COS-CNS develops the causal-dynamics module of the Collapsing-Structure (COS) program. The manuscript studies a verifiable class of nonunitary, discrete-time dynamics on structures equipped with a causal partial order, focusing on operational no-signaling, finite-speed influence propagation, and scheduling robustness. The framework is formulated at the level of completely positive trace-preserving channels, instruments, local algebras, dependency neighborhoods, and locally implementable causal admissibility filters. It carefully separates unconditional branch-ignored dynamics from conditional trajectory or postselected descriptions, so that no-signaling is defined through operational marginal statistics rather than through selected branches. The main results apply to a restricted and auditable class of local, filtered channels satisfying explicit locality, support-propagation, causal-filtering, and scheduling/confluence assumptions. Within this class, the paper formulates no-signaling criteria, a strict discrete causal-cone statement, and robustness targets for approximate or leakage-affected dynamics. These results are not claimed to hold for arbitrary COS microdynamics or for nonlocal global projectors. COS-CNS also identifies failure modes in which the assumptions break down, including nonlocal Kraus support, nonlocal causal filtering, deterministic branch control, and nonconfluent scheduling. These counterexamples clarify why the locality and admissibility conditions are necessary for an operational causality minimum. The release includes a technical supplement with reproducibility protocols, numerical demonstrations, algorithmic details, supplementary proofs, negative controls, and audit conventions. The numerical material illustrates no-signaling tests, influence-cone diagnostics, and scheduling-robustness checks under controlled benchmark conditions. COS-CNS therefore serves as the causality and finite-speed-influence verification layer for COS-QD-like discrete open-system dynamics, while treating the connection to relativistic microcausality, Lorentz symmetry, and continuum causality as a restricted and future-facing interface rather than a completed derivation.
Attila Görhöny (Sun,) studied this question.