Sharp convergence of heat-kernel Sinkhorn metrics
Scott Schubr, October 21, 2026

Contents
  Sharp_Heat_Kernel_Sinkhorn_Metrics.pdf - complete seven-page paper.
  main.tex - complete LaTeX source, including bibliography.
  README.txt - reader and build instructions.
  SHA256SUMS.txt - checksums for the three files above.

Scope
  Smooth positive densities on a fixed-dimensional flat torus with
  an h-dependent periodic heat-kernel cost. Sharp L2 and Sobolev
  tensor rates, second-order intrinsic density-family geometry,
  a population residual bound and an explicit projected scale.


Reproduction: the manuscript gives the analytic proof.
  Compile main.tex with a current LaTeX distribution using pdflatex twice,
  or run: tectonic main.tex
  Packages used are listed in the source. The bibliography is embedded;
  BibTeX and external bibliography files are unnecessary.
  A compiler may name the rebuilt PDF main.pdf. PDF byte identity can
  depend on compiler/version metadata; compare the mathematical text.
  The supplied PDF was built with Tectonic 0.17.0 from this source.

Integrity
  Check SHA256SUMS.txt against the three named files. It does not checksum
  itself. These hashes establish file identity, not theorem correctness.
