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| Format: | Recurso digital |
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Zenodo
2025
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| Accès en ligne: | https://doi.org/10.5281/zenodo.18011260 |
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- <p><strong>The Arc Theorem: A Geometric Theory of Transformation Rates</strong></p> <p>This repository contains the complete formal derivation, validation record, and supporting evidence for the <strong>Arc Theorem</strong> — a theorem establishing that observed scaling exponents in rate laws are geometric invariants arising from traversal through imaginary space.</p> <p>The theorem states:</p> <p><span><span><span>α=dT+dC×ϕ2π\alpha = d_T + d_C \times \frac{\phi}{2\pi}</span><span><span><span>α</span><span>=</span></span><span><span><span>d</span><span><span><span><span><span><span>T</span></span></span><span></span></span></span></span></span><span>+</span></span><span><span><span>d</span><span><span><span><span><span><span>C</span></span></span><span></span></span></span></span></span><span>×</span></span><span><span><span><span><span><span>2<span>π</span><span>ϕ</span></span><span></span></span></span></span></span></span></span></span></span></p> <p>where:</p> <ul> <li> <p><span><span>α\alpha</span><span><span><span>α</span></span></span></span> is the observed scaling exponent</p> </li> <li> <p><span><span>dTd_T</span><span><span><span><span>d</span><span><span><span><span><span><span>T</span></span></span><span></span></span></span></span></span></span></span></span> is the terminal (mode-counting) dimension</p> </li> <li> <p><span><span>dCd_C</span><span><span><span><span>d</span><span><span><span><span><span><span>C</span></span></span><span></span></span></span></span></span></span></span></span> is the cycling dimension</p> </li> <li> <p><span><span>ϕ\phi</span><span><span><span>ϕ</span></span></span></span> is the traversal angle in imaginary space</p> </li> </ul> <p>The Arc Theorem demonstrates that historically empirical laws across physics, chemistry, biology, and dynamical systems are projections of trajectories through structured imaginary space.</p> <p>This release (v4) establishes theorem status through:</p> <ul> <li> <p>Independent derivations from Wigner threshold theory</p> </li> <li> <p>Instanton and Euclidean action formalism</p> </li> <li> <p>Classical evanescent wave analysis (Maxwell-only)</p> </li> <li> <p>Cross-domain validation and preregistered tests</p> </li> </ul> <p>The repository includes formal proofs, derivation manuscripts, empirical validation figures, preregistration documents, reproducibility code, and interactive visualizers. All results are fully reproducible using included data and scripts.</p> <p>This is an archival scientific release. No files are reorganized or rewritten.</p> <p>See <code>README_V4.md</code> and <code>CHANGELOG.md</code> for full version details.</p>