Odyssey arXiv 2606.27593 defines sheaf-based foundries for local verifiable models

The ODYSSEY framework specifies foundries as sheaves carrying argumentation components. Generic foundries cover evidence, operational decisions, institutional constraints, and evaluation harnesses. Universal Foundry Learning applies left Kan extensions to roll artifacts into candidates and right Kan extensions to enforce gluing, obstruction, and restriction maps. TICKET certification admits external models into durable state. The paper reports full implementation across domain construction, sheaf diagnostics, and grounded Toulmin scrutiny.

Standard scaling discussions focus on parameter count and centralized training. ODYSSEY instead treats context covers and obstruction policies as first-class objects. This directly targets hallucination by requiring local representation families to satisfy explicit gluing rules before promotion. Residual-obstruction ledgers record mismatches that centralized post-training alignment cannot surface.

FSQL provides typed queries over maintained artifacts. The same machinery supports replay, causal-claim extraction, and human-facing views. A 2.5-hour ICML 2026 tutorial will demonstrate deployment on heterogeneous sources.

Operationally the approach replaces single-model trust with composable local verification. Deployment records will show whether TICKET-certified slices maintain consistency across updates at rates exceeding current retrieval-augmented baselines.