oss(langgraph): clarify usage of thread_id in checkpointer configuration (#1658)

Author: mdrxy

src/oss/langgraph/persistence.mdx

@@ -17,7 +17,7 @@ When using the LangGraph API, you don't need to implement or configure checkpoin
 
 A thread is a unique ID or thread identifier assigned to each checkpoint saved by a checkpointer. It contains the accumulated state of a sequence of [runs](/langsmith/assistants#execution). When a run is executed, the [state](/oss/langgraph/graph-api#state) of the underlying graph of the assistant will be persisted to the thread.
 
-When invoking a graph with a checkpointer, you **must** specify a `thread_id` as part of the `configurable` portion of the config.
+When invoking a graph with a checkpointer, you **must** specify a `thread_id` as part of the `configurable` portion of the config:
 
 :::python
 ```python
@@ -35,7 +35,9 @@ When invoking a graph with a checkpointer, you **must** specify a `thread_id` as
 ```
 :::
 
-A thread's current and historical state can be retrieved. To persist state, a thread must be created prior to executing a run. The LangSmith API provides several endpoints for creating and managing threads and thread state. See the [API reference](https://langchain-ai.github.io/langgraph/cloud/reference/api/) for more details.
+A thread's current and historical state can be retrieved. To persist state, a thread must be created prior to executing a run. The LangSmith API provides several endpoints for creating and managing threads and thread state. See the [API reference](https://reference.langchain.com/python/langsmith/) for more details.
+
+The checkpointer uses `thread_id` as the primary key for storing and retrieving checkpoints. Without it, the checkpointer cannot save state or resume execution after an [interrupt](/oss/langgraph/interrupts), since the checkpointer uses `thread_id` to load the saved state.
 
 ## Checkpoints