Causal Architecture Theory (CAT). The VERCETTI Principle and Canonical Branch Selection

Causal Architecture Theory (CAT). The VERCETTI Principle and Canonical Branch Selection | 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 Research Article Causal Architecture Theory (CAT). The VERCETTI Principle and Canonical Branch Selection David Alfyorov, Igor Shnyukov This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9541310/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 gives a canonical formulation of Causal Architecture Theory (CAT). It replaces a collection of discrete branch choices with a single physical selection principle, VERCETTI, short for Variational Endpoint-Resolved Causal Entropic Terminal Trace Invariance. The principle states that the realized branch must be the minimal terminal spectral structure that allows a finite causal observer, working inside a two-endpoint Alexandrov diamond, to extract scalar observables from the spectral action without internal orientation ambiguity, without introducing a new continuous modulus, and without changing the strict SCT core. The central result is a derivation of VERCETTI, within the stated class, from first physical principles F 0–F 8: finiteness of the observer, Lorentzian causality, scalar instrument readout, the spectral variational principle, chirality of the low-energy sector, absence of hidden continuous moduli, non-tautological selector status, Wilsonian semigroup behavior, and terminality of scalar completion. Within this explicit class, VERCETTI has theorem-level status relative to F 0–F 8, while its application to nature remains conditional on the physical validity of those principles. The resulting branch data, including the Pati–Salam finite algebra, the binary algebra C⊕C, the CM point τ⋆ = i √ 2, j(τ⋆) = 8000, the automorphism σ7, the profile e−u , and ξ = 1/6, are treated as a single minimal repair chain for three deficits: chiral gauge structure, two-endpoint orientation, and pro-torsor scalarization. The manuscript also clarifies the status of the CJ bridge formula: the N8/ 9 scaling follows only under the single-active-shell hypothesis and is not promoted to core status. All algebraic checks reported in the paper were verified exactly by the supplied Python/SymPy scripts, with supporting Lean formalization files provided as Online Resource 1. Full Text Additional Declarations No competing interests reported. Supplementary Files OnlineResource1CATsupportingfiles.zip 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. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9541310","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":631229650,"identity":"e99b3cd4-363e-46f2-ba05-223856206cf8","order_by":0,"name":"David Alfyorov","email":"data:image/png;base64,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","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"David","middleName":"","lastName":"Alfyorov","suffix":""},{"id":631229652,"identity":"52d9ec54-4c14-4a2d-8d86-e2b62bb1da85","order_by":1,"name":"Igor Shnyukov","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Igor","middleName":"","lastName":"Shnyukov","suffix":""}],"badges":[],"createdAt":"2026-04-27 11:54:41","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9541310/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9541310/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108182833,"identity":"3a7065af-c255-4706-8b6c-297dadf7a64f","added_by":"auto","created_at":"2026-04-30 08:59:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":379804,"visible":true,"origin":"","legend":"","description":"","filename":"catoverviewfopmanuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9541310/v1_covered_ba98fda9-36c3-486e-8b76-345a91e28c0a.pdf"},{"id":108168371,"identity":"edbf2082-7191-4d1e-bbb9-c427db158208","added_by":"auto","created_at":"2026-04-30 06:26:34","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":374052,"visible":true,"origin":"","legend":"","description":"","filename":"OnlineResource1CATsupportingfiles.zip","url":"https://assets-eu.researchsquare.com/files/rs-9541310/v1/5d727b0439b194b2a26fecbe.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"Causal Architecture Theory (CAT). 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