LOCATING QUINTIC OBSTRUCTIONS IN THE RIEMANN THETA PRODUCT
A certified transition and minimum-degree theorem
Scott Schubr | Luminary Oddities LLC | October 17, 2026

REVIEWED REVISION
Three separately tasked AI subagents reviewed the proof, verification code,
and originality/literature positioning. Review reports and resolutions are
included under review/. This is not external human peer review.
The revision clarifies adaptive range reduction, interval scope, and the
negative ellipse at the transition; adds related-work citations; and hardens
mesh progress and evidence/source bindings. The numerical theorem is unchanged.
The October 17 initial package remains preserved in its original folder/ZIP.

PUBLICATION FILES
Locating_Quintic_Obstructions_Transition_and_Minimum_Degree.pdf
main.tex: complete manuscript source; NewTX text and mathematics.
supplement/: Python standard-library verification and witness-location code.
evidence/: complete interval certificate, exact-rational replay, root signs,
explicit witnesses, printed-claim checks, and PDF/build verification.
CITATION.cff: citation metadata.
SHA256SUMS.json: file integrity inventory.
review/: independent AI reviews, dispositions, and exact arithmetic audit.

MAIN RESULT
On 3.64 <= x <= 3.66, the odd quintic block has exactly one transition x_*:
3.64888758188562 < x_* < 3.64888758188563.
The full degree-five moment matrix has inertia (5,1,0), (5,0,1), and
(6,0,0), respectively below, at, and above x_* in this interval.
Degree five is the minimum obstructing degree for 3.64 <= x < x_*.
This is a fixed-center, finite-degree theorem on the stated interval.

REPRODUCE EVERYTHING
Python 3.11 or later; no third-party numerical libraries required.
From this directory, choose a NEW work directory on your own machine:

python -B -O supplement/reproduce_all.py --workdir E:/your-new-proof-run

The command creates new scripts/evidence folders and recomputes all mathematical
certificates without reading the retained evidence. It checks every printed
numerical claim. Existing output paths are refused. Expected final result:
PASS_FRESH_REPRODUCTION. On the preparation host this took about two minutes.

LOCATE AN ADDITIONAL WITNESS
python -B -O supplement/locate_quintic.py --x 729/200 --output NEW_witness.json

The implemented moment routines accept 3 <= x <= 4 where the leading odd
block is certified positive. The uniform theorem concerns [3.64,3.66].
Candidate coefficients are chosen on successively finer rational grids and
accepted only if the full-tail contraction has a negative upper endpoint.
The fixed-precision implementation may return UNRESOLVED; the manuscript's
adaptive termination theorem allows increasing precision and truncation.

ARITHMETIC VERIFICATION
verify_transition.py: directed Decimal intervals, 60 significant digits,
80-term exponential Taylor enclosure, all 1,000 closed interval cells.
verify_rational_replay.py: exact Fraction arithmetic, outward 10^-50 grid,
100-term Taylor enclosure, every interval cell, alternate determinant derivative.
These share the analytic moment assembly; they are not separate human reviews.
verify_ordered_pair_center.py: preserved earlier independent central expansion,
7-by-7 ordered pairs and complete infinite tails, outward rational 10^-90 grid.
check_publication.py: coverage, source hashes, printed bounds, cross-checks.
No mathematical gate relies on Python assert or a floating-point eigenvalue.

COMPILATION
Compile main.tex with a current LaTeX installation and NewTX packages.
The supplied PDF was compiled with Tectonic 0.17.0 and all six pages reviewed.
Keep generated build products and any TeX caches in a separate temporary folder.

PROVENANCE
This manuscript strengthens the October 16 systematic locating-method proof.
Earlier papers, sources, archives, and certificates remain in their existing
folders. The prior ordered-pair verifier is copied byte-for-byte and is not
represented as newly authored code. Earlier proof files are not overwritten.
The new package has not been externally uploaded or submitted.
