CUP-Ω* v7c as a closed topological formulation and completely positive local evolution law for the C/S/H model

This paper presents a closed, operationally well-defined reformulation of the core equation proposed within the C/S/H model, denoted CUP-Ω* v7c. The model is expressed as a Gorini–Kossakowski–Sudarshan–Lindblad (GKLS) generator acting on a finite-energy sector, ensuring linearity, complete positivity, and trace preservation. A bounded “topological tension” channel, implemented by a saturating functional calculus of the Hamiltonian, prevents high-energy divergences and yields a distinctive, falsifiable saturation law for dephasing. A minimal “triangular closure” jump structure fixes a stationary attractor state and, under KMS detailed balance, produces quantitative thermal-rate relations. We provide explicit mathematical closure results, physical interpretation, and benchmark numerical predictions (T2 saturation vs. frequency; detailed-balance ratios at cryogenic temperatures), together with a minimal experimental protocol in superconducting qubit platforms.