Research Article · Preprint Mathematics
First-Hit Stopping and Bias-Corrected Score Inference in Dimension Three
- Primary subject
- Mathematics
- Subject subfield
- Probability and Statistics
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 1 · Permanent link
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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
Scope of the work
Fixed positive C8 densities on the unit three-torus, a fixed deterministic query, the exact periodic heat kernel, and the same observations at both bandwidths. The sealed manuscript treats 2/17 < κ < 1/3 and 0 < γ < 3/4.
Reproduction notes
The publication package contains the complete 20-page manuscript, six LaTeX source files, a portable local PDF build helper, citation metadata, and reader instructions. Manuscript version 1.1 is an exposition revision for this initial public edition and a linked dimension-three follow-up to the earlier d1/d2 paper.
The manuscript
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Author disclosures
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Cite this edition
Scott Schubr. (2026). First-Hit Stopping and Bias-Corrected Score Inference in Dimension Three (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/first-hit-stopping-bias-corrected-score-inference-dimension-three/v/1
BibTeX
@techreport{luminary_first_hit_stopping_bias_corrected_score_inference_dimension_three_v1,
title = {First-Hit Stopping and Bias-Corrected Score Inference in Dimension Three},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 1},
url = {https://research.luminaryoddities.com/first-hit-stopping-bias-corrected-score-inference-dimension-three/v/1}
}Loading discussion…