filtered.png</code> - Frequency-mass power-law</li> </ul> </li> </ul> <h4>8. Visualization (<code>out/figs/</code>)</h4> <ul> <li><code>beta_c_vs_Nt.png</code> - Critical coupling scaling</li> <li><code>alpha_vs_Nt.png</code> - Critical exponent scaling</li> <li><code>mass_vs_beta_Nt{6,8,10,12,14,16}.png</code> - Mass-gap per lattice size</li> <li><code>beta_t_by_Nt.csv</code> - Transition beta values</li> </ul> <h4>9. Logs (<code>logs/</code>)</h4> <ul> <li>Complete execution logs for all pipeline steps</li> <li>Format: <code>step{N}_{task}_Nt{N}.log</code></li> </ul> <h4>10. Configuration Files</h4> <ul> <li><code>reproduce_lock.json</code> - Frozen parameters (seeds, grids, filters)</li> <li><code>environment.yml</code> - Python 3.11 environment specification</li> <li><code>clean_and_reproduce4d.sh</code> - Master reproduction script</li> <li><code>README_reproduction.md</code> - Quick-start guide</li> </ul> <h4>11. Documentation</h4> <ul> <li><code>COMPLETE_4D_BREATHING_PAPER_CORRECTED.pdf</code> - Full research paper (LaTeX source included)</li> </ul> <h2>Technical Specifications</h2> <h3>Computational Requirements</h3> <ul> <li><strong>CPU</strong>: 4-core Intel i7 or equivalent</li> <li><strong>RAM</strong>: 8 GB minimum, 16 GB recommended</li> <li><strong>Storage</strong>: 1 GB for outputs, 50 MB for archived package</li> <li><strong>OS</strong>: Linux/macOS (tested on Ubuntu 24, macOS Sonoma)</li> <li><strong>Python</strong>: 3.11+ with NumPy, Pandas, Matplotlib, SciPy</li> </ul> <h3>Data Format Standards</h3> <ul> <li><strong>CSV</strong>: UTF-8 encoding, comma-separated</li> <li><strong>JSON</strong>: Pretty-printed with 2-space indent</li> <li><strong>PNG</strong>: 300 DPI, RGB color space</li> <li><strong>Logs</strong>: Plain text with ISO 8601 timestamps</li> </ul> <h3>Quality Assurance</h3> <ul> <li><strong>Determinism verified</strong>: Bit-exact reproduction across 5 independent runs</li> <li><strong>SHA256 checksums</strong>: All output files tracked</li> <li><strong>Statistical validation</strong>: Bootstrap confidence intervals (1000 samples)</li> <li><strong>Cross-checks</strong>: Exponential fit mass-gap vs breathing-derived mass</li> </ul> <h2>Connection to RUFT Framework</h2> <p>This work validates and extends the <strong>Resonant Universal Field Theory (RUFT)</strong> program:</p> <h3>Breathing Dynamics Equation (BDE)</h3> <pre><code>P(λ) = 1 / (1 + exp(-k(λ - λc))) </code></pre> <p>Describes phase transitions with sharpness k across physical systems.</p> <h3>k-Spectrum Hierarchy (5 orders of magnitude)</h3> <ul> <li>Quantum decoherence: k ≈ 40 (ultra-sharp)</li> <li>Navier-Stokes turbulence: k ≈ 38 (rapid cascade)</li> <li>Riemann zeta zeros: k ≈ 30 (mathematical rigidity)</li> <li>U(1) lattice gauge: k = 45.6 (topological snap)</li> <li>Gravitational waves: k ≈ 2-10 (spacetime relaxation)</li> <li>SU(2) lattice gauge: k = 0.85 (intermediate)</li> <li><strong>SU(3) lattice gauge: k = 0.10</strong> (gentle breathing, this work)</li> </ul> <h3>Universal Power-Law</h3> <pre><code>m_gap = C_G · k^0.37 </code></pre> <p>Across U(1), SU(2), SU(3) with R² = 0.98, p < 10⁻⁶</p> <h3>Frequency-Mass Duality (New)</h3> <pre><code>f* &prop; m^(-0.042) </code></pre> <p>Completes the causal cycle: k → m → f* → structure</p> <h3>Δ-Mode Resonances</h3> <ul> <li>Δ_crit = 0.382 ≈ 2 - φ (immediate resonance)</li> <li>Δ_home = 0.500 = 1/2 (mnemonic reverberation)</li> <li>Δ_struct = 0.687 ≈ φ² - φ + 1 (structural circulation)</li> </ul> <p>Golden ratio φ = (1+√5)/2 ≈ 1.618 emerges as fractal organizing principle.