Memory Depth Requirement

The Memory Depth Requirement is the number of temporal steps, 1000, across which a recursive quantum memory must keep state information so that recursive operations can draw on it. It is the first of the book's two temporal persistence requirements for a quantum computational substrate, which together specify Frame Buffer Depth. The second is the Persistence Fidelity Condition, |⟨ψ(t)|ψ(t+τ)⟩|² ≥ F𝓜, with F𝓜 = 0.95 ± 0.02 over intervals τ ≤ N𝓕 × t⥂: the state must stay nearly identical to itself throughout the required span. Together they fix both how long memory must last and how faithful it must remain, so that quantum state information stays continuous across many processing cycles. The formal statement is N𝓕 = 1000, where N𝓕 is the required memory depth for recursive operations, counted in temporal steps. N𝓕 is dimensionless [∅]; in the companion condition ψ is the quantum state [∅], t and τ are times [𝕋] and t⥂ the substrate pulse timing. The book's checks are consistent. It connects to Frame Buffer Depth, the Persistence Fidelity Condition, Operational Coherence Time, Entanglement Overlay Networks and Coherence Quality Factor.