First-Hit Stopping and Bias-Corrected Score Inference in Dimension Three
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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.
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- First_Hit_and_Corrected_Score_Dimension_Three_v1_1.pdf189.3 KiB · pdf
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15509552b3087b6ee3a9e1cbba78ebc8b7baac9263cabaa852850ed4ee4556a2 - Dimension_Three_First_Hit_Publication_Package_v1_1.zip219.2 KiB · package
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Research details
- Subjects
- Mathematics · Probability and Statistics
- Keywords
- entropic self-transport, symmetric Sinkhorn, score estimation, first-hit stopping, bias correction
- Manuscript date
- 2026-10-20
- Reader reuse
- No additional permission granted
Scope
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.
Disclosures
AI tools assisted mathematical development, literature discovery, drafting and checking. The author is responsible for the content.
Reproduction
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.