Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
Physical selectors (lasers choosing a mode, Ising machines settling on a ground state, condensates occupying a spin state) produce high-dimensional signatures at the moment of decision: full field amplitudes, multimode interference patterns, or scattering responses. These signatures are richer than the winner's index, yet they are routinely discarded. We show that when the signatures are repeatable across trials (stereotyped) and linearly independent across routes, a single linear decoder compiled from calibration data maps them to arbitrary payloads, merging selection and memory access into one event and eliminating the fetch that dominates latency and energy in sparse routing architectures. The construction requires one SVD of measured device responses, which certifies capability and bounds worst-case error for any downstream payload before the task is chosen. Runtime error separates into two independently diagnosable channels, decoding fidelity (controlled by dictionary conditioning
σmin(Φ)) and routing reliability (controlled by the margin-to-noise ratio
Δ/Teff), each with a distinct physical origin and targeted remedy. We derive the full error decomposition, give Ising-machine selector constructions, and validate the predicted scalings on synthetic speckle-signature simulations across three measurement modalities. No hardware demonstration exists; we provide a falsifiable four-step experimental protocol specifying what a first experiment must measure. Whether real device signatures satisfy stereotypy is the central open question.