An Explicit Quintic Obstruction for the Riemann Theta Kernel
An Independent Rational Reconstruction
Scott Schubr, Luminary Oddities LLC
October 16, 2026

CONTENTS
main.tex and proof.tex: complete manuscript source.
Quintic_Theta_Obstruction_Independent_Reconstruction.pdf: compiled manuscript.
supplement/verify_reconstruction.py: standalone exact rational verifier.
supplement/certificate.json: freshly generated exact arithmetic output.
supplement/moment_table.json: outward 21-place moment intervals and contraction.
SHA256SUMS.json: byte sizes and SHA-256 checksums of the distributed files.

MATHEMATICAL SCOPE
At s0=log(13/(4*pi))/4, the signed derivative functional for
p_s(t)=Phi(s+t/2)*Phi(s-t/2)/Phi(s)^2 and
P(X)=X^5-264X^3+10952X satisfies the exact rational enclosure
[-1412370791.837791749, -1412370791.837791748].
The complete theta series is retained through an explicit infinite-tail bound.
The manuscript proves the odd/full Hankel consequences and the existence
of a negative direction for every sufficiently small six-point spacing.
It supplies no explicit spacing, degree-minimality, averaged sign, or RH claim.

REPRODUCTION
Requires Python 3.10 or later, standard library only; no package installation
or network access. From this package directory, run:

  python -B supplement/verify_reconstruction.py --output reproduced_certificate.json

Use a NEW output filename. Existing files, including certificate.json, are
never overwritten. The parent output directory must already exist.
Without --output, the verifier prints its exact JSON to standard output.
All mathematical checks raise explicit errors, even under Python's -O option.
Successful completion reports "Verification passed" and writes exact rational
intervals, including the full derivative, tail, moment, and contraction data.
The verifier reads no retained certificate and does not import another checker.

The method generates derivatives through order ten using a formal power
series over Q[z]. It retains twelve theta summands and bounds every term
with n>=13 by an absolute monomial geometric majorant. Exponentials are
enclosed with alternating partial sums of degrees119/120 at t/1024, followed
by ten outward interval squarings on the rational grid 10^-100. Final
moment boxes are rounded outward to21 decimal places. The source verifies
the two printed contraction numerators and the nine-place theorem interval.

The certificate was freshly generated on October16,2026 using Python3.12.10.
The source hash in certificate.json identifies verify_reconstruction.py.
Reproduction with unchanged source should produce the same mathematical
JSON data. Preserve retained evidence and write new results separately.

TYPESETTING
With a current standard LaTeX installation, compile main.tex using pdfLaTeX
(two passes) or Tectonic. The project uses standard article, geometry,
lmodern, amsmath, amssymb, amsthm, microtype and hyperref packages.
For example:

  pdflatex main.tex
  pdflatex main.tex

Compilation may create intermediate files in the chosen build directory;
keep those separate from the distributed manuscript and certificates.
The included PDF was compiled successfully with Tectonic0.17.0 and all
pages were rendered and visually reviewed before delivery.

The paper includes the author's AI-assistance disclosure. This package is
prepared for review or submission; it has not been submitted or published.
