Preprint Mathematics
Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-Transport
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Overview
Abstract
We study observable residual stopping for the half-self-Sinkhorn iteration with samples from a fixed positive smooth density on the one- or two-dimensional torus. Under stated bandwidth and tolerance conditions, the first residual hit preserves the pointwise Gaussian limit of the exactly scaled empirical score. We determine the leading stopping count, bound the attained residual, and give an obstruction at the upper tolerance exponent. The proof controls the common empirical trajectory and nonuniform initialization.
Keywords entropic self-transport · Sinkhorn iteration · statistical stopping · score estimation · pointwise inference
Scope of the work
Fixed positive C⁶ density, dimensions one and two, and a fixed query under sufficient asymptotic bandwidth windows. The result concerns the first residual hit; it makes no finite-sample coverage, simultaneous-query or wall-clock speed claim. A separate follow-up to Residual Certificates and Empirical Sharpness for Entropic Self-Transport Scores.
Reproduction notes
The complete package contains the thirteen-page paper, six LaTeX files, proof and review records, build/integrity tools and manifest. The source ZIP supplies the self-contained manuscript sources. The results are analytic; build and integrity checks are not numerical theorem verification.
The manuscript
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Cite this edition
Scott Schubr. (2026). Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-Transport (Version 1). Luminary Research Archive. https://luminaryoddities.com/researcharchive/residual-stopping-pointwise-inference-nonuniform-entropic-self-transport/v/1
BibTeX
@techreport{luminary_residual_stopping_pointwise_inference_nonuniform_entropic_self_transport_v1,
title = {Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-Transport},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Preprint},
note = {Version 1},
url = {https://luminaryoddities.com/researcharchive/residual-stopping-pointwise-inference-nonuniform-entropic-self-transport/v/1}
}Reader correspondence
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