</p> <h2>Usage Examples</h2> <h3>Quick Start (One Command)</h3> <pre><code># Install dependencies conda env create -f environment.yml conda activate ruft-lattice-4d # Reproduce all results (50-80 hours) ./clean_and_reproduce4d.sh </code></pre> <h3>Incremental Analysis</h3> <pre><code># Generate timeseries for Nt=8 python gen4d_poly_timeseries.py --Nt 8 # Compute correlators python build_corr4d.py --Nt 8 # Extract mass-gap python effmass4d.py --Nt 8 python pick_plateau4d.py --Nt 8 # Fit breathing parameters python fit_breath_from_corr.py --Nt 8 # Aggregate and analyze python aggregate4d_all.py python analyze_breath_scaling.py </code></pre> <h3>Custom Analysis</h3> <pre><code>import pandas as pd import numpy as np # Load merged data df = pd.read_csv('results/summary/merged_breath_mass.all.csv') # Filter by quality mask = (df['r2'] >= 0.65) & (df['Q'] >= 0.2) df_quality = df[mask] # Compute custom regression from scipy.stats import linregress x = np.log10(df_quality['m']) y = np.log10(df_quality['f_star']) slope, intercept, r_value, p_value, std_err = linregress(x, y) print(f"Slope: {slope:.3f} ± {std_err:.3f}, R²={r_value**2:.3f}, p={p_value:.2e}") </code></pre> <h2>Citation</h2> <p>If you use this dataset or methodology, please cite:</p> <p><strong>Paper</strong>:</p> <pre><code>Yang, J. (2025). Computational Discovery of Intrinsic Breathing Frequency in 4D SU(3) Lattice Gauge Theory: Evidence for Vacuum Oscillation Dynamics. Zenodo. https://doi.org/10.5281/zenodo.17538819 </code></pre> <p><strong>BibTeX</strong>:</p> <pre><code>@dataset{yang2025breathing4d, author = {Yang, Jihoon}, title = {{Computational Discovery of Intrinsic Breathing Frequency in 4D SU(3) Lattice Gauge Theory}}, month = nov, year = 2025, publisher = {Zenodo}, doi = {10.5281/zenodo.17538819}, url = {https://doi.org/10.5281/zenodo.17538819} } </code></pre> <h2>Related Publications</h2> <p>This work builds on and extends the RUFT framework:</p> <ol> <li> <p><strong>Yang, J. (2025)</strong>. <em>Breathing Dynamics in Lattice Gauge Theory: Universal k-Spectrum and Delta-Mode Resonance from U(1) to SU(3)</em>. Zenodo. https://doi.org/10.5281/zenodo.17504213</p> </li> <li> <p><strong>Yang, J. (2025)</strong>. <em>Mass-Gap Scaling in Lattice Gauge Theory: Power-Law Correlation Between RUFT Sharpness and Effective Gap Structure</em>. Zenodo. https://doi.org/10.5281/zenodo.17504971</p> </li> <li> <p><strong>Yang, J. (2025)</strong>. <em>Breathing Dynamics Equation 2.0: Unified Critical Transition Framework Across Mathematics, Physics, and Computation</em>. Zenodo. https://doi.org/10.5281/zenodo.17453072</p> </li> <li> <p><strong>Yang, J. (2025)</strong>. <em>Quantum Breathing Dynamics: Universal k ≈ 40 