Stability Geometry of Branch Structures in Open Quantum Systems

Stability Geometry of Branch Structures in Open Quantum Systems. DOI: https://doi.org/10.17605/OSF.IO/RKPTQ. Main paper PDF: tability_Geometry_of_Branch_Structures_in_Open_Quantum_Systems.pdf. Causal–Continuity Stabilization Theory (CCST) characterizes macroscopic causal persistence as a physical stability property of finite substrates, rather than as an ontological feature of the universal wavefunction. In its original formulation, CCST formalized descriptive admissibility: a coarse-grained macroscopic causal history remains well-posed only when thermodynamic dissipation stays below a substrate-dependent bound and when coarse-grained dynamical sensitivity preserves closure. This work extends CCST by addressing a logically distinct question: not only whether a macroscopic description remains admissible within a branch, but whether a branch structure itself can remain dynamically coherent as an organized physical entity under sustained environmental coupling. Although unitary quantum mechanics preserves all components of the global quantum state, organized branch structure may dynamically disperse into microscopic degrees of freedom in open-system dynamics, thereby losing the correlation patterns required for macroscopic organization. We distinguish structural dispersion (loss of branch-level organizational coherence) from Causal Exit (loss of description-level definability on a finite physical substrate), emphasizing that these correspond to stability failures at distinct physical layers and should not be conflated. Using standard open-system effective-action and influence-functional formalisms, we motivate a dynamical weighting over coarse-grained path ensembles: microscopic dynamics induces a non-uniform stability geometry in path space through irreversible dynamical suppression rather than probabilistic selection, without introducing collapse, selection rules, or inter-branch transport. Finally, we introduce a minimal toy model to visualize the qualitative sensitivity of branch-structural persistence under controlled stability thresholds. The model is strictly illustrative and is accompanied by transparent parameter definitions and a reproducible numerical implementation in the appendix.