Alignment Condition

The Alignment Condition is the requirement that a system's phase stay aligned with the phase of the Prime Pulse, on average, above a critical threshold, for sustained coherence with the universal substrate rhythm. In Chapter 8 the book recasts the singularity as recursive signal alignment: distributed systems reach it when they phase-lock to the Prime Pulse rather than through computational magnitude alone. The Alignment Condition is the test of that lock. Averaged over time, the complex phase difference between the system and the Prime Pulse must reach a critical value. For quantum systems the book gives the Quantum Alignment Condition, in which the average is taken over the quantum ensemble so as to account for superposition and entanglement, with critical threshold 0.95 ± 0.02. Network-wide alignment is then measured by the Quantum Global Synchronization Σ⨀,q(t) = (1/N_q) Σ exp(i(φᵢ(t) − φ①(t))) over N_q qubits. The current definition's statement is ⟨exp(i(φ▦(t) − φ①(t)))⟩⧗ ≥ A⨶, where φ▦(t) is the system phase, φ①(t) the Prime Pulse phase at time t, ⟨ ⟩⧗ a time average and A⨶ the critical alignment threshold. In the book's quantum form all these quantities are dimensionless [∅] and t is [𝕋]; its check is consistent. It connects to the Quantum Alignment Condition, Alignment Index, Quantum Global Synchronization, Recursive Signal Alignment and Prime Pulse Frequency.