fix(llm): satisfy lowercase json_object prompt checks (#887)

* fix(llm): satisfy lowercase json_object prompt checks

* style(llm): preserve JSON acronym in prompt

src/llm/backends/openai.py

@@ -30,11 +30,12 @@ def _json_object_instruction(response_format: type[BaseModel]) -> str:
     instruction — the deriver issues one structured call per batch on the worker
     hot path and would otherwise re-walk the schema + re-serialize it every call.
     """
-    # "JSON" must appear in the messages to satisfy the json_object contract.
+    # Some OpenAI-compatible providers enforce this JSON-object precondition with
+    # a case-sensitive substring check, so include lowercase "json" explicitly.
     return (
-        "You must respond with a single JSON object that conforms exactly to "
-        "the following JSON schema. Do not include any text, markdown, or code "
-        "fences outside the JSON object.\n\nJSON schema:\n"
+        "You must respond with a single JSON object (json) that conforms "
+        "exactly to the following JSON schema. Do not include any text, "
+        "markdown, or code fences outside the JSON object.\n\nJSON schema:\n"
         f"{json.dumps(response_format.model_json_schema())}"
     )
 

tests/llm/test_backends/test_openai.py

@@ -808,6 +808,7 @@ async def test_structured_output_json_object_mode_request_shape() -> None:
     assert system_messages, "expected a system message carrying the schema"
     system_content = system_messages[0]["content"]
     assert "JSON" in system_content
+    assert "json" in system_content
     assert "answer" in system_content  # schema property serialized in
     assert isinstance(result.content, _StructuredResponse)
     assert result.content.answer == "ok"
@@ -943,4 +944,6 @@ async def test_stream_structured_output_json_object_mode() -> None:
     call = _await_kwargs(client.chat.completions.create)
     assert call["response_format"] == {"type": "json_object"}
     system_messages = [m for m in call["messages"] if m["role"] == "system"]
-    assert system_messages and "JSON" in system_messages[0]["content"]
+    assert system_messages
+    assert "JSON" in system_messages[0]["content"]
+    assert "json" in system_messages[0]["content"]