Curvature as Decoder State: Exact Cache–Update Frontiers for Strongly Convex Unlearning

Machine unlearning depends on what task-dependent state survives deployment and what a later deletion request reveals. We separate pre-request decoder state $M$ from post-request delivery $B$ and study reconstruction of a fixed retraining procedure under an explicit serialized interface. For smooth strongly convex objectives, parameters plus a revealed deletion gradient leave an exact $d$-dimensional compatible-target ball, while exact curvature on $s$ orthogonal directions removes precisely $s$ dimensions from the high-rate description length. A request-oblivious cache that must hedge $r$ future directions instead preserves $p_r=rd-r(r-1)/2$ symmetric degrees of freedom, distinguishing the state-only and request-time coefficients. Ridge regression realizes these statements through an exact Woodbury downdate: retained rows and exact sufficient statistics require no additional transcript under their stated interfaces, whereas parameters alone require $\Theta (d\log (1/\epsilon ))$ bits on a compact family. A fixed float64 audit covering $270$ cells, $2,880$ paired requests, and $17,280$ state/interface evaluations confirms that sufficient statistics are dominated by parameters on all nine identifier-only surfaces but become nondominated when requests expose deleted values. Gaussian-design tests recover the predicted $\sqrt{k}$ request scaling and $m^{-3/2}$ curvature fluctuations for retained sample size $m$, while the selected curvature caches in our main comparison reduce delivery by $6.8\%$–$19.6\%$ only by increasing serialized state and requiring repeated requests to amortize it. The resulting frontier prices curvature as decoder state, not free compression, and makes no zero-memory, universal finite-bit, or end-to-end neural-converse claim.