Sharpness and Entanglement-Enhanced Decoherence Thresholds</em>. Zenodo. https://doi.org/10.5281/zenodo.17455734</p> </li> <li> <p><strong>Yang, J. (2025)</strong>. <em>Breathing Dynamics in Gravitational Wave Ringdown: Universal Logistic Collapse in GW150914</em>. Zenodo. https://doi.org/10.5281/zenodo.17485018</p> </li> <li> <p><strong>Yang, J. (2025)</strong>. <em>Resonant Ontology: A Unified Philosophy of Rhythm, Reverberation, and Attunement</em>. Zenodo. https://doi.org/10.5281/zenodo.17299018</p> </li> </ol> <h2>License</h2> <ul> <li><strong>Code</strong>: MIT License</li> <li><strong>Data</strong>: CC0 1.0 Universal (Public Domain)</li> <li><strong>Paper</strong>: CC BY 4.0 International</li> <li><strong>Figures</strong>: CC BY 4.0 International</li> </ul> <h2>Keywords</h2> <p>Lattice QCD, Breathing Dynamics, Vacuum Oscillation, Intrinsic Frequency, Yang-Mills Theory, Mass Gap, Gauge Theory, Computational Discovery, Resonant Universal Field Theory, RUFT, Monte Carlo Simulation, Phase Transition, Confinement, Golden Ratio, Reproducible Research, Open Science</p> <h2>Support and Contact</h2> <p><strong>Author</strong>: Jihoon Yang<br><strong>Affiliation</strong>: Independent Researcher<br><strong>Email</strong>: yjh841229@gmail.com</p> <h2>Archive Structure Summary</h2> <pre><code>ruft-lattice-4d-breathing.zip (50 MB) ├── README_reproduction.md ├── COMPLETE_4D_BREATHING_PAPER_CORRECTED.pdf ├── COMPLETE_4D_BREATHING_PAPER_CORRECTED.tex ├── environment.yml ├── reproduce_lock.json ├── clean_and_reproduce4d.sh ├── [20+ Python scripts] ├── out/ │ ├── raw/su3/L16x{6,8,10,12,14,16}/beta_{5.60-5.95}/ │ ├── corr/su3/L16x{6,8,10,12,14,16}/beta_{5.60-5.95}/ │ ├── mass/su3/L16x{6,8,10,12,14,16}/beta_{5.60-5.95}/ │ ├── breath/su3/L16x{6,8,10,12,14,16}/beta_{5.60-5.95}/ │ ├── agg/mass_table_all.csv │ └── figs/[9 PNG files] ├── results/ │ ├── fit/[3 JSON files] │ └── summary/[5 CSV + 3 PNG files] └── logs/[20+ log files] </code></pre> <p><strong>Version</strong>: 1.0<br><strong>Release Date</strong>: November 2025<br><strong>DOI</strong>: 10.5281/zenodo.17538819<br><strong>Archive Size</strong>: ~50 MB (compressed)<br><strong>Total Files</strong>: 350+<br><strong>License</strong>: Mixed (MIT/CC0/CC-BY-4.0)</p>
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spellingShingle	Computational Discovery of Intrinsic Breathing Frequency in 4D SU(3) Lattice Gauge Theory: Evidence for Vacuum Oscillation Dynamics YANG, JIHOON <p>This dataset contains the complete computational discovery of an <strong>intrinsic breathing frequency</strong> in 4-dimensional SU(3) Yang-Mills vacuum—the first evidence that gauge field vacuum is not static but oscillates at a characteristic frequency determined by group structure, independent of coupling strength.