Odyssey Framework Builds Verifiable, Truth-Preserving Foundation Models

The paper introduces ODYSSEY, a novel categorical framework designed for building foundation models that are both verifiable and preserve local truth. This framework operates by composing architectural building blocks called "foundries." Each foundry specifies a local context, representation families, rules for restriction and gluing, policies for handling obstructions, update obligations, and human-facing views, essentially acting as an organized "sheaf of knowledge" with an integrated argumentation component. ODYSSEY formalizes the construction of these foundries through Universal Foundry Learning (UFL), which uses left and right Kan extensions. Left Kan extensions aggregate local artifacts into candidate foundries, while right Kan extensions enforce the necessary conditions for promotion, such as restriction, gluing, obstruction, and argumentation. The framework also includes Foundry SQL (FSQL), a specialized query language for interacting with maintained foundry artifacts, and TICKET certification for securely integrating external models into the ODYSSEY state. The system has been fully implemented and tested across a diverse range of concrete foundries, demonstrating its capability to support domain construction, artifact replay, diagnostics, grounded scrutiny of local LLMs, and optimized causal-claim extraction from heterogeneous sources. This comprehensive approach aims to create more transparent, auditable, and reliable foundation models.