Langflow is a tool for building and deploying AI-powered agents and workflows. From 1.0.0 until 1.10.1, Langflow did not verify flow ownership in the deprecated POST /api/v1/build/{flow_id}/vertices and POST /api/v1/build/{flow_id}/vertices/{vertex_id} handlers. Through version 1.7.1, an unauthenticated caller who knew another user's flow UUID could reach these handlers; from version 1.7.2 through 1.10.0, callers had to authenticate but needed no elevated privileges. Such a caller could cause retrieve_vertices_order to load and cache the private graph, enumerate its vertex identifiers, and use build_vertex to execute selected vertices and receive their results. build_graph_from_db_no_cache performed a primary-key lookup without an owner filter. This could disclose private flow structure, configured values, and selected outputs and could trigger victim-configured side effects and build-history records, although it did not expose the victim's variable-store credentials or permit modification of the stored flow. This issue is fixed in Langflow 1.10.1 and langflow-base 0.10.1.

Affected: PyPI: langflow, PyPI: langflow-base

### Summary

Before **Langflow 1.10.1**, two deprecated but still-routed endpoints in the chat API did not check that the authenticated caller owns the flow referenced in the URL path:

- `POST /api/v1/build/{flow_id}/vertices` (`retrieve_vertices_order`) - `POST /api/v1/build/{flow_id}/vertices/{vertex_id}` (`build_vertex`)

Any authenticated user who knows (or obtains) another user's `flow_id` could load that user's private flow graph, enumerate its vertex IDs, and build (execute) individual vertices of it, receiving the vertex results in the response.

Both routes are declared with `deprecated=True, include_in_schema=False`, so they do not appear in the OpenAPI docs, but they remained registered on the router. The Langflow UI no longer calls them (it uses `POST /api/v1/build/{flow_id}/flow`), so they are only reachable by direct HTTP requests.

The issue is fixed in **Langflow 1.10.1** (`langflow-base` 0.10.1) by [#13153](https://github.com/langflow-ai/langflow/pull/13153).

### Details

In affected versions, both handlers go straight to the graph loader:

- `retrieve_vertices_order` (`src/backend/base/langflow/api/v1/chat.py`, lines 81-159 in 1.9.1) only required authentication via `dependencies=[Depends(get_current_active_user)]`. The user was never injected into the handler, and the flow was loaded with `build_graph_from_db(flow_id=flow_id, ...)`. - `build_vertex` (`chat.py`, lines 320-491 in 1.9.1) receives `current_user`, but only uses it for variable resolution (`us…