feat(docs,core): Adds error reference pages and populate codes on errors in core

docs/core_docs/docs/troubleshooting/errors/GRAPH_RECURSION_LIMIT.mdx

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+# GRAPH_RECURSION_LIMIT
+
+Your LangGraph app reached the maximum number of steps before hitting a stop condition.
+
+This is usually a sign of an infinite loop, but complex graphs may hit this naturally.
+
+## Troubleshooting
+
+- If you are not expecting your graph to go through many iterations, you likely have a cycle. Check your logic for infinite loops.
+- If you have a complex graph, you can pass in a higher `recursionLimit` value into your `config` object when invoking your graph like this:
+
+```ts
+await graph.invoke({...}, { recursionLimit: 100 });
+```

docs/core_docs/docs/troubleshooting/errors/INVALID_GRAPH_UPDATE.mdx

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+# INVALID_GRAPH_UPDATE
+
+A LangGraph app received an unexpected return value from a node and failed to update its state at the end of a step.
+
+One way this can occur is if you are using a [fanout](https://langchain-ai.github.io/langgraphjs/how-tos/map-reduce/)
+or other parallel execution in your graph and you have defined a state with a value like this:
+
+```ts
+const StateAnnotation = Annotation.Root({
+  someKey: Annotation<string>,
+});
+
+const graph = new StateGraph(StateAnnotation)
+  .addNode(...)
+  ...
+  .compile();
+```
+
+If a node in the above graph returns `{ someKey: "someStringValue" }`, this will overwrite the state value for `someKey` with `"someStringValue"`.
+However, if multiple nodes in e.g. a fanout within a single step return values for `"someKey"`, the graph will throw this error because
+there is uncertainty around how to update the internal state.
+
+To get around this, you can define a reducer that combines multiple values:
+
+```ts
+const StateAnnotation = Annotation.Root({
+  someKey: Annotation<string[]>({
+    default: () => [],
+    reducer: (a, b) => a.concat(b),
+  }),
+});
+```
+
+This will allow you to return the same key from nodes executed in parallel safely.
+
+## Troubleshooting
+
+The following may help resolve this error:
+
+- If your graph executes nodes in parallel, make sure you have defined relevant state keys with a reducer.

docs/core_docs/docs/troubleshooting/errors/INVALID_PROMPT_INPUT.mdx

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+# INVALID_PROMPT_INPUT
+
+A [prompt template](/docs/concepts#prompt-templates) received missing or invalid input variables.
+
+## Troubleshooting
+
+The following may help resolve this error:
+
+- Double-check your prompt template to ensure that it is correct.
+  - If you are using the default format and you are using curly braces `{` anywhere in your template, they should be double escaped like this: `{{`.
+- If you are using a [`MessagesPlaceholder`](/docs/concepts/#messagesplaceholder), make sure that you are passing in an array of messages or message-like objects.
+  - If you are using shorthand tuples to declare your prompt template, make sure that the variable name is wrapped in curly braces (`["placeholder", "{messages}"]`).
+- Try viewing the inputs into your prompt template using [LangSmith](https://docs.smith.langchain.com/) or log statements to confirm they appear as expected.
+- If you are pulling a prompt from the [LangChain Prompt Hub](https://smith.langchain.com/prompts), try pulling and logging it or running it in isolation with a sample input to confirm that it is what you expect.

docs/core_docs/docs/troubleshooting/errors/MODEL_RATE_LIMIT.mdx

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+# MODEL_RATE_LIMIT
+
+You have hit the maximum number of requests that a model provider allows over a given time period and are being temporarily blocked.
+Generally, this error is temporary and your limit will reset after a certain amount of time.
+
+## Troubleshooting
+
+The following may help resolve this error:
+
+- Contact your model provider and ask for a rate limit increase.
+- If many of your incoming requests are the same, utilize [model response caching](/docs/how_to/chat_model_caching/).
+- Spread requests across different providers if your application allows it.
+- Set a higher number of [max retries](https://api.js.langchain.com/interfaces/_langchain_core.language_models_base.BaseLanguageModelParams.html#maxRetries) when initializing your model.
+  LangChain will use an exponential backoff strategy for requests that fail in this way, so the retry may occur when your limits have reset.

docs/core_docs/docs/troubleshooting/errors/OUTPUT_PARSING_FAILURE.mdx

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+# OUTPUT_PARSING_FAILURE
+
+An [output parser](/docs/concepts#output-parsers) was unable to handle model output as expected.
+
+To illustrate this, let's say you have an output parser that expects a chat model to output JSON surrounded by a markdown code tag (triple backticks). Here would be an example of good input:
+
+````ts
+AIMessage {
+  content: "```\n{\"foo\": \"bar\"}\n```"
+}
+````
+
+Internally, our output parser might try to strip out the markdown fence and newlines and then run `JSON.parse()`.
+
+If instead the chat model generated an output with malformed JSON like this:
+
+````ts
+AIMessage {
+  content: "```\n{\"foo\":\n```"
+}
+````
+
+When our output parser attempts to parse this, the `JSON.parse()` call will fail.
+
+Note that some prebuilt constructs like [legacy LangChain agents](/docs/how_to/agent_executor) and chains may use output parsers internally,
+so you may see this error even if you're not visibly instantiating and using an output parser.
+
+## Troubleshooting
+
+The following may help resolve this error:
+
+- Consider using [tool calling or other structured output techniques](/docs/how_to/structured_output/) if possible without an output parser to reliably output parseable values.
+  - If you are using a prebuilt chain or agent, use [LangGraph](https://langchain-ai.github.io/langgraphjs/) to compose your logic explicitly instead.
+- Add more precise formatting instructions to your prompt. In the above example, adding `"You must always return valid JSON fenced by a markdown code block. Do not return any additional text."` to your input may help steer the model to returning the expected format.
+- If you are using a smaller or less capable model, try using a more capable one.
+- Add [LLM-powered retries](/docs/how_to/output_parser_fixing/).