Latent Generativity and Counterfactual Capability: An Identification Framework for Finite Traces

A diagnostic for generativity exploitation compares a participant's effective generative capability across arrangements. Its object is a set of viable trajectories reachable under declared conditions. Nothing observable is that set: what can be recorded is a finite sample of realized trajectories, produced under conditions that actually obtained and through a channel that may project, censor, aggregate, or add noise. Three constraints sharpen the difficulty. A trajectory is an observation of generativity rather than generativity itself, and two distinct dynamical systems can share one locally. Future repertoires cannot be predicted and past generativity is hard to evaluate, because trajectories only sample it. And chained counterfactual reasoning about unrealized generation is a form legal reasoning generally declines. Together these threaten the surrounding programme with unfalsifiability. This paper responds by decomposing the problem into six inferential layers with independent failure modes, and by establishing where evidence does and does not constrain the capability object. The negative half is transferred with attribution from two companion projects, which established that exact equality of accessible history laws fixes binary discrimination at chance, that behaviorally silent structure is invisible, and that enlarging a probe family refines an equivalence partition. The paper's own contribution concerns a target those results do not reach: a reachable repertoire is set-valued and is indexed to conditions that were never realized. Writing the repertoire as a superlevel set of a reachability functional converts a question about set equality into a question about how far that functional moves across an observational equivalence class. Five results follow. The counterfactual repertoire is sharply bounded by the core and hull of the class. A model class permitting on-regime behavior to be spliced to arbitrary off-regime behavior collapses those bounds to whatever the class alone permits, so the lift fails maximally. Otherwise uncertainty about the organization confines uncertainty about the repertoire to a band around the reachability threshold, whose width is the class's off-regime deviation. A capability comparison is identified across the entire class whenever the gap between assessed and baseline functionals exceeds the combined ambiguity. And under uniformly condition-Lipschitz kernels that ambiguity is at most twice the Lipschitz constant times the distance from the counterfactual condition to the observed regime. The surgery construction and the Lipschitz bound bracket the problem: without a structural tie between off-regime and on-regime behavior no counterfactual information is available, and with a uniform tie the bounds degrade gracefully with counterfactual distance. Four theses argue that non-identifiability is a property of a model class paired with a design rather than evidence against the object, that the framework is falsifiable exactly because it returns determinate negatives, that identification failure allocates an evidential benefit to the party controlling the records, and that existence claims reach conclusions magnitude claims cannot. The paper establishes no estimator, no general non-identifiability theorem, and no valuation method, and classifies no observed relation.