ssmrecall

the question

Where must a diagonal SSM's eigenvalues sit to recall recent inputs with the best conditioning, and do deployed initializations achieve it?

what came out

A diagonal SSM recalls exactly its last d inputs, aliasing input d+1 (error ~1e-15 jumping to order one). The d-th roots of unity uniquely minimize conditioning: cond(M)=1 and readout noise gain 1/sqrt(d), beating 200 random placements. Deployed S4D-Lin and HiPPO inits recover strictly fewer at d=64, and the recall horizon is independent of spectral radius.

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