One Layer, Both Gaps: A Persistent-Modulation Recurrence that Generalizes Copy and Tracks Non-Solvable Group State

We present DABSN, a single recurrent block design that closes both the copy memory-bandwidth gap and the non-solvable group state-tracking gap. Separately trained instances generalize copy to 50 times training length and track the A5/60 word problem to 64 times training length. Causal ablations isolate the nonlinear recurrent state and learned retrieval primitives responsible for the two capabilities.