Proposition: Inert and transmissive exceptional blocks

1. If the exceptional channel factorizes as ${\Phi }_P\otimes {\Phi }_Q$, with no cross relocation or classical flow, it can be replaced by singleton channels. The original-metric cone continues to apply.

2. Lossless one-tick bit transport from $P$ to $Q$ violates the original-metric radius-$r$ cone.

3. The geometry change alone neither creates nonlinearity nor permits universal deterministic cloning.

Proof. (a) is equality of the two product updates. For (b), prepare bit $0$ or $1$ at $P$, transport it with the same rule, and read at $Q$. The laws are ${\delta }_0,{\delta }_1$.

For (c), finite compositions of complete instruments are linear on unnormalized hybrid states. They remain CPTP after ignored systems are traced out. Using root fidelity $F(\rho ,\sigma )=\Vert \sqrt{\rho }\sqrt{\sigma }{\Vert }_1$, CPTP maps do not decrease fidelity Watrous. A deterministic cloner of two nonorthogonal pure states of overlap $0<f<1$ would change fidelity from $f$ to $f^2<f$, impossible.