The consistency statement in causal inference: a definition or an assumption?

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Estimating Average Causal Effects Under Interference Between Units (2013, background): “Interference represents a departure from the traditional causal inference scenario wherein units are assigned directly to treatment or control, and the potential outcomes that would be observed for a unit in either the treatment or control condition are fixed (Cole and Frangakis, 2009) and do not de”
Propensity score matching and subclassification in observational studies with multi‐level treatments (2015, neutral): “…with more than two treatment levels (exceptions include Imbens, 2000; Robins, Hernan, and Brumback, 2000; Lechner, 2001; Foster, 2003; Hirano and Imbens, 2004; Imai and Van Dyk, 2004; Cole and Frangakis, 2009; Cadarette et al., 2010; Cattaneo, 2010; Mc-Caﬀrey et al., 2013; Rassen et al., 2013).”