Instant TravelLuminary Oddities — Enter the Portal
Research Archive

Research Article · Preprint Mathematics

Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-Transport

Scott Schubr

Luminary Oddities LLC

  • Mathematics
  • Probability and Statistics
Primary subject
Mathematics
Subject subfields
Probability and Statistics
Paper type
Research Article
Manuscript stage
Preprint
Manuscript
Archived
Edition
1 · Permanent link
Read / download PDF Publication filesCite this edition

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

Read the paper

Open PDF

The complete manuscript, as published in this edition.

If the reader is unavailable on your device, open or download the PDF directly.

References and related publications

  1. Residual Certificates and Empirical Sharpness for Entropic Self-Transport Scores (edition 1)

A stable scholarly record

Cite this edition

Scott Schubr. (2026). Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-Transport (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/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 = {Research Article},
  note = {Version 1},
  url = {https://research.luminaryoddities.com/residual-stopping-pointwise-inference-nonuniform-entropic-self-transport/v/1}
}

Loading discussion…