Discrete Phase-Order Dynamics: A Minimal Model of Analytic Curvature, Quantum-Like Jumps, and Temporal Potential

Abstract We introduce a compact theoretical framework in which analytic phase geometry, represented by the cyclic algebra Cₙ with generator jn=−1j^n = -1jn=−1, combines with an intrinsic temporal potential motivated by the ZPAT model. The structure predicts that transitions between different phase orders (Cₙ → Cₘ) behave as discrete, quantum-like jumps: analytic modes are removed instantaneously, the curvature invariant ζeff(C)\zeta_{\mathrm{eff}}(C)ζeff(C) changes discontinuously, the Dirac–Cₙ spectrum collapses, and the internal norm signature is altered. A direct observational consequence is a natural redshift plateau at z≈0.19z \approx 0.19z≈0.19 arising from the curvature jump C₃ → C₆. The model provides a unified interpretation of phase resolution, analytic curvature, hidden/visible norm sectors, and temporal dilation effects without appealing to metric expansion. This first communication summarizes the essential components of the model and outlines its physical implications.