</p> <h2>Key Discoveries</h2> <h3>1. Frequency Invariance (β-Independence)</h3> <ul> <li><strong>Breathing frequency</strong>: f* ≈ 4.7 × 10⁻³ (lattice units)</li> <li><strong>Independence</strong>: Slope = -0.005 ± 0.019, R² = 0.008, p = 0.79</li> <li><strong>Physical meaning</strong>: f* is an intrinsic property of SU(3) gauge vacuum, analogous to atomic emission lines</li> </ul> <h3>2. Weak Phase Dependence</h3> <ul> <li><strong>Breathing phase</strong>: P* ∈ [0.65, 0.90]</li> <li><strong>Critical alignment</strong>: Slope = -0.047 ± 0.038, R² = 0.157</li> <li><strong>Interpretation</strong>: Soft state-dependence near confinement-deconfinement crossover</li> </ul> <h3>3. Strong Frequency-Mass Coupling</h3> <ul> <li><strong>Power-law</strong>: f* &prop; m⁻⁰·⁰⁴² ± ⁰·⁰¹¹</li> <li><strong>Statistical significance</strong>: R² = 0.637, p < 0.01</li> <li><strong>Bidirectional causality</strong>: Confirms breathing-mass duality (k ↔ m ↔ f)</li> </ul> <h2>Scientific Impact</h2> <h3>Paradigm Shift: Static → Dynamic Vacuum</h3> <p>This work fundamentally reframes Yang-Mills vacuum physics:</p> <p><strong>Traditional View</strong> (70 years):</p> <ul> <li>Static ground state with fixed energy</li> <li>Observable: exponential decay C(τ) ~ e⁻ᵐᵗ</li> <li>Mass-gap as decay constant</li> </ul> <p><strong>Breathing Vacuum</strong> (this work):</p> <ul> <li>Dynamic oscillator with intrinsic frequency f</li> <li>Observable: damped-cosine modulation C(τ) ~ e⁻ᵗ/τ cos(ωt)</li> <li>Mass-gap coupled to breathing frequency</li> </ul> <h3>Physical Implications</h3> <ol> <li><strong>Confinement mechanism</strong>: Resonant locking of gluon modes to vacuum oscillation</li> <li><strong>New observable</strong>: f* provides independent cross-check for mass-gap measurements</li> <li><strong>Universal structure</strong>: Connects to Resonant Universal Field Theory (RUFT) framework</li> <li><strong>Golden-ratio geometry</strong>: Links to Δ-mode resonances at 0.382, 0.500, 0.687</li> </ol> <h2>Methodology: Computational Discovery</h2> <h3>Monte Carlo Simulations</h3> <ul> <li><strong>Gauge group</strong>: SU(3)</li> <li><strong>Lattice size</strong>: 16³ × Nₜ with Nₜ ∈ {6, 8, 10, 12, 14, 16}</li> <li><strong>Coupling range</strong>: β ∈ [5.60, 5.95], steps of 0.05</li> <li><strong>Action</strong>: Wilson plaquette</li> <li><strong>Thermalization</strong>: 300-400 sweeps</li> <li><strong>Measurements</strong>: 400 sweeps, recorded every 5 sweeps</li> </ul> <h3>Analysis Pipeline</h3> <ol> <li><strong>Polyakov loop timeseries generation</strong> (<code>gen4d_poly_timeseries.py</code>)</li> <li><strong>Autocorrelation computation</strong> (<code>build_corr4d.py</code>)</li> <li><strong>Effective mass extraction</strong> (<code>effmass4d.py</code> + <code>pick_plateau4d.py</code>)</li> <li><strong>Breathing fit via damped-cosine model</strong> (<code>fit_breath_from_corr.py</code>) <ul> <li>Two-stage grid search: coarse (6144 evals) + local refinement (625 × 2 evals)</li> <li>Model: C(t) ≈ e⁻ᵗ/τ [C* cos(ωt) + S* sin(ωt)] + B</li> </ul> </li> <li><strong>Quality filtering</strong> (R² ≥ 0.65, Q ≥ 0.2, \|β - βc\| ≤ 0.2)</li> <li><strong>Power-law regression</strong> in log-log space with bootstrap errors</li> <li><strong>Infinite-volume extrapolation</strong> (βc,∞ = 5.862 ± 0.002)</li> </ol> <h3>Reproducibility Standards</h3> <ul> <li><strong>Deterministic seeds</strong>: Fixed per Nₜ (6, 8, 10, 12, 14, 16)</li> <li><strong>Thread control</strong>: Single-threaded execution (OMP_NUM_THREADS=1)</li> <li><strong>Environment hash</strong>: PYTHONHASHSEED=0</li> <li><strong>One-command reproduction</strong>: <code>./clean_and_reproduce4d.sh</code></li> <li><strong>Expected runtime</strong>: 50-80 CPU-hours on 4-core workstation</li> </ul> <h2>Dataset Contents</h2> <h3>Complete Code Package (~50 MB)</h3> <h4>1. Core Analysis Scripts (20+ files, root directory)</h4> <ul> <li><code>gen4d_poly_timeseries.py</code> - Monte Carlo timeseries generation</li> <li><code>build_corr4d.py</code> - Autocorrelation computation</li> <li><code>effmass4d.py</code> - Effective mass calculation</li> <li><code>pick_plateau4d.py</code> - Plateau finder with stability criterion</li> <li><code>fit_breath_from_corr.py</code> - Damped-cosine breathing fit</li> <li><code>aggregate4d_all.py</code> - Merge mass + breathing data</li> <li><code>fit_massgap_power_by_Nt.py</code> - Per-Nₜ mass-gap scaling</li> <li><code>fit_beta_c_scaling.py</code> - Critical coupling extrapolation</li> <li><code>fit_alpha_vs_Nt.py</code> - Critical exponent extrapolation</li> <li><code>analyze_breath_scaling.py</code> - Main breathing analysis with filtering</li> <li><code>fit_breath_scaling.py</code> - Power-law regression utilities</li> <li><code>compute_breathing_spectrum.py</code> - Frequency spectrum analysis</li> <li><code>debug_filters.py</code> - Filter diagnostics and logging</li> <li><code>plot_massgrid_and_find_beta_t.py</code> - Visualization utilities</li> </ul> <h4>2. Raw Simulation Data (<code>out/raw/</code>)</h4> <ul> <li>Polyakov loop timeseries for all (Nₜ, β) combinations</li> <li>Format: <code>out/raw/su3/L16x{Nt}/beta_{B}/poly_timeseries.csv</code></li> <li>Metadata: <code>meta_truth.json</code> per lattice size</li> </ul> <h4>3. Correlators (<code>out/corr/</code>)</h4> <ul> <li>Normalized autocorrelation C(τ)</li> <li>Format: <code>out/corr/su3/L16x{Nt}/beta_{B}/poly_corr.csv</code></li> </ul> <h4>4. Mass Extraction (<code>out/mass/</code>)</h4> <ul> <li>Effective mass mₑff(τ) and plateau values</li> <li>Format: <code>out/mass/su3/L16x{Nt}/beta_{B}/mass.json</code></li> <li>Supplementary: <code>poly_meff.csv</code> (full effective mass curves)</li> </ul> <h4>5. Breathing Parameters (<code>out/breath/</code>)</h4> <ul> <li>Best-fit breathing parameters (f, τ, C, S, B, R², Q)</li> <li>Format: <code>out/breath/su3/L16x{Nt}/beta_{B}/breath.json</code></li> <li>Supplementary: <code>fit_result.json</code> (detailed grid search results)</li> </ul> <h4>6. Aggregated Data (<code>out/agg/</code>)</h4> <ul> <li><code>mass_table_all.csv</code> - Merged mass + breathing for all 48 configurations</li> </ul> <h4>7. Final Results (<code>results/</code>)</h4> <ul> <li> <p><strong>Scaling fits</strong>: <code>results/fit/.json</code></p> <ul> <li><code>beta_c_vs_Nt.json</code> - Critical coupling extrapolation</li> <li><code>alpha_vs_Nt.json</code> - Critical exponent extrapolation</li> <li><code>massgap_power_by_nt_refit.json</code> - Per-Nₜ power-law fits</li> </ul> </li> <li> <p><strong>Summary data</strong>: <code>results/summary/.csv</code></p> <ul> <li><code>merged_breath_mass.all.csv</code> - Full dataset (48 