A FINITE-ORDER OBSTRUCTION TO TOTAL POSITIVITY OF AN ARITHMETIC THETA TRACE KERNEL
Scott Schubr, Luminary Oddities LLC. October 25, 2026.

main.pdf is the manuscript; main.tex is the complete editable source.

PRIMARY EXACT CERTIFICATE (Python standard library only)
  python verify_rational.py
  python -O verify_rational.py
Both must print status PASS. This reconstructs the complete infinite kernel's
6-by-6 ordered minor, including outward exponential errors and every omitted atom:
  -978/10^59 < determinant < -977/10^59.
No saved output or checksum substitutes for the exact calculation.

INDEPENDENT RECONSTRUCTION (optional numerical dependency)
  python -m pip install -r requirements.txt
  python verify_order_six_arb.py
  python -O verify_order_six_arb.py
This independently builds the same full-series matrix using python-flint 0.9.0
directed Arb balls at 512 and 1024 bits. Both runs must certify the same endpoints.

ADDITIONAL TWELFTH-ORDER CHECKS
  python verify_order_twelve.py
  python -O verify_order_twelve.py
These standard-library runs check the additional ordered-node witness in the appendix.
  python verify_arb.py
  python -O verify_arb.py
These optional Arb runs check the different twelfth-order confluent derivative
determinant and complete signed jet tails in the appendix. They are not checks
of the sixth-order matrix. Every script raises an exception on a failed gate.

BUILD
  tectonic main.tex
Alternatively compile with a current LaTeX installation and the packages listed
in main.tex until references settle. No images or external bibliography are used.
PDF binary identity can vary with compiler metadata; mathematical text must agree.

SCOPE
The arithmetic trace kernel fails PF6. No smallest failing order, global PF5,
off-critical-line zeta zero, original even Riemann theta counterexample or RH
conclusion is claimed. Positive-mixture nonclosure, transform criteria and the
general certificate methods are classical. The paper identifies the literal
preprint version corrected. AI-assisted checking is not external human refereeing.

MANIFEST
MANIFEST.sha256 identifies every other public member. Compute SHA-256 for each
named member and compare the digests. No private reviews or receipts are included.
