General and Restricted Finite Operational Theory

Real decision and control systems operate under finite observation, time, computation, evidence, authority, human attention, resources, and reversibility. The central problem is not only how to optimize inside a given model, but whether the current problem representation remains sufficient for the decision being made. Complex systems can fail even when every local component is individually reasonable: one valid intervention can alter another operational space's feasible region, consume a shared finite quantity, invalidate a previously applicable rule, or reduce future reachability. General Finite Operational Theory (GFOT) treats such local-to-global failure as a problem-formation issue when the relevant coupling or boundary change is decision-relevant and insufficiently represented. Restricted Finite Operational Theory (RFOT) is the lower-complexity form used when relevant cross-space effects are fixed, weak, non-binding, negligible, or already encoded in the active model or specialized solver. The framework separates three conceptually different causes of an inadequate result: solver insufficiency, representation insufficiency, and an undetermined cause. Solver insufficiency permits solver reselection while preserving the current representation; representation insufficiency requires problem reconstruction; an undetermined cause preserves UNKNOWN and supports bounded observation or test rather than forcing a false diagnosis. Stable discovered structure can be compressed from GFOT to RFOT and then toward deterministic handling, while applicability assumptions remain subject to re-evaluation. The same discipline applies to reusable experience: prior validity or prior success does not by itself establish current applicability, transferability, or authority to execute. Reused knowledge must remain conditioned on the current problem class, dependencies, version, evidence, resources, and operating context. LimFlex operationalizes the selected feasible state into bounded next actions and preserves the separation between solver output, judgment, authority, and execution. The paper is a public conceptual framework; it does not disclose implementation-specific thresholds, proprietary transition logic, patent-claim mappings, or production control policies.

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