Complexity and gravitational statements

Harlow–Hayden analyzes computational restrictions in particular radiation-distillation thought experiments HH. Our low-memory Clifford programme is not a generic decoding-complexity theorem and does not overturn those restrictions. The amplification count $O(2^k)$ is a message-dimension dependence in the declared construction, not a universal lower bound.

Clifford Hayden–Preskill algorithms use special operator structure and measurement feedback YoshidaClifford. The tractability of such dynamics is not a proof of efficient recovery for unspecified black-hole evolution.

Replica-wormhole calculations address fine-grained entropy in specified gravitational settings Replica. An entropy calculation is not a register-level recovery programme. None of our emission thresholds is inferred from an island formula.