Linear-Readout Floors and Threshold Recovery in Computation in Superposition

ArXi:2605.01192v1 Announce Type: new Two recent approaches to computation in superposition reach different recursive capacity regimes: H\"anni certify $\tilde{O}(d^{3/2})$ computable features in width $d$ via an approximate-linear recursive template, while Adler and Shavit reach near-quadratic capacity (up to logarithmic factors) using thresholded Boolean recovery. The main contribution of this paper is conceptual: we argue these results are not contradictory because they maintain different interface invariants, and we formalize the distinction.