Adaptive Recursive Convergence and Semantic Turning Points: A Self-Verifying Architecture for Progressive AI Reasoning

Adaptive Recursive Convergence and Semantic Turning Points: A Self-Verifying Architecture for Progressive AI Reasoning | 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 Article Adaptive Recursive Convergence and Semantic Turning Points: A Self-Verifying Architecture for Progressive AI Reasoning Ziping Liu, Moriba Jah This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6605714/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract Current AI reasoning architectures typically rely on static representational capacities, inherently limiting their ability to adaptively respond when confronted with escalating semantic complexity. Consequently, these models frequently mistake superficial coherence for genuine semantic resolution. To address this fundamental limitation, we introduce the novel paired mechanisms of Adaptive Recursive Convergence (ARC) and Cascading Re-Dimensional Attention (CRA). ARC orchestrates recursive semantic contraction within shared atomic memory, systematically refining representational granularity. In parallel, CRA retroactively evaluates epistemic sufficiency through a rigorously derived confidence score computed via geometric attention measures. When representational saturation occurs—indicating epistemic insufficiency—CRA proactively triggers targeted dimensional escalation, driven entirely by intrinsic semantic detection rather than fixed heuristics. We instantiate and empirically validate ARC/CRA through a publicly available Semantic Turning Point Detector 1 a concrete system capable of segmenting dialogue into epistemically grounded segments by pinpointing structural shifts frequently overlooked by static-dimensional models. This approach demonstrably achieves progressive cognition—dynamically expanding representational scope precisely when necessary, conserving computational resources, and incorporating rigorous self-verification directly into the reasoning process. Ultimately, ARC/CRA reconceptualizes intelligence as a recursive, introspective, and self-adaptive process, continuously capable of recognizing and responding to its own representational limitations, thereby offering a robust blueprint for AI systems to evolve autonomously whenever epistemic certainty breaks down. 1 We define a semantic turning point as a location within a dialogue or narrative where the underlying semantic structure undergoes a significant shift, necessitating adaptive representational adjustment. For further information, visit: https://github.com/gaiaverseltd/semantic- turning-point-detector. Physical sciences/Mathematics and computing/Computer science Physical sciences/Mathematics and computing/Applied mathematics Adaptive computation progressive cognition dynamic attention semantic turning point contraction mappings token efficiency Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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. 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-6605714","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":458370760,"identity":"5b54b772-b511-4594-b78c-0757a167906e","order_by":0,"name":"Ziping Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYDACZgaGAwwMNmAGFDA2EKMljRQtEHCYBHfJt/MePFzw67xdfzvzM4mPe+rkGNgP47eFsZkv4fDMvtvJMw6zmUnOeHbYmIEnEb8WZmYeg8O8PbeTgW4zNuY5cAConoAWNoiWc8nyh9k/G/85UFffwP8QvxYekBaeHwfsgKThY4YDzAkMEgRskWAG+oW3ITnB8DBP4cOeA4cN2yQI2CLff/bwZ54/dvZy549vOPDjQJ08P3/6A7xagE4DBlsbkpfZCKiHaGH4w2BPWOEoGAWjYBSMWAAAdK5HFcKJ4XQAAAAASUVORK5CYII=","orcid":"","institution":"Gaiaverse LTD","correspondingAuthor":true,"prefix":"","firstName":"Ziping","middleName":"","lastName":"Liu","suffix":""},{"id":458370761,"identity":"a567128a-531d-4a59-a953-00a2a46281b8","order_by":1,"name":"Moriba Jah","email":"","orcid":"","institution":"Gaiaverse LTD","correspondingAuthor":false,"prefix":"","firstName":"Moriba","middleName":"","lastName":"Jah","suffix":""}],"badges":[],"createdAt":"2025-05-06 18:25:56","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6605714/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-6605714/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86192821,"identity":"82ebbb7c-ecc8-4268-84d2-17ee2060152b","added_by":"auto","created_at":"2025-07-07 19:57:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":468378,"visible":true,"origin":"","legend":"","description":"","filename":"main.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6605714/v2_covered_1c684dd5-5211-43a8-95b6-754bcddceef7.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"Adaptive Recursive Convergence and Semantic Turning Points: A Self-Verifying Architecture for Progressive AI Reasoning","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":"Adaptive computation, progressive cognition, dynamic attention, semantic turning point, contraction mappings, token efficiency","lastPublishedDoi":"10.21203/rs.3.rs-6605714/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6605714/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCurrent AI reasoning architectures typically rely on static representational capacities, inherently limiting their ability to adaptively respond when confronted with escalating semantic complexity. Consequently, these models frequently mistake superficial coherence for genuine semantic resolution. To address this fundamental limitation, we introduce the novel paired mechanisms of \u003cstrong\u003eAdaptive Recursive Convergence\u003c/strong\u003e (ARC) and \u003cstrong\u003eCascading Re-Dimensional Attention\u003c/strong\u003e (CRA). ARC orchestrates recursive semantic contraction within shared atomic memory, systematically refining representational granularity. In parallel, CRA retroactively evaluates epistemic sufficiency through a rigorously derived confidence score computed via geometric attention measures. When representational saturation occurs—indicating epistemic insufficiency—CRA proactively triggers targeted dimensional escalation, driven entirely by intrinsic semantic detection rather than fixed heuristics. 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Ultimately, ARC/CRA reconceptualizes intelligence as a recursive, introspective, and self-adaptive process, continuously capable of recognizing and responding to its own representational limitations, thereby offering a robust blueprint for AI systems to evolve autonomously whenever epistemic certainty breaks down.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e1 \u003c/sup\u003e\u003csub\u003eWe define a semantic turning point as a location within a dialogue or narrative where the underlying semantic structure undergoes a significant shift, necessitating adaptive representational adjustment. 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