logos/knowledge_base/doc_index.md

## [DOC] https://docs.pydantic.dev/latest/
**Analysis:**
### Pydantic Validation & Schema Definition
**Core Concepts:**
1.  **Type Hints**: Uses Python standard type hints for schema validation.
2.  **Rust Core**: Core validation logic is written in Rust for significant speed improvements (Pydantic V2).
3.  **JSON Schema**: Models can emit standard JSON Schemas for integration.
4.  **Strict/Lax Modes**: Supports precise type enforcement or flexible coercion.
5.  **Serialization**: Custom serializers allow complex data processing flows.

**Relevance to LOGOS:**
- Useful for validating `AtomicState` and `Tensor` objects in the Neural Router.
- Can formalize the `ManifoldState` schema.
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