A Control-Theoretic Model for Stochastic Interaction under Hidden-State Uncertainty and Demand-Sensitive Response Degradation

Gonzalo Emir Durante (Independent Researcher; Origin Node, Project Manifold 0. 56; Symbiotic Autoprotection System) Version 1. 2. 0 Background: Partially observable stochastic systems often exhibit demand-sensitive degradation — a nonlinear response reduction when accumulated external pressure crosses a hidden threshold. Classical POMDP formulations address partial observability but leave accumulated demand, degradation thresholds, and channel preservation implicit. Objective: To formalize a control model for interactions between a strategic controller-observer (A) and a partially observable agent (B) whose response degrades nonlinearly beyond a hidden demand threshold θB. Methods: We extend the POMDP framework with exponentially decayed accumulated demand DA (t), a smoothness-based channel preservation reward Vₗink (t), Bayesian belief updating over five hidden states, and a cost function J with calibrated free parameters. Safe exploration is formalized via quantile-based threshold estimation. Value iteration over discretized belief space provides an auditable policy derivation. Results: A five-state simulation under a conservative low-demand trajectory achieves 59. 5% entropy reduction from maximum uncertainty (1. 609 nats) to 0. 651 nats, converging toward the ambivalent state (p = 0. 84). All free parameters are now operationally defined with calibrated indicative ranges. Conclusions: The model provides a formal architecture for reasoning about stochastic interactions with hidden state and demand-sensitive degradation, expressed as a reviewable, calibratable, and extensible technical artifact. A formal research conjecture links the belief entropy index χₜ to the SAS structural integrity index ISIₜ, opening a bridge between static semantic stability and dynamic interactional stability. "likelihoodₙote": "The MVP uses the five-state appendix likelihood matrix. The reduced three-column table in the paper is treated as didactic compression. "