Zero Point Spiral: A General Dynamical Framework for Preservation-update Asynchrony

We propose the Zero Point Spiral (ZPS), a general dynamical framework grounded in a single axiom: preservation and update are generally asynchronous, and their phase difference Δφ ≠ 0 is the generative source of state transitions. From this axiom we derive a discrete dynamical system in which the state difference Δ(t) = x(t) − x̄(t) between the current state and a power-law weighted historical average drives self-amplifying updates near critical points and gradual stabilization as history accumulates. The update coefficient α(t) = α₀ exp(λ|Δ(t)|) / (1 + κZ△(t)) encodes a two-phase mechanism: explosive amplification at the Zero Point and deceleration through history depth Z△(t). The system converges to a stable particle when |Δ(t)| < ε and |Z△(t+1) − Z△(t)| < η. We demonstrate that this dynamical structure — difference generation, history accumulation, and attractor convergence — exhibits structural self-similarity across cosmological, biological, cognitive, and social domains. Scale invariance here refers to structural invariance of the ZPS update topology across domains, not strict metric invariance in the renormalization-group sense. ZPS is thus positioned as a dynamical structural philosophy: a formal framework complementing domain-specific theories by identifying the common dynamical skeleton underlying persistent change across scales.