Recursive Coherence Envelope

The Recursive Coherence Envelope is the spatial function, written R(x,t) and dimensionless, that bounds how far quantum coherence extends and where wave-particle duality gives way from one regime to the other, depending on the strength of measurement interaction and on environmental conditions. The book uses it in its account of wave-particle duality: in the coherence regime the envelope modulates the standard wave function, ψ∿(x,t) = A × exp(i×k×x − i×ω×t) × R(x,t), and in the particle regime localization weights the Dirac delta by its squared magnitude, ψ⚛(x,t) = δ(x - x_0) × |R(x_0,t)|². The same chapter's quantum-scale predictions expect discrete energy signatures in ultra-high-precision spectroscopy, showing temporal quantization with the periodicity of the Pulse Rhythm, ①⥂⧖⌂ = ①⥂⧗⌂/2. The Recursive Coherence Envelope connects to Coherence Factor, Phase Coherence, Decoherence Mechanisms, Quantum Indeterminacy and Phase-Locked Toroidal Entanglement.