11.3 Finite operators and propagated uncertainty

The finite-operator study, DIAL-SKFM–1B, removes the exact-operator assumption and estimates both intervention operators independently from finite noisy state–velocity samples, estimates their row covariances, and propagates both sources of uncertainty through the commutator by parametric sampling. A frozen classifier then compares the uncertain residual with the registered repair templates and abstains when neither fit nor posterior separation supports a typed extension. The reported record is the registered v2 execution; v1 stopped before any admission data were opened, and v2 made only a serialization-type correction, so the two records are not independent trials. Across \(1{,}620\) preregistered admission worlds, the operator intervals were close to nominal coverage: their empirical 95% coverage on nonzero entries was 93.6%. The uncertainty-aware rule covered 69.1% of supported worlds and was correct on 96.5% of the supported cases on which it acted, with no false extension in closed worlds. It nevertheless failed the complete admission contract: overall action accuracy was 71.7%, below the registered 85% threshold, and unsupported-case abstention was 81.9%, below the registered 90% threshold. No confirmation run was therefore opened.

This failure is diagnostic rather than merely aggregate. At observation noise \(0.2\), overall accuracy was 89.3% and unsupported abstention was perfect; at noise \(1.2\), they fell to 49.6% and 62.2%. With structural strength \(1.0\), accuracy reached 87.0% and unsupported abstention 94.4%; with strength \(0.2\), they were 55.7% and 65.6%. The difficult unsupported class was the noncentral extension, on which the method abstained 73.7% of the time, whereas it abstained on 90.0% of two-latent extensions. Thus uncertainty propagation successfully protects the precision of admitted repairs, but the registered residual language still aliases weak noncentral structure with closed or supported worlds.

Experiment: DIAL-SKFM–1B. World: two independently estimated linear intervention operators, with finite samples, observation noise, and supported and unsupported closure repairs.
Uncertainty: row-wise least-squares covariance propagated jointly through the commutator by 80 parametric draws.
Result: 93.6% operator-interval coverage, 96.5% selective accuracy, and zero false extensions, but only 71.7% overall accuracy and 81.9% unsupported abstention. The preregistered admission decision is abstain.
Lesson: calibrated operator uncertainty is necessary but not sufficient; a complete method must acquire evidence that separates weak noncentral extensions from the registered repair family.