THE ABSOLUTE-CLAIM COMPATIBILITY FRAMEWORK (ACCF)

Descriptions of the same person, process, or system may initially appear incompatible when one description is interpreted as an uninterrupted or absolute condition while another is interpreted as requiring an activity or state that appears to compete with it. Such apparent conflicts can arise from genuine resource constraints, but they can also result from semantic ambiguity, mismatched time scales, unstated assumptions, or unsupported inferences.This manuscript introduces the proposed Absolute-Claim Compatibility Framework (ACCF), using THE COOL GEEK'S PARADOX (CGP) as its primary case study. The case concerns the apparent tension between a description of a person as being continuously occupied with studying or personal work and retrospective reports that the person's interpersonal behavior was very good. The case becomes formally incompatible only under additional assumptions, such as strict temporal exclusivity and a positive requirement for separate interpersonal-contact time.The proposed core mechanism, the Claim Operationalization-Constraint Feasibility Mechanism (COCFM), separates natural-language claims, semantic interpretation, operational definitions, constraint construction, joint-feasibility assessment, and extreme-regime analysis. A mathematical representation is introduced using a state space, operational predicates, a feasible-set definition, and an indicator for joint satisfiability. A conditional monotonicity proposition establishes that strengthening constraints cannot enlarge the feasible set when the constraint sets are nested. A time-allocation example demonstrates how infeasibility follows under explicitly stated exclusive-time assumptions, while also identifying circumstances under which no contradiction follows.The framework integrates philosophical, epistemological, systems- theoretical, mathematical, computational, and methodological components. It proposes twelve analytical layers, a three-stage analysis cycle, a fourteen-gate research protocol, and a thirty-case validation plan. These are research-design specifications rather than completed empirical findings. The framework's originality, explanatory advantage, cross-domain scope, and usefulness must be evaluated against established work on paradoxes, constraint satisfaction, resource allocation, measurement, and scientific methodology.