THE PERSISTENT CORE EXTREMIZATION-MACROSTATE VIABILITY REGULATION THEORY (PCEM-VRT)

This manuscript presents the Persistent Core Extremization-Macrostate Viability Regulation Theory (PCEM-VRT), a proposed general framework for investigating a particular relationship in complex dynamical systems: an internal process may exhibit a persistent tendency toward a high or low state while the aggregate functional state remains near a reference condition or returns to an admissible operating region.The theory distinguishes internal dynamics from macrostate dynamics, the reference state from the viability region, endogenous restoration from active feedback regulation, and present admissibility from future recoverability. Its primary case, Persistent-Core Extremization with Macrostate Restoration (PCEMR), concerns the possible persistence of internal extremization after aggregate recovery.A normalized scalar model is introduced to illustrate bidirectional extremal tendencies. A separate macrostate equation represents internal coupling, external disturbance, endogenous restoration, and control input. The manuscript defines a general state-space extension, an admissible state set, a conceptual viability kernel, a recovery feasible set, and operational measures of internal extremity, macrostate deviation, control effort, recovery time, and core-macrostate decoupling.The architecture contains twenty-six theoretical layers, twelve proposed mechanisms, fifteen candidate research domains, twelve testable hypotheses, and a twenty-four-stage research roadmap. Competing explanations, boundary cases, falsification criteria, simulation procedures, and empirical validation requirements are specified.PCEM-VRT is a conditional research proposal, not an established universal law. The mathematical examples demonstrate properties of the stated equations only. Whether the proposed internal-aggregate decoupling provides additional explanatory or predictive value must be established through a systematic review of existing theories, formal analysis, parameter identification, and independent empirical testing.Keywords: complex systems; extremal dynamics; macrostate regulation; viability; nonlinear dynamics; feedback control; state-space models; recovery feasibility; internal-aggregate decoupling; critical transitions; falsifiable theory.