Operational Coherence Time

The Operational Coherence Time is the length of time a qubit stays usable, the longer of its relaxation and dephasing times, which BPT requires to exceed the substrate pulse period by a factor of 1000. The book measures coherence requirements against the fundamental substrate timing, the Pulse Rhythm t⥂ = ①⥂⧖⌂ = 2²⁰²·f²⁰²·ↁℨ⧖ = ①⥂⧗⌂/2. A coherence time a thousand times longer than this ensures that recursive operations remain stable across many cycles. It is the first of the book's quantitative performance criteria for a quantum computational substrate; the second, the Coherence Quality Factor Q≋ = T_op/t⊡⊶ ≥ 10⁴, requires that many gate operations fit inside the coherence window. Measured against these, the book finds existing platforms short of PulseCore standards. The formal statement is T_op = max(T₁, T₂) ≥ 1000 × t⥂, where T_op is the operational coherence time, T₁ the relaxation time (amplitude decay), T₂ the dephasing time (phase decay) and t⥂ the substrate pulse timing. Dimensions from the book's Where-list: T_op, T₁, T₂, t⥂ [𝕋]; 1000 [∅]. It connects to the Coherence Quality Factor, Dephasing Time Gap, Relaxation Time, Frame Buffer Depth and PulseCore Qubit Validation.