Phase Coupling Equation

The Phase Coupling Equation gives the coupling strength between two pulse systems as a function of their phase difference: C(φ_1, φ_2) = α cos(Δφ) + β sin(Δφ), with Δφ = |φ_1 - φ_2|. Individual pulses do not evolve in isolation but resonate through phase coupling: comparing phase differences lets harmonic layers align, so synchronization arises from simple phase relations and binds local pulses into collective order. The book uses it in the pre-ignition stage, where the coupling strength that enhances memory accumulation is raised by phase coupling: system memory evolves as S_n = S_{n-1} × α𝓜 + I▷ × β⧱, so that fluctuations either decay or self-organize into lasting loops. In the equation, C(φ₁, φ₂) is the coupling strength [∅], α the cosine coupling coefficient [∅], β the sine coupling coefficient [∅], φ₁ and φ₂ the two phases [∅], and Δφ their difference [∅]; the memory relation checks in the older basis as [𝕄·𝕃²·𝕋⁻²·Θ⁻¹] × [∅] + [𝕄·𝕃²·𝕋⁻²·Θ⁻¹] × [∅] = [𝕄·𝕃²·𝕋⁻²·Θ⁻¹]. It connects to Phase-Synchronized Pulse Sequences, Harmonic Pulse Resonance Condition, Pulse Phase Function, Phase Synchronization and Recursive Coupling Constant.