Red Queen Pressure Allostatic Collapse and Stewardship Control - Toward a Mathematical Architecture for Shared Humanistic AI (SHAI)

AbstractTwo prior theoretical frameworks address related but non-overlapping aspects of AI systemstability. The Allostatic Curvature framework (Smith, 2026a) models internal geometricdegradation of neural parameter manifolds, formalising the Allostatic Load Functional (ALF) asa monotonically non-decreasing measure of information-geometric stress and defining theHomeostatic Collapse Set (HCS) as the regime of negative scalar curvature. The Red Queen'sTrap (Smith, 2026b) models external contest pressure, establishing a derived necessarycondition empirically unmet by a factor of approximately 1, 170 for simultaneoushigh-acceleration and high-integrity system states. Neither framework explains how externalcontest pressure affects the rate of internal collapse risk accumulation. This paper proposes a dynamical coupling between these frameworks and introducesstewardship as a stabilising control variable. The core contribution is a modulated loadequation: d (ALF) /dt = sqrt (gᵢj * dtheta/dt) * Phi (P, S), where contest pressure P acceleratesallostatic load accumulation and stewardship S attenuates it. Two competing formal definitionsof P are presented — Option A (derived from Red Queen acceleration Ae) and Option B (P as anindependent environmental observable) — and both are retained for external adjudication. Wederive a modified collapse threshold Lcritical (S), stewardship-dependent recovery dynamics, an explicit stability condition (Eq. A9), Conjecture C1 (Stewardship Stability), a parameteridentifiability analysis, and five testable hypotheses (H4-H8). The resulting three-layer SHAIarchitecture positions stewardship as a control layer on system parameters. The paper is atheoretical bridge contribution; no empirical data are presented. Keywords: allostatic load, information geometry, contest pressure, stewardship control, SHAI, adaptive AI governance, Red Queen dynamics, homeostatic collapse, Fisher metric, Lyapunovstability