Odyssey: Constructing Verifiable Local Truth-Preserving Foundation Models

Odyssey：构建可验证的局部真值保持基础模型

Abstract: 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, representation families, restriction maps, gluing rules, obstruction policies, update obligations, and human-facing views.

摘要： 我们引入了一个名为 ODYSSEY 的范畴论框架，用于构建可验证的、局部真值保持的基础模型。该框架将模型构建为“铸造厂”（foundries）的组合——这是一种基础架构组件，用于定义局部上下文的覆盖、局部表示族、限制映射、粘合规则、阻碍策略、更新义务以及面向人类的视图。

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.

“铸造厂”是一种有组织的知识层（sheaf），其内部包含一个论证组件。具体的铸造厂由通用铸造厂构建而成，例如证据/论证、运营决策、制度/金融、市场含义、科学挑战、研究项目、助手构建以及评估工具铸造厂。

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.

通用铸造厂学习（UFL）将铸造厂的构建形式化为左 Kan 扩张和右 Kan 扩张的组合：左 Kan 扩张将局部工件（artifacts）整合为候选铸造厂，而右 Kan 扩张则强制执行提升（promotion）所需的限制、粘合、阻碍和论证条件。

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.

Foundry SQL (FSQL) 是一种小型类型化查询界面，用于切分维护中的铸造厂工件。它使用 TICKET（基于因果 Kan 扩张 Transformer 的拓扑集成）认证，将外部或预构建的模型纳入持久的 ODYSSEY 状态中。

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.

ODYSSEY 已在广泛的具体铸造厂中得到全面实现和测试。结果表明，同一套范畴论机制能够支持领域构建、工件重放、层诊断、基于 Toulmin/局部大语言模型的扎根审查、残余阻碍分类账，以及跨异构源的优化 TICKET 兼容因果声明提取。

This paper is to be presented as a 2.5 hour tutorial at ICML 2026.

本文将在 ICML 2026 大会上作为一场 2.5 小时的教程进行展示。