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)

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) | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Short Report 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Programme Based on the Hilbert Hermetic Seal (Squared-Circle) Vicente Merino Gallardo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8673041/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version 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. Theoretical Physics open quantum systems GKLS/Lindblad generator complete positivity KMS condition Hilbert space Spinoza conatus decoherence superconducting qubits process tomography Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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