Theorem: The RAC violation does not identify an environmental quantum-memory resource

A violation of $3/4$ in the present delayed single-receiver task does not imply quantum non-Markovianity or quantum environmental memory.

The winning code can use identity storage and no persistent environmental register.

Proof. Use Theorem thm:qubit and identity interval channels. Every interval acts on the current carrier only. The process is Markovian on that carrier, while the score is $1/2+1/(2\sqrt{2})$.

The stored qubit retains input information, but no cross-interval environmental memory is needed.