Proposition: A sufficient carrier-only memory witness

Suppose two admissible past carrier-instrument histories, each with positive probability, produce different conditional scar distributions ${\pi }_0,{\pi }_1$. After the same carrier reset $\tau$, suppose a common future experiment has an effect $F$ for which

Then no history-independent carrier-only channel can describe both conditional futures after that causal break. The reduced process violates the corresponding operational Markov condition under the admitted experiment.

Proof. Both carrier inputs after the break are $\tau$. A carrier-only channel acting on that same input must produce the same output. Equation (eq:memory) contradicts that requirement. The distinction is retained in the scar distribution.