The Coherence Evolution Model (CEM): Addressing Critical Feedback with Prime-Ordered Quantum Matter

This paper introduces the Coherence Evolution Model (CEM), a new framework that uses the mathematical structure of prime numbers to engineer and preserve quantum coherence in complex materials. The key contributions are: 1. Mathematical Foundations Hardy-Ramanujan & Homotopy: Prime-indexed subspaces are justified via the Hardy-Ramanujan theorem (which describes prime distribution) and interpreted as topologically distinct homotopy classes, ensuring robustness against scattering. 2. Comparison to Existing Theories BCS, SYK, AdS/CFT: Unlike BCS’s phonon-mediated continuum or the randomness of SYK, CEM enforces discrete “coherence rails” tied to primes, suppressing decoherence from composite-mode interactions. 3. Experimental Predictions ARPES Intensities: Quantitative predictions for node intensities () in materials like Bi-2212 and FeSe, complete with model vs. experimental error bars. Moiré Engineering Protocols: Detailed recipes for twisting and straining TMDs (e.g., MoS_2, WSe_2) to realize lattice spacings that approximate prime numbers. 4. Falsifiability Tests Noise-Injection Protocol: Replace prime-indexed elements in the Hamiltonian with composites and measure the collapse of the characteristic thermal conductivity scaling and ARPES sharpness. 5. Open-Science Commitment Zenodo Repository: All simulation code (Julia/Python) and data publicly available (DOI: 10.5281/zenodo.15306863). Collaboration Portal: A sign-up interface for experimentalists to propose or join follow-up ARPES and thermal-conductivity campaigns. 6. Bayesian Model Evidence Savage-Dickey Analysis: A Bayes factor favoring CEM over the ΛCDM-style baseline for coherence phenomena, with full derivation in an appendix. Overall, the paper transforms a speculative prime-based coherence idea into a rigorous, testable physical framework, offering clear pathways for both theoretic al exploration and laboratory validation.