Odyssey: Constructing Verifiable Local Truth-Preserving Foundation Models

Tabular foundation models cannot reason about data produced by running systems without access to the rules that govern them. We make this statement falsifiable. The \emph{Operational Turing Test} (OTT) constructs pairs of legal and rule-violating database states whose $1$- and $2$-way column-value marginals match to a total variation of $<0.02$; Le~Cam's lemma then bounds any values-only classifier at $\geq0.49$ Bayes error. Three values-only baselines (XGBoost, TabICL, TabPFN) hit the bound exactly (accuracy $0.50$, pre-registered two one-sided tests (TOST) $p<0.002$), raw row-level access does not help, exposing relational value consistency closes most of the gap, and only a classifier fed by seven executable rule-derived audits reaches $1.00$ classification accuracy. In three matched $100$-state frontier large-language-model (LLM) runs, models given the schema, trigger source, rule tables, and state files classify at most $2/50$ legal states as LEGAL; GPT-5.5 accepts $0/50$ legal states even with higher reasoning effort and a Structured Query Language (SQL) executor. The access-ladder pattern also appears on a second schema with structurally distinct rule families (banking ledger: cross-row balance, cumulative aggregate). The barrier is identifiability, not capacity: scale, data, and richer features cannot cross it without operational grounding.

Foundation models have progressed from learning and reasoning over existing knowledge, to increasingly learning through action, tool use, and outcome feedback. We argue that the next frontier is a further transition: from solving and acting within problems specified by humans to participating in the process by which new problems, representations, explanations, and knowledge are created. We refer to this capability as Discovery Intelligence. We formulate Discovery Foundation Models (DFMs) as general-purpose model systems for open-ended discovery. A DFM operates over a revisable research state and supports seven coupled capabilities spanning problem discovery, formulation, representation construction, hypothesis formation, intervention, evidence-grounded revision, and continual discovery improvement. We instantiate this framework with Zetema, which couples explicit research-state dynamics, verification and experimental gating, external grounding, and cross-task Discovery Skill evolution. We further ground the framework with GALILEO, a real therapeutic-discovery system in which Dry-Lab reasoning, robotic and hands-on Wet-Lab experimentation, external biological evidence, and iterative hypothesis and design revision form a closed physical discovery loop. We then formulate a unified approach to capability formation and process-centered evaluation, enabling discovery behavior to be trained, improved, and measured beyond final-answer performance. Together, these components establish discovery as a learnable, executable, and evaluable capability of foundation-model systems. We view this shift as a broader progression in intelligence scaling: from learning over existing knowledge, to learning from action outcomes, and ultimately to participating in the construction, testing, and revision of the structures through which new knowledge is discovered. Code: https://github.com/Gen-Verse/DFM-Plans

Foundation models (FMs) are increasingly deployed in open-world settings where distribution shift is the rule rather than the exception. The out-of-distribution (OOD) phenomena they face -- knowledge boundaries, capability ceilings, compositional shifts, and open-ended task variation -- differ in kind from the settings that have shaped prior OOD research, and are further complicated because the pretraining and post-training distributions of modern FMs are often only partially observed. Our position is that OOD for foundation models is a structurally distinct problem that cannot be solved within the prevailing model-centric paradigm, and that agentic systems constitute the missing paradigm required to address it. We defend this claim through four steps. First, we give a stage-aware formalization of OOD that accommodates partially observed multi-stage training distributions. Second, we prove a parameter coverage ceiling: there exist practically relevant inputs that no model-centric method (training-time or test-time) can handle within tolerance $\varepsilon$, for reasons intrinsic to parameter-based representation. Third, we characterize agentic OOD systems by four structural properties -- perception, strategy selection, external action, and closed-loop verification -- and show that they strictly extend the reachable set beyond the ceiling. Fourth, we respond to seven counterarguments, conceding two, and outline a research agenda. We do not claim that agentic methods subsume model-centric ones; we argue that the two are complementary, and that progress on FM-OOD requires explicit recognition of the agentic paradigm as a first-class research direction.