What we have observed
The Hidden State Emulation manuscript describes a local width-5,376 capture fitted with a sparse Green inverse operator using 16,126 coefficients. The reported mean-coordinate R² is 0.693733 on the protected rows. This is evidence about one local approximation and its split.
What we are looking into
The next experiment should put the approximation back into the surrounding network and measure token probabilities, sequence quality, and downstream task behavior. Conversation-aware splits and prespecified dense baselines matter because a good isolated fit can hide distribution shift.
What would change our mind
If small local errors compound into large behavioral changes, the operator may still be useful as an analysis tool or initialization. It would not yet justify replacing that transformation. We want the compression claim to survive a complete behavioral test.