Three-point positivity for weighted products of Riemann theta density powers
Scott Schubr

Read main.pdf for the complete self-contained analytic proof. Theorem 1 covers
all real alpha >= 5/8 and every nonnegative center measure with positive finite
normalization. Theorem 2 gives the general log-curvature criterion. Section 6
explains the necessary local threshold and a generic four-point obstruction.
The result is finite-order positivity.

Files
  main.pdf             complete manuscript
  main.tex             editable LaTeX source, bibliography included
  exact-controls.py    optional exact symbolic/rational checks
  requirements.txt     checker dependency
  CITATION.cff         citation metadata
  MANIFEST.sha256      hashes of these reader files (excluding the manifest)

Build the paper with a current LaTeX installation, for example:
  tectonic main.tex
or run pdflatex main.tex twice. Required standard packages are fontenc,
geometry, amsmath, amssymb, amsthm, booktabs and hyperref. No external images,
bibliography database, private input files or network mathematical service is
needed. Tectonic may download its normal TeX support bundle on first use.

To check the finite identities using Python 3:
  python -m pip install -r requirements.txt
  python exact-controls.py
  python -O exact-controls.py
Both runs should print verdict PASS and the same exact check results. The
program reads and writes no files and uses exact rational/symbolic arithmetic.
These checks complement the manuscript's analytic all-n tail arguments.

The alpha exponent is applied to Phi before averaging. Repeated positions give PSD;
three distinct positions give PD. The power threshold is sufficient.

No reuse license is specified in this package.


Building the manuscript
-----------------------
From the directory containing main.tex, run `tectonic main.tex`. The packaged primary PDF contains the same manuscript as these editable sources. The accompanying mathematical code and certificate data are retained with their original scope.
