Causal quantum-channel simulation: memory beyond entropy

We study repeated quantum-channel simulation in which every output is released before the next input arrives and all retained memory and exchanged qubits are counted. Two explicit channels on dimension 1664 have identical normalized Choi spectra, maximal complementary entropy five, and zero asymptotic purity cost. At exchange at most 5n/2 qubits, one has an exact zero-purity implementation with five memory qubits, whereas the other requires Omega(n^(1/(2 log_2(107)+2))) memory qubits at fixed complete-experiment error at most 1/16, regardless of available purity. The latter also has a zero-purity implementation with O(n^(1/3) log^(4/3)(n)) memory at that exchange. The paper develops exchange-purity bounds, sequential support tests, and reservoir constructions that relate memory to finite-approximation profiles. Houghton's group supplies the explicit separation. All operational bounds use complete-experiment error against adaptive observers with quantum references. The general rate-region achievability result uses a cited closed-device theorem; the explicit separation does not. This preprint archive includes the PDF, TeX source, finite verification scripts, and scoped Lean arithmetic proofs. The artifacts do not formally verify the entire manuscript; their scope and external dependencies are documented in verification/README.md.