This article develops the relational action layer of the Finite-Horizon Structures programme. Building on the completed finite-horizon propagation domain obtained from regular propagation, singular transition data, and stratified gluing, it introduces an action-selection framework defined only on admissible histories. The article defines admissible stratified histories, regular stratum Lagrangians, singular transition costs, optional endpoint terms, relational action functionals, maintained variations, restricted relational stationarity, maintained criticality, and the matching conditions produced at regular corners, active thresholds, and singular transition events. Its purpose is not to derive admissibility from an unrestricted least-action principle, but to determine how an action functional can compare, penalise, and select among histories that are already admissible within a completed finite-horizon propagation structure. The framework distinguishes propagation admissibility from action selection. Ordinary Euler--Lagrange equations are recovered on smooth regular free intervals, while constrained intervals, threshold contacts, corners, and singular transitions lead to variational inequalities or relational matching conditions. The article also clarifies the projective covariance of the action, the non-uniqueness of action data, and the conditions under which optional received-influence cones or metric-type structures may arise from additional quadratic action layers. This work provides the relational action-selection layer of the Finite-Horizon Structures programme and prepares the ground for later effective geometric and physical realisation layers, including metric, Hamiltonian, gauge-like, field-theoretic, or dissipative extensions. This article forms part of the Ranesis framework developed by Alexandre Ramakers.
Alexandre Ramakers (Fri,) studied this question.