Corollary: Nonempty promised history

The word (eq:fiveword) is legal on every compatible fixed-token input and returns accepted complete outputs. Its incidence occurs at the frozen selected deficit ${\mu }_1=\pi /2+6\arctan (1/64)$. Its sole catalogue-deficit replacement occurs at the regular source command.

Replacing the supplied token by zero, with zero source expectation, selects the reference family. It need not be identity on an arbitrary old catalogue packet.

Proof. The three flow intervals stay in their declared epochs. The source and incidence guards are exact, and each uses only its own available permission. Theorem thm:composition applies. The zero-token statement follows from ${\mu }_0$.