Declared output and exact closure

Landmark I characterizes destructive Enter as Born readout with destructive projective update within its stated strategy class I. We retain this semantics. Its record theorem does not supply a preparation of an external field functional or a classical gravitational gauge identity.

For an encoding $\iota$ and a program $P$, the closure boundary is the declared classical output together with every returned quantum output. Write its complete selective record as ${\mathsf{Rec}}_P(\iota (a))$. Exact convolution-orbit invariance means

For differentiable records this is equivalent to vanishing orbit derivative everywhere, not merely at one representative.

A record is informative about its scalar input if it is nonconstant as a function of that scalar. Exact recovery is stronger. Whole-algebra invariance implies (eq:invariance); failure on the convolution witness orbit therefore already defeats whole-algebra closure.

No invariant convolution handoff is assumed. On this inherited coefficient orbit, $a$ is pure gauge at fixed $\epsilon$, not an observable that Enter has failed to invariantize. The separately quoted ramp cancellation does not change this premise.