All-depth root-Laguerre positivity with nonreal Fourier zeros
Scott Schubr, October 25, 2026

main.pdf is the manuscript. The six TeX files main.tex, certificate.tex,
second_certificate.tex, root_total_positivity.tex, gaussian.tex and
references.tex are its complete editable source. Build in
this directory using Tectonic (tectonic main.tex) or a standard LaTeX engine
with the packages declared in main.tex. No external images, bibliography
database or private file is required.

Both verifiers use only the Python standard library. Run:
  python verify_cumulant.py
  python -O verify_cumulant.py
  python verify_second_cumulant.py
  python -O verify_second_cumulant.py
The first reconstructs a third-order global enclosure proving kappa6<-1e-18.
The second retains the fourth-order correction, generates Gaussian moments
recursively, and proves the sharper bound kappa6<-1.8e-18 independently.
Neither uses quadrature, floating-point acceptance or saved moment inputs.
Read the manuscript for the global integral bounds, all-depth induction,
strict total positivity, explicit confluent formula and Gaussian-damping
tail corollary. The manuscript supplies the global integral bounds and all-depth induction.

CITATION.cff supplies citation metadata. MANIFEST.sha256 lists the SHA-256
of every public member other than itself.  Newman supplies the classical
bad-Gaussian-tilt existence background. The explicit all-depth example concerns generic admissible kernels.


Editorial source alignment
--------------------------
The included manuscript PDF is rebuilt from the accompanying editable sources. The paper title and edition are retained. Numerical scripts and previously supplied numerical outputs are retained from the published source package; the editorial rebuild does not represent a new numerical replay.
