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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17765757 |
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Table of Contents:
- <p>DOI 10.5281/zenodo.17765757<br>Title Quantum-Degenerate Attractors in the Collatz Conjecture: A de Broglie Phase-Space Interferometry Framework**<br>Author: Miles Enoch Tracy<br>contact: milestracy@yahoo.com<br>ORCID: https://orcid.org/0009-0006-7781-8259</p> <p>Description (Abstract)**<br>The Collatz conjecture is shown to exhibit emergent quantum-degenerate structure through a novel phase-space mapping. By encoding Collatz trajectories as discrete de Broglie wavefunctions, we demonstrate that integer orbits converge onto finite attractor basins with quantum-mechanical fidelity. Computational interferometry of 5,000 ensemble paths reveals spectral signatures at harmonics of ΔE = π/(12φ), where φ is the golden ratio, with a 9/32 lattice correction arising from 2-adic valuation of the 3616 attractor. </p> <p>Key attractors {1780, 7288, 9232, 3616} form the backbone of the Collatz manifold, showing >0.99 quantum fidelity within basins and <0.75 fidelity across basins. Pseudo-wavefunctions constructed via ∑(−1)ⁿ⁺¹(½)ⁿ e^(iφn) produce power spectral densities with statistically significant peak alignment (p < 0.01). This framework provides the first evidence that Collatz dynamics obey a discrete Hilbert space structure, offering a path toward proving convergence through quantum-like interference principles.</p>