Terrain-Contingent Gain in Adaptive Governance Systems: Identifiable response geometry and budgeted closed-loop recalibration

Abstract

A context-sensitive response curve can be well defined yet unidentifiable from its controller's observations, and an identifiable curve may not merit recalibration before a resource-limited task. This paper builds the terrain-contingent gain interface of the Affective Gain Module (AGM) on these distinctions. Version 1's Hill family (threshold, slope and ceiling channels) is kept with explicit domains, the exact slope supremum and a corrected reading of slope modulation. Identifiability is judged on the observed response law, not a simulator's latent gain. Inverting admissible Hill curves gives a common-dose condition and a task-relative criterion for paid calibration. In a finite loop of probing, belief update, governed work, context change and requalification, an exact planner certifies both tasks in 196 of 320 design cells, 160 without probing and 90 if identifying first. A myopic rule succeeds for every hidden scale in 192 cells, certainty-equivalent control only in the 160 needing no identification, terrain-blind control in none. In 800 repeated noisy fits, held-out mean-response error stays below 9% of the noise standard deviation while the slope estimate varies by about 6%. Version 1's five synthetic programs rerun reproducibly, but their strongest results rest on a surrogate score, boundary fits, a truth-initialized noise-free fit or starting vectors kept after nonfinite objectives; two financial programs lack inputs; a price-impact test of the slope channel is specified instead. Visual-attention studies quantify threshold and response-gain changes without identifying AGM terrain. The contribution is a testable calibration-to-action interface, not a new gain-scheduling principle, universal coefficient signs or affect-specific superiority. Note on Version 2.0. This version replaces Version 1 (May 2026; then subtitled "A Calibration Framework for Context-Dependent Affective Response") and is a full rewrite (about 4,700 to 13,000 words). Version 1's Hill family is kept with explicit domains and a corrected reading of slope modulation, identifiability is now judged on the observed response law, and a finite loop of probing, governed work, context change and requalification is analysed exactly. The Version 1 synthetic programs rerun reproducibly, but their strongest results are reported as resting on a surrogate score, boundary fits or a truth-initialized fit, and its two financial programs lack inputs. Files: the manuscript as PDF and a supplement archive (108 files) with the noisy response fits, the finite 320-cell control grid, the 800 repeated fits and the five unchanged legacy programs with their observed failures. The Version 1 files remain available in the previous version of this record. Series. Paper C of the Affective Gain Module (AGM) programme. The integrative flagship, Affective Governance in Adaptive Systems, and the other companion papers (A, B and D to 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).