Detectability and coverage under restricted access: linear-Gaussian pilots of the blind set

Abstract

This record contains the technical note and complete reproducibility package for two linear-Gaussian pilot studies of the “blind set” in physical-state inference. The blind set is defined here as errors that are simultaneously not exposed by the inference system’s available ground-truth-free diagnostics and not covered by its own reported uncertainty in a decision-relevant quantity. The pilots examine the conjecture that such confident, invisible error arises through the interaction of physical access and prior support. Pilot 1 tests whether detectability can be predicted from the model and observation operators alone. Predicted detectability ranked 52 misspecification directions in agreement with realised detection (Spearman ρ = 0.91); the least detectable directions were nevertheless largely covered by the system’s reported uncertainty. Pilot 2 varies access and model-side prior support separately. Errors beyond sensor reach escaped the diagnostics, while the strongest loss of coverage occurred for errors receiving little or no prior support. The results suggest that prior support, rather than binary representability, is the operative model-side factor. The studies are deliberately limited to linear-Gaussian inference on a two-dimensional synthetic degradation field. They are offered as reproducible preliminary evidence and a controlled test of the proposed object, not as evidence that the same behaviour holds for learned, non-linear inference. The accompanying reproducibility package contains all scripts underlying the reported results and Figure 1, fixed random seeds, pinned software versions, raw computational results, a single run_all.py reproduction script, a README mapping each reported result to its generating script, and results/summary.md comparing the reported and reproduced values.