secularmode

the question

Does RWKV-7's diagonal-plus-rank-1 transition have a real interlacing spectrum making retention safe, with instability entering only through the bottom eigenvalue?

what came out

The spectrum solves an exact secular equation and Cauchy-interlaces the decay values, pinning the top eigenvalue at max(w)<1, so retention can never expand. Instability enters only via the bottom eigenvalue at the exact boundary sum a_i kappa_i^2/(w_i+1)=1. Smaller decay lowers the removal budget needed, so decay worsens instability.

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