SHARP CONVERGENCE OF HEAT-KERNEL SINKHORN METRICS
Scott Schubr, Luminary Oddities. October 21, 2026. Archive edition 2.

Scope
Sharp population tensor convergence for smooth strictly positive densities
on a fixed-dimensional flat torus: O(h) in full L2 and O(h^(1+r/2)) from
H^r to L2 for 0<=r<=2, including parameter derivatives and finite-family
intrinsic geometry. The normalization residual result is projected and
population-based, with the known density and Sobolev residual required.
It is not an empirical stopping theorem or a practical runtime bound.

Reader files
- Sharp_Heat_Kernel_Sinkhorn_Metrics.pdf: complete paper.
- main.tex: complete editable source and inline bibliography.
- build_pdf.py: portable local PDF build helper.
- CITATION.cff: citation metadata.
- README.txt: these instructions.
- MANIFEST.sha256: checksums of the five payload files; self-excluded.

Build
Use Python 3 and Tectonic with the needed LaTeX resources. From the extracted
directory run:
  python build_pdf.py --output-dir ../sharp-sinkhorn-reader-build
Add --tectonic PATH_TO_TECTONIC when needed, --only-cached for offline builds,
or --cache-dir PATH to select an existing TeX cache. The output directory must
be new. Logs stay there. SOURCE_DATE_EPOCH=1792540800 is October 21, 2026 UTC.
An ordinary compatible LaTeX installation can also compile main.tex.

The analytic proofs require no numerical data. The subsequent bias/positive
correction and empirical inference papers are cited as separate extensions.
This paper supplies the convergence baseline for the subsequent
population bias-and-correction analysis.
