First-Hit Stopping and Bias-Corrected Score Inference in Dimension Three

Overview

Abstract

The actual first residual crossing of the symmetric half-Sinkhorn iteration is studied for observations from a fixed positive smooth density on the three-dimensional torus. A two-scale score correction computed from the same sample removes first-order population bias. In a specified power-bandwidth and tolerance range, stopping each run at its first observable residual hit preserves the corrected estimator’s fixed-query Gaussian limit. The paper gives the leading stopping count, an attained-residual bracket, the joint covariance, and an explicit correction-specific lower-bandwidth obstruction.

Keywords entropic self-transport · symmetric Sinkhorn · score estimation · first-hit stopping · bias correction