Zero Point Spiral v3: History Phase-Lift and the Logarithmic Spiral Representation

This short technical note supplements the ZPS v1 dynamical framework. It corrects an inconsistency in an earlier draft—which conflated the argument of the complex history embedding zH = x + iZΔ with a phase κZΔ —and instead constructs a separate phase-lift ζ = ReiθZ , with θZ := κZΔ defined from history depth and R := R0eλZΔ from accumulated amplification. In this lift, history generates phase and amplification generates an exact logarithmic spiral R (θZ ) = R0e(λ/κ)θZ . The result is a representation theorem: R and θZ are both defined from ZΔ , so the spiral follows by construction, and empirical relevance requires an independent interpretation of R . This is offered as a supplement, not as a standalone theory.