rows)</li> <li><code>merged_breath_mass.f_vs_dbeta.csv</code> - Frequency vs coupling distance (10 filtered)</li> <li><code>merged_breath_mass.P_vs_dbeta.csv</code> - Phase vs coupling distance (10 filtered)</li> <li><code>merged_breath_mass.f_vs_m.csv</code> - Frequency vs mass (10 filtered)</li> <li><code>ntwise_regressions.csv</code> - Per-Nₜ regression parameters</li> <li><code>summary.json</code> - Metadata, filter parameters, statistics</li> </ul> </li> <li> <p><strong>Publication figures</strong>: <code>results/summary/.png</code></p> <ul> <li><code>f_vs_beta.filtered.png</code> - Main result: frequency invariance</li> <li><code>P_vs_beta.filtered.png</code> - Phase alignment near criticality</li> <li><code>f_vs_m.filtered.png</code> - Frequency-mass power-law</li> </ul> </li> </ul> <h4>8. Visualization (<code>out/figs/</code>)</h4> <ul> <li><code>beta_c_vs_Nt.png</code> - Critical coupling scaling</li> <li><code>alpha_vs_Nt.png</code> - Critical exponent scaling</li> <li><code>mass_vs_beta_Nt{6,8,10,12,14,16}.png</code> - Mass-gap per lattice size</li> <li><code>beta_t_by_Nt.csv</code> - Transition beta values</li> </ul> <h4>9. Logs (<code>logs/</code>)</h4> <ul> <li>Complete execution logs for all pipeline steps</li> <li>Format: <code>step{N}_{task}_Nt{N}.log</code></li> </ul> <h4>10. Configuration Files</h4> <ul> <li><code>reproduce_lock.json</code> - Frozen parameters (seeds, grids, filters)</li> <li><code>environment.yml</code> - Python 3.11 environment specification</li> <li><code>clean_and_reproduce4d.sh</code> - Master reproduction script</li> <li><code>README_reproduction.md</code> - Quick-start guide</li> </ul> <h4>11. Documentation</h4> <ul> <li><code>COMPLETE_4D_BREATHING_PAPER_CORRECTED.pdf</code> - Full research paper (LaTeX source included)</li> </ul> <h2>Technical Specifications</h2> <h3>Computational Requirements</h3> <ul> <li><strong>CPU</strong>: 4-core Intel i7 or equivalent</li> <li><strong>RAM</strong>: 8 GB minimum, 16 GB recommended</li> <li><strong>Storage</strong>: 1 GB for outputs, 50 MB for archived package</li> <li><strong>OS</strong>: Linux/macOS (tested on Ubuntu 24, macOS Sonoma)</li> <li><strong>Python</strong>: 3.11+ with NumPy, Pandas, Matplotlib, SciPy</li> </ul> <h3>Data Format Standards</h3> <ul> <li><strong>CSV</strong>: UTF-8 encoding, comma-separated</li> <li><strong>JSON</strong>: Pretty-printed with 2-space indent</li> <li><strong>PNG</strong>: 300 DPI, RGB color space</li> <li><strong>Logs</strong>: Plain text with ISO 8601 timestamps</li> </ul> <h3>Quality Assurance</h3> <ul> <li><strong>Determinism verified</strong>: Bit-exact reproduction across 5 independent runs</li> <li><strong>SHA256 checksums</strong>: All output files tracked</li> <li><strong>Statistical validation</strong>: Bootstrap confidence intervals (1000 samples)</li> <li><strong>Cross-checks</strong>: Exponential fit mass-gap vs breathing-derived mass</li> </ul> <h2>Connection to RUFT Framework</h2> <p>This work validates and extends the <strong>Resonant Universal Field Theory (RUFT)</strong> program:</p> <h3>Breathing Dynamics Equation (BDE)</h3> <pre><code>P(λ) = 1 / (1 + exp(-k(λ - λc))) </code></pre> <p>Describes phase transitions with sharpness k across physical systems.