Per-Sample Invariant Tracking on MNIST with Certainty-Validity Diagnostics

Standard evaluation metrics conflate different kinds of error. A confident incorrect predic tion and an uncertain incorrect prediction are both counted identically, even though they reflect different epistemic states. This paper uses the Certainty-Validity (CVS) framework to track how those states migrate during learning. The Minimal Operative Unit (MOU) ring serves as a synthetic diagnostic environment in which quadrant migration, lock thresholds, and interven tion timing can be calibrated under controlled conditions before the same procedure is applied per-sample on MNIST. On the ring, baseline training drives CVS from 0.79 to 0.07 while accu mulating confident-incorrect states, whereas CVS-regulated and CVS-gated regimes stabilize CVS in the 0.62–0.75 range and reduce confident-incorrect predictions by 11×. On MNIST, freeze-based CVS interventions preserve aggregate CVS but also preserve still-learnable uncer tainty, showing that aggregate control is too coarse on its own. Per-sample tracking localizes the residual instability to a small tail rather than broad model degradation: at confidence threshold θ =0.7, MNIST exhibits no persistent uncertainty population, but it does exhibit a small per sistent confident-error tail, a boundary-adjacent volatile set, and a small number of drift cases. In this setting, the main value of CVS is diagnostic: it identifies where commitment is stable, where it is forced, and where uncertainty remains unresolved during training.