Affective Endurance and Closed-Loop Access to Adaptive Change: An integrative framework for residual-guided repair, governed action and recursive feasibility

Abstract

Adaptive systems can preserve a reserve yet lose access to a required change. AGM-CL couples response proposals, source-bound residual history, guarded model repair and executed action through a shared resource ledger and fixed task contract. Conditional one-step results separate response, information and affordability; a finite reach-avoid characterization extends them to observation-contingent continuation and whole-information-set handoff. In the declared finite reference, continuation-first admission completes 9 of 16 information states (18 of 32 hidden-sign assignments), while an equally informed probe-first policy completes 25 assignments by accepting a paid observation on uncertifiable branches. A same-policy conventional controller ties exactly. Removing sensitivity leaves the original 192 assigned paths unchanged, so that grid tests the information-resource interface rather than affect-specific efficacy. Exact implementation checks, reproduced component scripts and external comparisons retain separate evidentiary status. The contribution is an operational interface with conditional guarantees; identified affective mechanisms and performance gains remain application-level tests. Note on Version 3.0. This version replaces Version 2 (May 2026; then titled "Affective Endurance and Emotional Criticality in Adaptive Governance Systems: A Dynamical Systems Theory of Emotional Governance") and is a full rewrite (about 10,100 to 23,700 words). The core is recast as AGM-CL, a closed-loop interface with conditional one-step results, a finite reach-avoid characterization and an executed finite reference. The Emotional Criticality Condition is kept as a lower-information warning proposal, and the criticality extensions are separated as conditional. Four synthetic legacy programs (L-AGM1 to L-AGM4) reproduce and are retained as component calculations, not as validation of the revised predictions; a fifth (L-AGM5) lacks its inputs and is excluded. Files: the manuscript as PDF and a supplement archive (78 files) with the finite reference model and its checks, the external arithmetic and the reproduction of the legacy programs. The Version 2 files remain available in the previous version of this record. Series. Paper E of the Affective Gain Module (AGM) programme. The integrative flagship, Affective Governance in Adaptive Systems, and the other companion papers (A to D 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).