A Dynamical Noether Framework via the Persistence Equation

We propose a re-formulation of Noether's theorem as a dynamic, entropy-weighted process governed by the Persistence Equation. In this model, conservation laws are not pre-existing axioms but emergent properties of stabilized symmetries filtered through entropy. The Planck scale is interpreted not as a fixed boundary but as a phase transition between a pre-informational domain and the onset of reversible information. Using the Persistence Equation as our generative principle, we derive conditions for the emergence of quantum coherence and macroscopic conservation, thereby linking the quantum and cosmological realms from first principles.