Fourier computation of empirical diffusion metrics
Scott Schubr — Luminary Oddities

Contents
  main.tex: complete manuscript source, with an internal bibliography.
  reference_implementation.py: floating reference algorithm and optional
    dense linear-algebra comparison.

Manuscript build
  Use a standard LaTeX installation with lmodern, AMS packages, mathtools,
  booktabs, geometry, microtype and hyperref. Run twice:
    pdflatex -interaction=nonstopmode -halt-on-error main.tex

Reference program
  Requires Python 3.10+ and NumPy. Examples:
    python reference_implementation.py
    python reference_implementation.py --dense-check --bootstrap
  The default program prints JSON and creates no files. An explicit output
  path can be supplied with --output. Dense comparison has quadratic storage
  and is intended for small examples.

The metric_inference function accepts torus positions, prescribed score
values, a bandwidth and a fixed number of extrapolation bands. The paper
states the asymptotic bandwidth/order selection. Optional weights are
positive integer sample multiplicities divided by sample_size; repeated
positions are merged. Covariance entries are ordered by pairs ia<=ib.

The program uses the positive Fourier features, actual fixed half-scaling
count, projected feature Gram, two reduced solves, original-weight metric,
normalization response and full influence covariance stated in the paper.
The dense comparison takes a second linear-algebra route to the same finite
formulas. It is a floating illustration; the paper's analytic proof supplies
the asymptotic and exact-real operation guarantees.

The cited statistical predecessor is Statistical inference for empirical
heat-kernel Sinkhorn metrics, Luminary Research Archive, edition 3:
https://research.luminaryoddities.com/statistical-inference-empirical-heat-kernel-sinkhorn-metrics/v/3

Additional archive contents
---------------------------
Fourier computation of empirical diffusion metrics.pdf: complete paper.
CITATION.cff: citation metadata.
SHA256SUMS.txt: SHA-256 checksums for all other archive members.
The supplied PDF was built with Tectonic 0.17.0 and
SOURCE_DATE_EPOCH=1793386800.
