Theorem: Complete-output induction

For every finite legal word of Definition def:commands, the output after each command has an accepted five-component certificate. Fixed-packet commands preserve the installed framed peripheral signature. A source command replaces the complete selected catalogue entry rather than changing only its deficit label.

For the stated persistent original-name domain, location transport is identity and remains valid. The matter state is unchanged, including all spectator and reference correlations.

Proof. A flow command is realized by Section sec:family, and every intermediate member is certified by Theorem thm:matching. A source command evaluates the entire construction at its new table entry, so Proposition prop:algebraic and Theorem thm:matching supply a complete new output. An incidence command uses the two germs of Theorem thm:event at the same $\mu$, with their common noncollapsing peripheral witness.

The declared persistent collar slots exist in each output. No internal matter gate has occurred. Induction over the word proves every assertion. For a more general location domain or patch composition, the location and gluing hypotheses must be supplied explicitly, as in Proposition prop:gluing.