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For agentic AI, probabilistic prediction and optimization rank options only within a fixed hypothesis space and do not indicate when these representational commitments fail. This work develops a category-theoretic formalism for regime thresholds, modeling discovery as a verified transition between admissible schemas that preserves and transports prior artifacts while exposing residual content.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/self-revising-discovery-systems-for-science-a-categorical-framework-for-agentic-artificial-intelligence/273390/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/self-revising-discovery-systems-for-science-a-categorical-framework-for-agentic-artificial-intelligence/273390.png","ImageObject",300,407,{"name":92,"@type":93},"Patrick","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",17,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"Why can’t probabilistic scoring alone determine scientific discovery in agentic AI?","Question",{"text":113,"@type":114},"Because probabilistic prediction and optimization operate within a chosen hypothesis space, they rank alternatives only when the admissible variables, artifacts, and tests are fixed, without signaling when representational commitments become inadequate.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the paper define discovery at the representational boundary?",{"text":118,"@type":114},"Discovery is defined as a verified regime transition between schemas that preserves accepted prior artifacts, transports evidence via left Kan extension, and reveals residual content not generated by transport.",{"name":120,"@type":111,"acceptedAnswer":121},"What are the two system case studies used to instantiate the framework?",{"text":122,"@type":114},"The paper instantiates the framework in Builder/Breaker and CategoryScienceClaw, where each system revises scientific representations and records how admissible content changes under structured gates and tests.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},273390,1789471213,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145,"preview_page_count":4},549758146520,"https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470","arXiv : 2606 .0 1444v2 [cs .AI] 2 1 Aug 2026  \nSelf-Revising Discovery Systems for Science: A Categorical Framework for  \nAgentic Artificial Intelligence  \nFiona Y. Wang1,2 Markus J. Buehler2,3,4*  \n1 Laboratory for Atomistic and Molecular Mechanics, MIT  \n2 Department of Biological Engineering, MIT  \n3 Departments of Civil and Environmental Engineering and Mechanical Engineering,  \n4 Center for Computational Science and Engineering, Schwarzman College of Computing, MIT  \nCambridge, MA 02139, USA;* Corresponding author: [mbuehler@mit.edu](mbuehler@mit.edu)  \nAbstract  \nScientific discovery is not merely the production of better answers, but the crossing of a threshold into a new representational regime in which previously unnameable ev dence becomes expressible, testable, and reusable. The central difficulty for agentic artificial intelligence is that probabilistic prediction and optimization operate within a chosen hypothesis space: they can rank alternatives once the admissible variables, artifacts, and tests are fixed, but they do not by themselves identify when those representational commitments have become inadequate. Discovery often occurs precisely at this boundary, when new objects, morphisms, descriptors, or ver fiers must be introduced for the ev dence to become expressible.  \nWe develop a category-theoretic formalism for this threshold. In a fixed regime with schema category Sb , the committed scientific state is a copresheaf It : Sb → Set, with realized provenance represented by the category of elements RS b It or by a multicategor cal analogue for multi-parent artifacts. Search updates this state within the same schema. Discovery is a ver fied transition u : Sb → Sb′ that preserves accepted prior artifacts, transports old ev dence by left Kan extension, and exposes residual content not generated by transport. The formalism therefore characterizes discovery as a change in admissible representation, rather than as a subjective novelty judgment or a higher model score. We instantiate the framework in Builder/Breaker and CategoryScienceClaw. Builder/Breaker revises a protein-mechanics symbolic world model under a min mum description length gate, retaining rejected edits and retractions; the accepted law expresses within-chain flex bility as all-mode elastic compliance conditioned by slow collective-mode partic pation. CategoryScienceClaw extends ScienceClaw with proof-carrying typed artifacts, lineage, gates, stress tests, and claim records. Its high-entropy-alloy fatigue case rejects threshold-only ∆Kth screening and records a two-axis damage-tolerance representation separating crack-growth threshold from Paris-slope stability. The resulting claim is a reproducible public-data hypothesis and prospective val dation target, not a substitute for new fatigue testing. Together, these cases show that categor cal structure can make  \nrepresentational novelty explicit, auditable, and operational in AI-driven scientific discovery.  \nKeywords: agentic AI; scientific discovery; mechanics; category theory; regime transition; endofunctor; minimum description length; provenance; multi-agent systems; materials science.  \n1. Introduction  \nArtificial intelligence is now embedded in most stages of the scientific process. Foundation models retrieve and summarize literature, propose hypotheses, write and debug code, run and interpret simulations, design proteins and materials, and draft figures and reports. Agentic systems built on top of these models call external tools, coordinate multiple specialized subsystems, manage long-running workflows, and increasingly take partial responsibility for experimental decisions, both in computational pipelines and in autonomous laboratories [1–12] . The trajectory is clear and suggests that AI is no longer only a way to predict an output for a fixed task, but an active participant in how scientific work is structured.  \nYet the central question for these systems remains underformalized. Existing A","cbCaih0CdQYrLLg8","https://ap.wps.com/l/cbCaih0CdQYrLLg8","pdf",2454802,38,"English","# Introduction\n## Representational boundaries in agentic AI\n## Category-theoretic formulation of discovery\n## Instantiations in Builder/Breaker and CategoryScienceClaw","[{\"question\":\"Why can’t probabilistic scoring alone determine scientific discovery in agentic AI?\",\"answer\":\"Because probabilistic prediction and optimization operate within a chosen hypothesis space, they rank alternatives only when the admissible variables, artifacts, and tests are fixed, without signaling when representational commitments become inadequate.\"},{\"question\":\"How does the paper define discovery at the representational boundary?\",\"answer\":\"Discovery is defined as a verified regime transition between schemas that preserves accepted prior artifacts, transports evidence via left Kan extension, and reveals residual content not generated by transport.\"},{\"question\":\"What are the two system case studies used to instantiate the framework?\",\"answer\":\"The paper instantiates the framework in Builder/Breaker and CategoryScienceClaw, where each system revises scientific representations and records how admissible content changes under structured gates and tests.\"}]","Self-Revising Discovery Systems for Science - A Categorical Framework for Agentic Artificial Intelligence | PDF",96]