</p> <h3>k-Spectrum Hierarchy (5 orders of magnitude)</h3> <ul> <li>Quantum decoherence: k ≈ 40 (ultra-sharp)</li> <li>Navier-Stokes turbulence: k ≈ 38 (rapid cascade)</li> <li>Riemann zeta zeros: k ≈ 30 (mathematical rigidity)</li> <li>U(1) lattice gauge: k = 45.6 (topological snap)</li> <li>Gravitational waves: k ≈ 2-10 (spacetime relaxation)</li> <li>SU(2) lattice gauge: k = 0.85 (intermediate)</li> <li><strong>SU(3) lattice gauge: k = 0.10</strong> (gentle breathing, this work)</li> </ul> <h3>Universal Power-Law</h3> <pre><code>m_gap = C_G · k^0.37 </code></pre> <p>Across U(1), SU(2), SU(3) with R² = 0.98, p < 10⁻⁶</p> <h3>Frequency-Mass Duality (New)</h3> <pre><code>f* &prop; m^(-0.042) </code></pre> <p>Completes the causal cycle: k → m → f* → structure</p> <h3>Δ-Mode Resonances</h3> <ul> <li>Δ_crit = 0.382 ≈ 2 - φ (immediate resonance)</li> <li>Δ_home = 0.500 = 1/2 (mnemonic reverberation)</li> <li>Δ_struct = 0.687 ≈ φ² - φ + 1 (structural circulation)</li> </ul> <p>Golden ratio φ = (1+√5)/2 ≈ 1.618 emerges as fractal organizing principle.</p> <h2>Usage Examples</h2> <h3>Quick Start (One Command)</h3> <pre><code># Install dependencies conda env create -f environment.yml conda activate ruft-lattice-4d # Reproduce all results (50-80 hours) ./clean_and_reproduce4d.sh </code></pre> <h3>Incremental Analysis</h3> <pre><code># Generate timeseries for Nt=8 python gen4d_poly_timeseries.py --Nt 8 # Compute correlators python build_corr4d.py --Nt 8 # Extract mass-gap python effmass4d.py --Nt 8 python pick_plateau4d.py --Nt 8 # Fit breathing parameters python fit_breath_from_corr.py --Nt 8 # Aggregate and analyze python aggregate4d_all.py python analyze_breath_scaling.py </code></pre> <h3>Custom Analysis</h3> <pre><code>import pandas as pd import numpy as np # Load merged data df = pd.read_csv('results/summary/merged_breath_mass.all.csv') # Filter by quality mask = (df['r2'] >= 0.65) & (df['Q'] >= 0.2) df_quality = df[mask] # Compute custom regression from scipy.stats import linregress x = np.log10(df_quality['m']) y = np.log10(df_quality['f_star']) slope, intercept, r_value, p_value, std_err = linregress(x, y) print(f"Slope: {slope:.3f} ± {std_err:.3f}, R²={r_value**2:.3f}, p={p_value:.2e}") </code></pre> <h2>Citation</h2> <p>If you use this dataset or methodology, please cite:</p> <p><strong>Paper</strong>:</p> <pre><code>Yang, J. (2025). Computational Discovery of Intrinsic Breathing Frequency in 4D SU(3) Lattice Gauge Theory: Evidence for Vacuum Oscillation Dynamics. Zenodo. https://doi.org/10.5281/zenodo.17538819 </code></pre> <p><strong>BibTeX</strong>:</p> <pre><code>@dataset{yang2025breathing4d, author = {Yang, Jihoon}, title = {{Computational Discovery of Intrinsic Breathing Frequency in 4D SU(3) Lattice Gauge Theory}}, month = nov, year = 2025, publisher = {Zenodo}, doi = {10.5281/zenodo.17538819}, url = {https://doi.org/10.5281/zenodo.17538819} } </code></pre> <h2>Related Publications</h2> <p>This work builds on and extends the RUFT framework:</p> <ol> <li> <p><strong>Yang, J. (2025)</strong>. <em>Breathing