Distortion-Corrected Emotional Criticality: Observation limits, protected evidence and budgeted closed-loop recovery

Abstract

An internally consistent report can conceal a dangerous state, while an integrity alarm can occur without task failure. This paper links distortion monitoring in the Affective Gain Module (AGM) to recoverable information and useful action. The six-channel quadratic score and capacity correction remain conditional models. Total variation bounds every detector's true-positive minus false-positive rate, and a protected-domain criterion states when task labels survive bounded corruption; both specialize standard results. In a synthetic test, a report-only residual detects incoherent alteration within ten steps in 99.4% of episodes. Coherent forgery has the clean report law by construction, with observed alarm rates of 27.3% versus 26.5%; a noisy protected reserve sensor yields 53.5% versus 25.3%. These samples do not establish empirical equivalence. In a finite reference with paid audit and repair, trusted operations add no certified coverage at the declared prices (536 of 640 cells): the common route's saved slot can fund recovery that offsets its higher work cost. They add 30 cells when each common-route operation costs one unit more, 54 without that route, and none where reports identify the regime. Legacy programs reproduce, but a no-event sentinel mislabels most forecast positives and neither archived channel ranking survives correction. The results establish conditional interfaces, not universal detection, affect-specific efficacy or deployed security. Note on Version 2.0. This version replaces Version 1 (May 2026; then subtitled "A Robustness Framework for Adversarial Governance Signals") and is a full rewrite (about 4,500 to 13,000 words). The six-channel quadratic score and capacity correction are retained as conditional models; detection limits, a protected-evidence criterion and a finite reference with paid audit and repair are added. The legacy programs reproduce, but a no-event sentinel mislabels most forecast positives and neither archived channel ranking survives correction. Files: the manuscript as PDF and a supplement archive (93 files) with the retained experiments and checks, the finite reference, independent audit outputs and the legacy programs. The Version 1 files remain available in the previous version of this record. Series. Paper D of the Affective Gain Module (AGM) programme. The integrative flagship, Affective Governance in Adaptive Systems, and the other companion papers (A to C, E and F) are archived separately. 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).