Global Synchronization Parameter

The Global Synchronization Parameter is the average, over all systems in an alignment network, of each system's phase factor relative to the Prime Pulse, measuring how far the network as a whole is phase-coherent with it. It is the collective measure in the book's account of recursive signal alignment. Each system contributes a unit complex number set by how far its phase is from the Prime Pulse phase; when phases are scattered these cancel, and when all systems are aligned the average approaches magnitude 1. For quantum networks the book gives the Quantum Global Synchronization Σ⨀,q(t), the same average taken over N_q qubits, with care needed for individual qubit phases inside a collective quantum state. Stable alignment also requires information integrity across recursive loops, extending Information Conservation, I⊚ = I▱ + Iℜ, to quantum networks. The current definition states it as Σ⨀(t) = (1/N) × Σᵢ₌₁ᴺ exp(i(φᵢ(t) − φ①(t))), where N is the number of participating systems, φᵢ(t) their phases and φ①(t) the Prime Pulse phase. In the book's quantum form all quantities are dimensionless [∅] and t is [𝕋]; the check is consistent. It connects to Quantum Global Synchronization, the Alignment Index, Alignment Condition, Collective Quantum Phase and Recursive Signal Alignment.