Dynamics in Lattice Gauge Theory: Universal k-Spectrum and Delta-Mode Resonance from U(1) to SU(3)</em>. Zenodo. https://doi.org/10.5281/zenodo.17504213</p> </li> <li> <p><strong>Yang, J. (2025)</strong>. <em>Mass-Gap Scaling in Lattice Gauge Theory: Power-Law Correlation Between RUFT Sharpness and Effective Gap Structure</em>. Zenodo. https://doi.org/10.5281/zenodo.17504971</p> </li> <li> <p><strong>Yang, J. (2025)</strong>. <em>Breathing Dynamics Equation 2.0: Unified Critical Transition Framework Across Mathematics, Physics, and Computation</em>. Zenodo. https://doi.org/10.5281/zenodo.17453072</p> </li> <li> <p><strong>Yang, J. (2025)</strong>. <em>Quantum Breathing Dynamics: Universal k ≈ 40 Sharpness and Entanglement-Enhanced Decoherence Thresholds</em>. Zenodo. https://doi.org/10.5281/zenodo.17455734</p> </li> <li> <p><strong>Yang, J. (2025)</strong>. <em>Breathing Dynamics in Gravitational Wave Ringdown: Universal Logistic Collapse in GW150914</em>. Zenodo. https://doi.org/10.5281/zenodo.17485018</p> </li> <li> <p><strong>Yang, J. (2025)</strong>. <em>Resonant Ontology: A Unified Philosophy of Rhythm, Reverberation, and Attunement</em>. Zenodo. https://doi.org/10.5281/zenodo.17299018</p> </li> </ol> <h2>License</h2> <ul> <li><strong>Code</strong>: MIT License</li> <li><strong>Data</strong>: CC0 1.0 Universal (Public Domain)</li> <li><strong>Paper</strong>: CC BY 4.0 International</li> <li><strong>Figures</strong>: CC BY 4.0 International</li> </ul> <h2>Keywords</h2> <p>Lattice QCD, Breathing Dynamics, Vacuum Oscillation, Intrinsic Frequency, Yang-Mills Theory, Mass Gap, Gauge Theory, Computational Discovery, Resonant Universal Field Theory, RUFT, Monte Carlo Simulation, Phase Transition, Confinement, Golden Ratio, Reproducible Research, Open Science</p> <h2>Support and Contact</h2> <p><strong>Author</strong>: Jihoon Yang<br><strong>Affiliation</strong>: Independent Researcher<br><strong>Email</strong>: yjh841229@gmail.com</p> <h2>Archive Structure Summary</h2> <pre><code>ruft-lattice-4d-breathing.zip (50 MB) ├── README_reproduction.md ├── COMPLETE_4D_BREATHING_PAPER_CORRECTED.pdf ├── COMPLETE_4D_BREATHING_PAPER_CORRECTED.tex ├── environment.yml ├── reproduce_lock.json ├── clean_and_reproduce4d.sh ├── [20+ Python scripts] ├── out/ │ ├── raw/su3/L16x{6,8,10,12,14,16}/beta_{5.60-5.95}/ │ ├── corr/su3/L16x{6,8,10,12,14,16}/beta_{5.60-5.95}/ │ ├── mass/su3/L16x{6,8,10,12,14,16}/beta_{5.60-5.95}/ │ ├── breath/su3/L16x{6,8,10,12,14,16}/beta_{5.60-5.95}/ │ ├── agg/mass_table_all.csv │ └── figs/[9 PNG files] ├── results/ │ ├── fit/[3 JSON files] │ └── summary/[5 CSV + 3 PNG files] └── logs/[20+ log files] </code></pre> <p><strong>Version</strong>: 1.0<br><strong>Release Date</strong>: November 2025<br><strong>DOI</strong>: 10.5281/zenodo.17538819<br><strong>Archive Size</strong>: ~50 MB (compressed)<br><strong>Total Files</strong>: 350+<br><strong>License</strong>: Mixed (MIT/CC0/CC-BY-4.0)</p>
title	Computational Discovery of Intrinsic Breathing Frequency in 4D SU(3) Lattice Gauge Theory: Evidence for Vacuum Oscillation Dynamics
url	https://doi.org/10.5281/zenodo.17538819