Phase Transitions in Artificial General Intelligence: Scaling Laws, Predictability Limits, and Singularity

Phase Transitions in Artificial General Intelligence: Scaling Laws, Predictability Limits, and Singularity | 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 Phase Transitions in Artificial General Intelligence: Scaling Laws, Predictability Limits, and Singularity Deep Bhattacharjee, Sanjeevan Singha Roy, Priyanka Samal This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9055490/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 We model AGI emergence as a critical transition in large-scale learning systems and propose a quantitative framework connecting scaling laws, dynamical stability, and safety-relevant control. Instead of treating the singularity as a date forecast, we define a measurable transition regime in terms of scaling efficiency, transfer generalization, recursive self-improvement depth, and governance latency. The analysis combines bifurcation-style phase-transition proxies, Lyapunov-inspired predictability horizons, information-theoretic diagnostics, and computational irreducibility constraints. We show how rapid capability gains can coexist with finite prediction windows, yielding practical limits on long-horizon control despite deterministic training dynamics. To operationalize the framework, we specify benchmark-linked indicators, threshold tests, and evaluation protocols for detecting critical behavior across model families. We further map these diagnostics to deployment policy through closed-loop safety gates, rollback criteria, and audit latency targets. The resulting perspective offers a cs.AI-oriented methodology for studying AGI transitions with empirically testable claims, reproducible measurements, and explicit interfaces to safety and governance. Theoretical Computer Science Artificial Intelligence and Machine Learning Artificial General Intelligence scaling laws phase transitions in intelligence computational irreducibility AI safety singularity dynamics 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. 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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-9055490","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":602192523,"identity":"cf36037f-87d9-4307-9327-352c46774f8b","order_by":0,"name":"Deep Bhattacharjee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtUlEQVRIiWNgGAWjYBACNiCWAGI5PmaitbBBtBizEa2FAaolsY1oHXzy7Q9vfKi4k97GzmP4gKHGJpoIh/EYW8448yy3jZnH2IDhWFpuAxFa2KR52w4DtbClSTA2HCZGC/sz6b//DqezMbOl/yBSC4OZNFBlAhsz8zEGIrXkGFv2HHtm2MbMfFgigRi/yDcff3jjR80deX7+g40fPtTYENYCBQcgVAKRypG0jIJRMApGwSjABgCmdTVtv357DAAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-0466-750X","institution":"Electro-Gravitational Space Propulsion Laboratory (EGSPL), India","correspondingAuthor":true,"prefix":"","firstName":"Deep","middleName":"","lastName":"Bhattacharjee","suffix":""},{"id":602192524,"identity":"fe739588-eeb8-45c7-8726-f54b64a2ebf0","order_by":1,"name":"Sanjeevan Singha Roy","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCElEQVRIiWNgGAWjYJACAzDJ3nzg8I8KIIOZuYFILTzHEh8znAFpYSSsBQIkcoyNGdtALAJa5NvPHij4UHFY3lwix0y6cF5tNH87UMuPim24HXUmL8FwxpnDhjt7npVJz9x2PHfGYcYGxp4zt/H4I8fAmLctjXHD8eRtErzbjuU2ALUwM7bh1iLf/8bA+O+/NPsNBxLMJHjnHMudT0gLww2gLYwNNokbTqQYG/M21ORuIKTF4MYbA8OeYzbJG84cS3w449iB3I1ALQfx+UW+P8fM4EeNhO2G480HDnyoqcudd/7wwQc/KvA4jIGBzQCJcxhMHsCnHgiYHyBx6ggoHgWjYBSMgpEIAP5mY37QFnXoAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-6148-1421","institution":"Birla Institute of Technology (BIT), Mesra, Jharkhand, India","correspondingAuthor":true,"prefix":"","firstName":"Sanjeevan","middleName":"Singha","lastName":"Roy","suffix":""},{"id":602192525,"identity":"fde109b7-86ca-45f4-a37d-e2fb3dce2870","order_by":2,"name":"Priyanka Samal","email":"","orcid":"https://orcid.org/0000-0002-2343-9169","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Priyanka","middleName":"","lastName":"Samal","suffix":""}],"badges":[],"createdAt":"2026-03-07 05:13:58","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9055490/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9055490/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104405417,"identity":"e0545f8d-ddff-4c5d-9c13-8adbb100526b","added_by":"auto","created_at":"2026-03-11 12:22:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":792667,"visible":true,"origin":"","legend":"","description":"","filename":"cursd.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9055490/v1_covered_eeef8014-aaa0-42fc-8bbf-982cb68e80ce.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003ePhase Transitions in Artificial General Intelligence: Scaling Laws, Predictability Limits, and Singularity \u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Artificial General Intelligence, scaling laws, phase transitions in intelligence; 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