Hidden stress is not merely readout noise

Let $K_{\theta ,\sigma }(u,\cdot )$ be the classical probability kernel of logits generated by hidden stress. It depends on the network dynamics. An additional, independent output measurement error would be another kernel $L$, giving the observed law

These are different operations.

The noise in (eq:forwardhidden) changes the internal computation before the classifier head. Calling it an extrinsic measurement POVM would misidentify the supplied experiment. No quantum measurement model is required or claimed here.

Even Gaussian noise does not universally decrease accuracy: for a binary Gaussian margin with negative mean $\mu <0$, $\Phi (\mu /(\sigma v))$ increases toward $1/2$ as $\sigma$ increases. Noise-induced degradation therefore requires a specified correct-margin regime or a direct certificate.