Bug | Reasoning on OpenAI's models doesn't work with `store=False`

[niv-hertz]

Describe the bug

When using Reasoning with OpenAI's models, and running with store=False, running models with reasoning doesn't work, due to not including the reasoning.encrypted_content in the responses API (https://platform.openai.com/docs/api-reference/responses/create#responses-create-include)

When you try to use it, you get this error:

Error getting response: Error code: 404 - {'error': {'message': "Item with id 'rs_68582a79cb90819a9167d188b812af9c0a03470b8e30fdc6' not found. Items are not persisted when `store` is set to false. Try again with `store` set to true, or remove this item from your input.", 'type': 'invalid_request_error', 'param': 'input', 'code': None}}. (request_id: req_b7bdc79b7db5caf9bea5f55ac43b02de)

There is no way to override this behavior, it is hard-coded in the responses wrapper used by the SDK.

Debug information

• Agents SDK version: (e.g. v0.0.18)

Repro steps

Create an Agent that uses reasoning, with the following model settings:

agent = Agent(
    name="example_agent",
    tools=[some_tools...],
    model="o3",
    model_settings=ModelSettings(
        store=False,
        reasoning=Reasoning(effort="low", summary="detailed")
    ),
    instructions="""some prompt"""
)

Expected behavior

Expecting the reasoning.encrypted_content to be passed to the API when the store=False parameter is set, and the SDK to send the encrypted reasoning message on following steps to be able to continue the conversation with the reasoning content.