docs: link the generated API reference from the README

README.md

@@ -1,5 +1,7 @@
 # Shinro Python Modules
 
+[![API Reference](https://img.shields.io/badge/API%20Reference-shinro--xyz.github.io-blue)](https://shinro-xyz.github.io/shinro-python-modules/)
+
 A clean, modular Python control framework built on five abstract base classes
 — **Controller**, **Plant**, **StateEstimator**, **TrajectoryGenerator**, and
 **PhysicsEngine** — with registry-based factories that compose them from TOML
@@ -19,6 +21,12 @@ Conceptual and operational documentation lives in
 - **[Control Architecture](https://docs.shinro.xyz/control-architecture/)** — why the five ABCs exist, how they compose, sim/hardware parity
 - **[Python Modules](https://docs.shinro.xyz/python-modules/)** — the operational guide: install, run, extend, component catalog
 
+**API Reference** — <https://shinro-xyz.github.io/shinro-python-modules/>
+Every exported symbol — the five ABCs, controllers, estimators, plants,
+trajectories, factories, utilities — with signatures, parameter tables and
+source links. Generated from the package's own `__all__` on every push, so it
+cannot go stale.
+
 The same guides live in-repo under [`docs/`](./docs/) (no internet required):
 
 - **[`docs/quickstart.md`](./docs/quickstart.md)** — install → build a controller from TOML → run a scenario → trace/lower. Start here.

mkdocs.yml

@@ -8,6 +8,7 @@
 # from each subpackage's __all__. Only prose pages are declared by hand below.
 
 site_name: shinro
+site_url: https://shinro-xyz.github.io/shinro-python-modules/
 site_description: Whole-body control framework — controllers, plants, estimators, trajectories, and a MuJoCo-backed simulation factory.
 docs_dir: docs
 site_dir: site