Coherence-Rupture-Regeneration Theory and Unistochastic Quantum Mechanics: Exploring Structural Correspondences in History-Bearing Systems

We explore structural correspondences between Coherence-Rupture-Regeneration(CRR) theory; a philosophically-motivated mathematical framework for systemsmaintaining identity through discontinuous change, and Barandes’ unistochasticformulation of quantum mechanics. CRR emerged from phenomenological obser-vations of development and adaptation, crystallising into an operator formalismthrough iterative mathematical refinement. It provides a mathematical structurefor temporality itself: coherence (accumulated past), rupture (present moment ofchoice), and regeneration (constrained future). Barandes’ approach reformulatesquantum mechanics using directed conditional probabilities on configuration spaces,providing rigorous foundations whilst remaining agnostic about wave-function on-tology. Both frameworks describe non-Markovian dynamics where entire historymatters, not just present state; a structure we argue naturally supports relationalrather than dualistic ontology. We demonstrate that coherence fields, being dis-tributed historical records rather than localised variables, provide a mechanism forevading Bell’s theorem assumptions: quantum correlations arise from past local in-teractions encoded in non-Markovian field structure, not faster-than-light influences.This offers a mathematically grounded argument for why quantum mechanics maybe compatible with appropriately refined causal locality. We identify suggestivecorrespondences: coherence accumulation appears to correspond to indivisibility;rupture events align with division events; both satisfy causal locality conditions.Whilst these correspondences currently remain conjectural rather than rigorouslyproven, several insights appear robust, particularly regarding non-Markovian fieldstructure and its implications for ontology. We provide careful analysis distinguish-ing established results from speculative proposals, identify concrete research ques-tions, and propose experimental tests. The framework resonates with philosophicaltraditions (process philosophy, phenomenology, Barbour’s Platonia) though theseconnections remain suggestive rather than proven. If validated, this synthesis couldprovide both rigorous quantum foundations and a general mathematical languagefor adaptive systems across scales, from quantum to ecological to cultural domains.Note: Mathematical development and LATEX compilation were conducted with assist-ance from Claude Sonnet 4.5 (Anthropic, 2025).