The Functional Direction-Purpose Mismatch Framework (FDPMF): A Goal-Relative Theory of Direct Functional Utility, Capability Acquisition, and Signal-Based Identity Inference

AbstractThis paper proposes the Functional Direction-Purpose Mismatch Framework (FDPMF),a goal-relative framework for analyzing operations whose functional direction may notcorrespond to an agent's specified purpose. The framework distinguishes structural direction-purpose relations from measured direct utility, capability acquisition from execution, anddirect utility from broader functional value.The mathematical core defines incremental direct utility as a difference between expectedgoal-related outcomes under an operation and a specified baseline. This definition enablesconditional statements about positive, zero, or negative contribution while avoiding theunsupported inference that a mismatch automatically makes an operation universally useless.A separate Signal-Identity Inference Module (SIIM) examines how an observed eventis used to infer an agent's identity or motive. Bayesian notation is used to formalize theevidential relationship between an observation and competing hypotheses. The frameworkdoes not treat any single learned or performed behavior as a deterministic indicator of sexualorientation.The primary illustrative case concerns a heterosexual self-identified male learner beingtaught a sexual behavior directed toward a male recipient, where the intended use is excludedfrom the learner's explicitly specified personal sexual goal. The case is conditional on theseassumptions and is distinguished from a control case in which the target of the learnedoperation is consistent with the learner's stated goal.The paper defines the framework's ontology, terminology, mathematical variables, coremechanism, propositions, boundary conditions, operationalization protocol, empirical hy-potheses, research domains, falsification criteria, and manuscript-development roadmap. Noempirical results are claimed. The paper concludes that the framework is conceptuallyspecified for investigation, while its empirical validity and novelty remain open.