Spectral Sheaf Heuristics for Consistency Detection in Multi-Agent Systems

Spectral Sheaf Heuristics for Consistency Detection in Multi-Agent Systems | 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 Spectral Sheaf Heuristics for Consistency Detection in Multi-Agent Systems Sepehr Bayat This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8830176/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 detecting global inconsistencies in distributed networks remains computationally expensive. We introduce the Phronesis Index (Φ), a computationally efficient spectral heuristic that quantifies consistency by approximating topological obstructions in cellular sheaves. Our method achieves O(N log N) complexity (versus O(N^3) for exact cohomology) with provable error bounds. We validate Φ across four scenarios: Logic Maze anomaly detection, safe reinforcement learning via Bellman consistency monitoring, multi-robot coordination, and scalability tests up to 50,000 agents. In the safe RL scenario, Φ-based reward shaping reduces cumulative safety violations compared to standard Q-learning (Welch t-test computed automatically by the experiment script). We provide comprehensive guidance for sheaf construction, robustness under noise, and practical deployment considerations. All code and data are publicly available at https://github.com/sepehrbayat/phronesis-index-nmi . Full Text Additional Declarations There is NO Competing Interest. Supplementary Files supplementaryinformation.pdf Supplementary Information for “Spectral Sheaf Heuristics for Consistency Detection in Multi-Agent Systems” 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. 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-8830176","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":589659576,"identity":"75a52109-fef3-4fda-a008-ce9916bb2163","order_by":0,"name":"Sepehr Bayat","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYJACZgaGAyCa8TGINCBBCzOzMcla2KSJ0iLf3nvwceGeO/IGx88fqy6osLE3Z+8xYPhRsQ2nFoMz55KNZzx7ZrjhTDLb7Rln0hJ39hxLYOw5cxu3FokcM2meA4cZNxwAauFtO5xgcCP5ADNjG24t8vPfmP8GarHfcP4xWzFQi73B/YcNeLUw3OAxYwZqSdxwI5mNGaiFccMNZvy2GJzJSwY67FnyzBuPjaV5gH7ZcCYt4SA+v8i3nz34mefAHdu+84kPP/MAQ8zg+BnDBz8q8DiMgQdCKRxAEjuARR2mFvkG/MpGwSgYBaNgBAMA+UNfMGTfwKUAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0005-7192-896X","institution":"Hooshex","correspondingAuthor":true,"prefix":"","firstName":"Sepehr","middleName":"","lastName":"Bayat","suffix":""}],"badges":[],"createdAt":"2026-02-09 12:04:52","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8830176/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8830176/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104085203,"identity":"ed64da00-17de-4170-b234-68c5c123e267","added_by":"auto","created_at":"2026-03-06 15:12:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2913845,"visible":true,"origin":"","legend":"Article File","description":"","filename":"mainmanuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8830176/v1_covered_5bfb3b6e-c8ef-4bb5-93db-9a03a922e5ec.pdf"},{"id":103062543,"identity":"f4ec45dc-846c-4eb2-b884-27a0ca097538","added_by":"auto","created_at":"2026-02-20 10:25:05","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":344712,"visible":true,"origin":"","legend":"Supplementary Information for \u0026#x201C;Spectral Sheaf Heuristics for Consistency Detection in Multi-Agent Systems\u0026#x201D;","description":"","filename":"supplementaryinformation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8830176/v1/be37320665b60234c1634aa5.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Spectral Sheaf Heuristics for Consistency Detection in Multi-Agent Systems","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":"","lastPublishedDoi":"10.21203/rs.3.rs-8830176/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8830176/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"detecting global inconsistencies in distributed networks remains computationally expensive. 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