Structured Outputs: Recursive schemas cause infinite loop

When using Structured Outputs with a recursive JSON schema (e.g., a tree structure where nodes can contain child nodes), the API enters what seems like an infinite loop and eventually times out.

{
  "type": "object",
  "properties": {
    "name": {"type": "string"},
    "children": {
      "type": "array",
      "items": {"$ref": "#"}
    }
  }
}

The request hangs for the full timeout period and then returns a 500 error. Non-recursive schemas work fine. Is recursive $ref supported?