What a radical-pair quantum reservoir would require: readable capacity, no quantum advantage, and a nuclear-register criterion

Abstract Whether the electron--nuclear spin coherence behind radical-pair magnetoreception could also support biological \emph{computation} has been conjectured for decades but never made quantitative. We treat a cryptochrome-type radical pair as a reservoir computer, solving the radical-pair master equation with electronic decoherence and driving it as a real turnover does---by the birth of a spin-correlated pair whose singlet character encodes the input. Three results follow, none of them the expected one. The reservoir is \emph{readable by ordinary chemistry}: the nuclear polarisation the product carries away gives an out-of-sample information-processing capacity of $4.7$ against its own memoryless floor of $2.0$, with no spectroscopy. There is no quantum advantage: a classical network matched channel-for-channel exceeds the five-spin reservoir by $49$--$123\%$. And the memory horizon is set not by the microsecond pair lifetime but by the turnover interval, because the nuclear register survives recombination in the diamagnetic product---so the binding constraint is chemical rather than temporal, namely that the \emph{same} register be reused between turnovers. Predicting the register's relaxation instead of assuming it makes that constraint testable: at the geomagnetic field a proton on the intact protein relaxes in milliseconds, not seconds, capping the horizon below the neural band unless the register's dipolar vector reorients about two and a half times faster than the protein ($\tau_{\rm eff}\lesssim6$~ns). What survives is a smaller claim on firmer ground: a criterion whose two constants can be measured in vitro, in place of one whose central relaxation time was never measured at all.