Realizing Possible Outcomes through Feasible Mechanism Paths in Generative Relational Models

A possible outcome can have several mechanism paths while depending on one shared condition. This paper develops a model of target availability through feasible paths in the generative relational framework. Feasibility is checked at every execution prefix before words are compressed to semigroup products. Persistent positive requirements yield finite minimal requirement families, while dependency cuts identify condition removals that disable every target route. An actor-control map separates condition multiplicity from independent control. Resource ledgers derive the minimum initial stock required by consumption and production at successive steps, and joint profiles preserve incompatible combinations of permissions and resources. Additive restoration is characterized by minimal deficit profiles. Under uncertain scenarios, the analysis distinguishes scenario-wise availability from a common route that can be selected with the available information. A finite deterministic information-state recursion characterizes adaptive feasible termination and distinguishes free observation refinement from costly diagnostic actions. Horizon comparisons separate remaining distance to a target from unrestricted reachability. For finite permission vocabularies and integer resources, an application of Dickson's lemma establishes finite availability bases for unbounded route families; continuous-resource counterexamples show the role of the domain assumptions. Probabilistic calculations distinguish shared-condition dependence, route selection, and realization; finite counterexamples show why more routes can coexist with lower success probability under a changed selection rule. A complete route illustration connects the constructions. The philosophical discussion examines possibility, access, agency, retained competence, dependence, and evaluation. The results are conditional on declared trajectories, requirements, information, and intervention assumptions. Empirical interpretation and the evaluation of outcomes require additional evidence and standards.