Unit-Centric Causal Transport: Separating Population Composition from Mechanism Change

USL-01 type contract

Let $E$ be an environment variable in one Population world. Source and target are the events $\{E=s\}$ and $\{E=t\}$, so their compositions are written directly as $P(U\in du\mid E=s)$ and $P(U\in du\mid E=t)$ rather than as laws of separately indexed worlds. Given admissible evidence $\mathcal O$, the world conditional is $P(U\in du\mid E=e,\mathcal O)$ and a deployed learner forms $Q_\phi(du\mid E=e,\mathcal O)\approx P(U\in du\mid E=e,\mathcal O)$; the approximation is evaluated, not definitional. These environment-conditioned marginals do not by themselves couple individuals across environments: same-individual source/target records require reliable attribution or an explicit cross-environment linkage law. They are also not automatically observed-row laws: inclusion and observation intensity can induce a different event-weighted mixture, so the observation protocol and unit- versus event-weighted target must be declared. Composition shift concerns these Population conditionals; mechanism shift concerns separately declared fixed-individual response or potential-outcome laws and can occur even when the same individual values remain in support. Fixing $u$ does not remove event/exogenous variation. This decomposition does not itself identify a causal transport estimand; consistency, positivity, exchangeability/invariance and the admissible-evidence protocol must be stated separately. Identity support, response-law support and covariate support are distinct. A claim that transports to new Individuals must declare the cross-unit shared response family, property map, geometry or invariance that makes extrapolation possible, together with its support or abstention condition.