MomentumSort: Distribution-Aware Sorting via Entropy Projection

Sorting is traditionally framed as a comparison-driven reconstruction problem evaluated un- der adversarial input assumptions. In practice, empirical data often exhibit stable distributional structure that is not exploited by conventional algorithms. This paper introduces Momentum- Sort, a two-stage sorting algorithm that separates distributional entropy removal from residual disorder resolution. The method first reconstructs an approximate rank geometry using low- order moment estimates and distribution-aware projection, then resolves remaining disorder locally using comparison-based sorting. The algorithm is correct for arbitrary inputs and de- grades gracefully as exploitable structure vanishes.