Residual Genesis and Dynamic Feedback Route Attribution in Hierarchical Recalibration

Abstract

Within Soft and Hard De-Attraction (SHDA), cross-level residual differences can arise from observation, translation, weighting and selection as well as state deviations. This paper separates residual values from routes that change future data and specifies model-conditional partial identification of residual sources with typed, certificate-backed outputs. Proposition R2 gives emptiness and boundedness criteria, attained intervals for named linear functionals (closed-form for a Euclidean error ball), decision identified sets and an information limit; Corollary R2' adds exact membership tests and certified outer bounds under operator uncertainty; and a certified-output contract fixes the certificate licensing each output. For noiseless linear observations of a common state, exact cross-level translators exist precisely when a kernel inclusion holds; the fixed-translator bound relaxes an exact joint compatibility test. Route diagnostics are finite-probe gains, distinct from uniform feedback envelopes; a four-valued screen certifies candidate signals of feedback-induced overfitting without establishing pathology. Proposition R9 bounds population selective risk by the allowance over positive decision coverage and sets information ceilings by identical-law classes. A planted-cause study illustrates these limits in a supplied catalogue with a built-in passive ceiling: two wrong low-budget singletons were observed, diagnosis-guided repair showed no material advantage over certified full refresh, and selected archived outputs have been rechecked against retained code. The contribution is typed evidence rules over established conditional mathematics, not universal causal diagnosis, response certification, algorithmic superiority or authority; route and screening designs remain untested. Note on Version 2.0. This version replaces Version 1.0 (September 2026; about 8,000 words) and is a substantial revision (about 20,300 words). It adds Proposition R9 on population selective risk, a certified-output contract, a four-valued screen for feedback-induced overfitting and a planted-cause study; selected archived outputs were rechecked against retained code. Files: the manuscript as PDF and a supplement archive (15 files) with the exact mathematical and identification-route checks and the frozen-law evidence recalculation; the full shared validation reports are in the supplement of the flagship record. The Version 1.0 file remains available in the previous version of this record. Publication role. Companion A 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, Companion C on family-scoped capability control, typed lineage and atomic re-entry, and the technical working paper SHDA Algorithms for Scoped Evidence Reuse and Recalibration. No deployment result is reported. AI use disclosure. Generative AI (GPT-6.0, OpenAI; Claude Opus 5.5, Anthropic) was used substantively in preparing this work, including source comparison, drafting and editing, and, where applicable, mathematical and counterexample checks and the writing and running of supplementary code. The research questions, framework and final claims were directed and reviewed by the author, who takes full responsibility for the content, including the accuracy of all references and reported numbers. Repository metadata were prepared with assistance from Claude (Anthropic).