This volume defines target violation severity metrics and diagnostics for feature risks, suggesting new analytical approaches.
This volume develops the target violation severity layer of the Re-Phase framework.Earlier Vol.4.x volumes studied tolerant compatibility, feature drift, feature risk, posterior reweighting, local directional fragility, and Fisher-weighted local compatibility. This volume separates feature risk from violation severity. Feature risk measures how much admissible or weighted mass leaves a target region; target violation severity measures how deeply failed feature values protrude outside the target.The note defines candidate-level target violation severity, set-level violation excess, weighted severity tails and moments, posterior violation severity, and drift-to-severity bounds. It also introduces local boundary-pressure diagnostics and Fisher-weak boundary-crossing diagnostics, while preserving the Re-Phase rule that the condition side and feature side are compared only through a common configuration, admissible set, or admissible direction.Fisher information is used as statistical visibility on admissible first-order directions, not as a feature-space distance to the target. The note distinguishes weakly visible directions from completely Fisher-invisible directions, treats positive semidefinite Fisher forms, and provides Gaussian-linear closed-form criteria for identifying Fisher-weak boundary-pressure directions.This volume is static, feature-level, metric, posterior-weighted, and first-order. Path-space severity, target-tube violation, first-exit structure, accumulated path severity, stochastic temporal severity, moving observers, and gauge-like continuation are deferred to later Vol.5.x and related volumes.
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Takashi Ito (2026) studied this question.
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