THE ARCHITECTURE-CONDITIONED FUNCTIONAL VIABILITY ENVELOPE PRINCIPLE (ACFVEP): A GENERAL CONDITIONAL FRAMEWORK FOR FUNCTIONAL PROCESSING, ARCHITECTURAL BALANCE, VARIATION, REGULATION, RESILIENCE, AND SYSTEM COLLAPSE

This paper proposes the Architecture-Conditioned Functional Viability Envelope Principle (ACFVEP), a conditional framework for analyzing whether a system can maintain a declared function under specified task demands, disturbances, architectural constraints, and regulatory capacities. The central claim is not that every system requires a universal optimal quantity of diversity. Rather, functional viability depends on the compatibility of the system's architecture, demand profile, usable response repertoire, coordination burden, resources, control policy, and admissible-state constraints.The theory defines a system-specific viability envelope. Within this envelope, the system satisfies its pre-specified functional requirements and applicable hard constraints. A balance point may be a scalar optimum, an interval, a near-optimal set, or a multidimensional region. It need not exist as a unique point. If the feasible set is empty, no admissible balance point exists under the declared system, task, and resource configuration.Variation is retained as the primary illustrative case and as a dedicated sub-branch. The Functional Variation Envelope Case (FVEC) examines conditional risks associated with insufficient usable response variety and excessive uncoordinated variation. The Variation Adequacy and Overload Mechanism (VAOM) separates task-relevant response adequacy from coordination overload. Neither low variation nor high variation is assumed to be intrinsically harmful in every system.The paper formalizes state transitions, functional specifications, architecture descriptors, variation metrics, regulatory capacity, viability sets, lower and upper thresholds, normalized distances, collapse-risk models, and uncertainty reporting. It addresses linear mechanical systems, information-processing systems, networks, and nonlinear or chaotic processes. Three worked mathematical examples illustrate constrained optimization, probabilistic collapse-threshold estimation, and the distinction between dynamical stability and noise-limited operating constraints.The framework is accompanied by ten core hypotheses, explicit falsification criteria, model-comparison procedures, an architecture-conditioned threshold-estimation protocol, a reproducibility checklist, and a research roadmap. All numerical examples are illustrative rather than empirical. The proposed framework requires domain-specific construct validation, parameter estimation, uncertainty quantification, held-out predictive evaluation, and independent replication before any stronger scientific claim is justified.Keywords: systems theory; functional viability; architecture; task demand; regulation; response variety; coordination overload; collapse risk; threshold estimation; resilience; stability; information processing