# Odyssey: Constructing Verifiable Local Truth-Preserving Foundation Models

arXiv: https://arxiv.org/abs/2606.27593 · HTML: https://mlsanity.com/paper/2606.27593/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [The AI Scientist-v2: Workshop-Level Automated Scientific Discovery via Agentic Tree Search](https://mlsanity.com/paper/2504.08066/) (2025)
- [Causal Reasoning and Large Language Models: Opening a New Frontier for Causality](https://mlsanity.com/paper/2305.00050/) (2023)
- [Causal Inference in Natural Language Processing: Estimation, Prediction, Interpretation and Beyond](https://mlsanity.com/paper/2109.00725/) (2021)
- [The IKEA ASM Dataset: Understanding People Assembling Furniture through Actions, Objects and Pose](https://mlsanity.com/paper/2007.00394/) (2020)
- [Agent Design Pattern Catalogue: A Collection of Architectural Patterns for Foundation Model based Agents](https://mlsanity.com/paper/2405.10467/) (2024)
- [Multi-Agent Causal Discovery Using Large Language Models](https://mlsanity.com/paper/2407.15073/) (2024)
- [A Survey on Extraction of Causal Relations from Natural Language Text](https://mlsanity.com/paper/2101.06426/) (2021)
- [An overview of domain-specific foundation model: key technologies, applications and challenges](https://mlsanity.com/paper/2409.04267/) (2024)
- [Training and Serving System of Foundation Models: A Comprehensive Survey](https://mlsanity.com/paper/2401.02643/) (2024)
- [Large Causal Models from Large Language Models](https://mlsanity.com/paper/2512.07796/) (2025)
- [A Survey of Event Causality Identification: Taxonomy, Challenges, Assessment, and Prospects](https://mlsanity.com/paper/2411.10371/) (2024)
- [Latent Confounded Causal Discovery via Lie Bracket Geometry](https://mlsanity.com/paper/2606.19610/) (2026)
- [PROMETHEUS: Automating Deep Causal Research Integrating Text, Data and Models](https://mlsanity.com/paper/2605.12835/) (2026)
- [Kan Extension Transformers: A Categorical Unification of Attention, Diffusion, and Predict-Detach Self-Conditioning](https://mlsanity.com/paper/2605.27259/) (2026)
- [How Non-Linguistic Is the Indus Sign System? A Synthetic-Baseline Scorecard](https://mlsanity.com/paper/2604.17828/) (2026)
- [TRACE: Toulmin-based Reasoning Assessment through Constructive Elements for LLM CoT Evaluation](https://mlsanity.com/paper/2605.29656/) (2026)

## Built on by (most cited first, 1 of 1)

- [Agentic Skill Optimization over Lie Algebroids](https://mlsanity.com/paper/2607.11493/) (2026)

## Abstract (arXiv)

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 https://bit.ly/4ajS0nA.