Unique-token extras and the ultrahomogeneous embedding squeeze are not leftover interpolating sequential type

Write F for a covering-law family and W_n for the set of unlabelled covering-process orders of cardinality n. A construction that is not a functor of one finite Hasse diagram may still be a functor of a covering-law Markov stepper. Sz.-Nagy--Foias dilation of the covering-law transition and the Doob--Martin boundary of its Green kernel are of that second kind: they fail leftover interpolant independence of covering-law steppers even when they pass a consult test that only forbids functors of one static Hasse diagram. A covering-independent object unique up to unique isomorphism, paired by a canonical functor, yields an object unique-of-F. Occupying leftover interpolating sequential type by citing a classification uniqueness theorem for such a token is too loose. Declaring leftover interpolating sequential type uninhabitable because unique tokens fail to break unique-of-F is too tight. Let U be the Fraisse limit of finite posets. Ultrahomogeneity implies that Aut(U) acts transitively on embeddings of any given finite poset. The Aut-quotient of the covering-class embedding bundle therefore recovers W_n. Any Aut-natural dynamics on that bundle whose weights are covering-class weights descends to a covering-law stepper. Kechris--Pestov--Todorčević non-amenability of Aut(U) is cited as literature and is not re-proved. A covering-independent process extra whose generation determines a unique law has a unique-token reading and a stipulated-choice reading; those readings do not jointly occupy leftover interpolating sequential type. Covering histories are finite posets of the mathematical type of finite causal sets. They are not identified with physical spacetime. This note does not claim Lorentz invariance. It does not replace the parent programme manuscript, and it is not a new version of Companions 13-47.