[docs] conductor docs

docs/source/design/conductor/index.md

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+# Mooncake Conductor
+
+[中文](../../zh/design/conductor/index.md)
+
+Mooncake Conductor keeps an in-memory view of reusable key-value (KV) cache
+blocks reported by inference engines and Mooncake Store. A router can query
+that view before choosing an inference engine. Use this page to find the guide
+for running Conductor, understanding its results, or integrating a client.
+
+## Choose a task
+
+### Run Conductor
+
+Follow the [usage guide](./usage.md) to build the C++ service, configure event
+sources, check registrations, query cache availability, and unregister a
+source.
+
+### Understand the result
+
+Read the [architecture guide](./conductor-architecture-design.md) to see how
+vLLM GPU events and shared Mooncake CPU or Disk events become per-engine query
+results.
+
+### Call the HTTP API
+
+Use the [HTTP API reference](./indexer-api-design.md) for the five implemented
+endpoints, their accepted fields, response bodies, and error formats.
+
+### Connect event sources
+
+Start with [KV Events](../kv-event/index.md) to compare the vLLM and Mooncake
+message paths. That section also explains what Mooncake publishes and what
+Conductor accepts.
+
+```{toctree}
+:maxdepth: 1
+:hidden:
+
+conductor-architecture-design
+usage
+```