[Question] How is Φ(s_i) implemented for language memory GT annotation? #5

Hi Cortex team,

Thanks for sharing this great work and releasing the code!

I have a question about the ground-truth language memory annotation used for System-2 training.

In Section 3.1, the paper defines the memory as:

$$ M^{(t)} = M^{(0)} \oplus \bigoplus_{i=1}^{k-1}\Phi(s_i) $$

where (\Phi(s_i)) encodes the completed state of subtask (s_i).

I understand how the subtask labels and boundaries are obtained, but I'm not clear about how (\Phi(s_i)) is implemented to generate the natural-language memory GT.

In the released cortex/inference/eval_subtask_dataset.py, _get_active_language_memory() appears to read action_config[subtask_id]["language_memory"] directly, so I couldn't find where these annotations are generated.

Could you please clarify:

1. How is (\Phi(s_i)) implemented? Is it based on deterministic templates/rules, an LLM/VLM, or manual annotation?
2. How is the accumulated memory constructed? Are completed-subtask descriptions simply concatenated, or is there an additional summarization/compression step?
3. Would it be possible to share the memory annotation script or prompt, or a minimal example showing how the language_memory field is generated?

This would be very helpful for reproducing the System-2 training pipeline.

Thank you!