Zero Point Spiral: A Minimal Dynamical System of Difference, Update, and History

This is a structural framework, not a physical theory. We propose the Zero Point Spiral (ZPS), a discrete dynamical framework grounded in a single axiom: preservation and update are generally asynchronous, and the residual phase difference Δϕ in which a state difference Δ(t ) = x (t ) − .x (t )—between the current state and a power-law weighted historical average—drives a self-amplifying update near critical points and a gradual stabilization as history accumulates, with an irreversible history depth ZΔ (t ) recording the trajectory. We position ZPS as a structural framework , not a physical theory: it identifies a recurring dynamical skeleton (difference, update, accumulation, convergence) and the relations among its parts, and complements rather than competes with the domain-specific laws of any particular system. This revised version restricts the scope to the dynamical core and treats cross-domain correspondences as informal working hypotheses; the layered phase structure and the observation layer are developed separately in later work.