Residual Genesis and Dynamic Feedback Route Attribution in Hierarchical Recalibration

Abstract

Differences in residuals across hierarchical levels can arise from observation, translation, weighting, and selection as well as state deviations. This paper distinguishes model-conditional decomposition of instantaneous residuals from routes that change future data and exposure, and connects both to a specification for recalibration inputs. We give conditions for the existence of cross-level translations, error bounds under uncertain observation, partial identification that preserves theta-dependent nuisance terms, and intervals for decision functionals. We specify the limits imposed by cancellation of mean gains across strata, coverage uncertainty near thresholds, deferred decisions, and the measurement of future risk labels. Evaluation gaps after exact distribution transport are not interpreted as feedback strength. Screening is evaluated using independent future targets, false alarms, decision coverage, and costs. The results comprise conditional mathematics and measurement and falsification specifications; they do not establish empirical performance or universal causal diagnoses. Publication role. Companion A (Version 1.0, dated 19 September 2026, about 8,000 words; unsubmitted) develops the residual-diagnosis branch of the Integrated Framework series on contract-preserving lower-to-upper recalibration (SHDA). The flagship and its Technical Supplement are archived separately, as are Companion B on intervention-disclosure visibility and time-bounded selective nondisclosure and Companion C on family-scoped capability control, typed lineage and atomic re-entry. No empirical study or deployment result is reported.