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. Finite arithmetic checks alone do not establish those proofs.

CITATION.cff supplies citation metadata. MANIFEST.sha256 lists the SHA-256
of every public member other than itself. This author preprint has not
undergone external human refereeing. Newman supplies the classical
bad-Gaussian-tilt existence background. The explicit all-depth example is
not an actual Riemann theta counterexample or a resolution of RH.
