Odyssey: Constructing Verifiable Local Truth-Preserving Foundation Models

Computer Science > Artificial Intelligence [Submitted on 25 Jun 2026] Odyssey: Constructing Verifiable Local Truth-Preserving Foundation Models Sridhar Mahadevan We introduce a categorical framework called ODYSSEY for constructing verifiable, local truth-preserving foundation models as compositions of foundries: building-block architectural components that specify a cover of local contexts, local representation families, restriction maps, gluing rules, obstruction policies, update obligations, and human-facing views. A foundry is an organized sheaf of knowledge that carries within it an argumentation component. Concrete foundries are built from generic foundries such as evidence/argument, operational decision, institutional/financial, market meaning, scientific challenge, research-program, assistant-build, and evaluation-harness foundries. Universal Foundry Learning (UFL) formalizes foundry construction as a composition of left and right Kan extensions, with left Kan extension rolling local artifacts into candidate foundries and right Kan extension enforcing the restriction, gluing, obstruction, and argumentation conditions required for promotion. Foundry SQL (FSQL) is a small typed query surface for slicing maintained foundry artifacts that uses TICKET (Topos Integration using Causal Kan Extension Transformers) certification for admitting external or pre-built models into durable ODYSSEY state. ODYSSEY is fully implemented and tested across a wide spectrum of concrete foundries, showing that the same categorical machinery supports domain construction, artifact replay, sheaf diagnostics, grounded Toulmin/local-LLM scrutiny, residual-obstruction ledgers, and optimized TICKET-compatible causal-claim extraction across heterogeneous sources. This paper is to be presented as a 2.5 hour tutorial at ICML 2026. The tutorial home page is at this https URL. Comments: 34 pages Subjects: Artificial Intelligence (cs.AI); Machine Learning (cs.LG) Cite as: arXiv:2606.27593 [cs.AI]   (or arXiv:2606.27593v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2606.27593 Focus to learn more Submission history From: Sridhar Mahadevan [view email] [v1] Thu, 25 Jun 2026 22:49:17 UTC (741 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-06 Change to browse by: cs cs.LG References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)