Functional Process Control Dynamics

This paper introduces Functional Process Control Dynamics (FPCD), an auditable framework for evaluating claims about functional roles, process recurrence, directed physical flows, operational control, and environmental feedback under uncertain protocols. FPCD addresses a recurring problem in complex systems research: observations of persistence, repeated behavior, energy use, organizational authority, or correlated system changes are often interpreted as evidence of selection, control, causal influence, or functional continuity. The framework prevents these category errors by specifying which conclusions are identified by the available evidence, which are only partially identified or bounded, and which remain undefined. The framework separates several analytically distinct layers. These include opportunity creation versus responses within pre-registered opportunities; functional-role classification versus quantitative role accounting; compositional change versus provenance-supported recurrence; recurrence versus functional selection; measured exergy flows versus controller exposure, institutional authority, and signed policy effects; and factorial interactions versus identifiable feedback-path effects. Multifunctional processes are represented using mutually exclusive role-complex categories, while provenance hypergraphs distinguish persistence, branching, merging, recombination, independent origin, import, and unresolved linkage. FPCD combines causal inference, partial identification, process provenance, control-system analysis, and thermodynamic exergy accounting. Directed exergy is measured using explicit physical boundaries, reference environments, ports, and changing inventories. Controller attribution requires an interventionally addressable policy, an information input, and an auditable actuator path; observed authority or association alone is insufficient. The paper also distinguishes population compatible-value regions, sampling uncertainty, measurement error, and cross-protocol transport error. Its principal output is a claim certificate that records the estimand, protocol, evidence, compatible-value region, decision threshold, and status of the claim. Possible statuses include supported, false conditional on maintained assumptions, not identified, protocol inconsistent, and comparison undefined. A synthetic data-centre microgrid example demonstrates closed energy and exergy balances, transient electrical and thermal inventories, workload and cooling policies, safety outcomes, and feedback-regime interactions. Additional countermodels show why identical endpoint observations can remain compatible with different recurrence, selection, convergence, import, and hidden-transmission explanations. FPCD is applicable to artificial, biological, human, organizational, cyber-physical, and hybrid systems. It does not treat intelligence, fitness, agency, value, or energy consumption as universal explanatory primitives. Instead, it provides explicit evidential requirements and stopping rules for constructing reproducible and falsifiable claims about functional processes in heterogeneous open systems.