CUP-Ω*v7c (Closed Topological Formulation): A Completely Positive Local Evolution Law for the CUCE/Spinoza/Hilbert Programme Based on the Hilbert Hermetic Seal (Squared-Circle)

Abstract This paper presents a closed, operationally well-defined reformulation of the universal equation proposed within the CUCE/Spinoza/Hilbert programme, denoted CUP-Ω* v7c. The prior geometric analogy (an infinite-dimensional Hilbert hypersphere) is replaced by the Hilbert Hermetic Seal, i.e., a squared-circle motif embedded in an infinite-dimensional separable Hilbert space. 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 versus frequency; detailed-balance ratios at cryogenic temperatures), together with a minimal experimental protocol in superconducting qubit platforms.