Large negative subspaces for positive Euler deformations
Scott Schubr

Contents
--------
main.tex             Complete mathematical manuscript.
verify_geometry.py   Exact finite progression-free and packet-support examples.
verify_geometric_windows.py  Exact fixed-spacing geometric-window controls.

The manuscript proves the analytic prime number theorem transfer, the complete
mixed-matrix estimates, the higher-prime-power bound and the asymptotic
negative-index lower bound at every sufficiently large support radius.
verify_geometry.py checks finite progression-free center constructions with
the stronger exclusion of every mixed window, including the introductory
progression collision. verify_geometric_windows.py checks the geometric
construction used for the all-support theorem: sum windows avoid all bands,
while difference windows may meet earlier bands. Two adverse examples have
an exact earlier-band collision, whose normalized exponential factor is
checked rather than discarded. It also checks the all-support interpolation.
Both programs use only integers and rational numbers. They verify finite
geometric inputs, not the analytic prime number theorem estimates.

Building the manuscript
-----------------------
Use a standard LaTeX installation with the article class and the lmodern,
amsmath, amssymb, amsthm, mathtools, geometry, microtype and hyperref packages:

    pdflatex -interaction=nonstopmode -halt-on-error main.tex
    pdflatex -interaction=nonstopmode -halt-on-error main.tex

The bibliography is included in main.tex; no separate bibliography processor
or downloaded data are needed.

Running the finite examples
--------------------------
Python 3.10 or later is sufficient. No third-party modules are required.

    python verify_geometry.py
    python -O verify_geometry.py
    python verify_geometric_windows.py
    python -O verify_geometric_windows.py

Each program retains its acceptance checks under -O and prints a JSON summary.
To save a summary at a chosen location:

    python verify_geometry.py --output geometry_checks.json

The program writes no file unless --output is supplied.

Additional archive contents
---------------------------
Large negative subspaces for positive Euler deformations.pdf: complete paper.
CITATION.cff: citation metadata.
SHA256SUMS.txt: SHA-256 checksums for all other archive members.
The supplied PDF was built with Tectonic 0.17.0 and
SOURCE_DATE_EPOCH=1793386800.
