Spiral Field Framework: On the Regime Transition from Reversible Cycles to Irreversible Spiral Dynamics

This manuscript presents a structural hypothesis concerning the regime transition between circular and spiral attractors in dynamical systems. Beginning from the ontological axiom that existence requires variance, the framework develops a deductive structure leading to oscillatory dynamics and distinguishes between reversible cyclic motion and irreversible scaling motion. It proposes that spiral attractor geometries arise generically in oscillatory systems exhibiting cumulative radial drift. The work is philosophical in nature but engages concepts from nonlinear dynamics, thermodynamics, and attractor theory as structural analogues. It is offered as a formalizable hypothesis rather than a mathematical proof.