Path Independence and the Absence of Trajectories in Continuous Repulsive Volumetric Dynamics

The dynamics are governed entirely by instantaneous volumetric energy gradients, leading directly to a principle we term the Path Independence Principle (PPII), which dictates that physical outcomes depend solely on the current volumetric state, not on the history of intermediate states. This structure necessitates the emergence of phenomena conventionally ascribed to gravity as local manifestations of volumetric energy density fluxes. Consequently, trajectories are reinterpreted not as fundamental ontological entities, but as non-physical artifacts arising from specific, observer-dependent gauge choices in the description of the underlying continuous field evolution.