Prescribed-gradient minimizers and coefficient stability
for homogeneous real-stable polynomials
Scott Schubr, October 22, 2026

Contents
  Prescribed_Gradient_Stable_Polynomials.pdf - complete research paper
  main.tex - complete editable LaTeX source, including bibliography
  verify_quartic.py - optional exact arithmetic for Section 6
  CITATION.bib - citation for this paper
  MANIFEST.sha256.json - SHA-256 identities of the other five files

The paper proves the all-fixed-degree prescribed-gradient minimizer theorem
and coefficient-l1 stability near the balanced gradient, with optimal
distance order and a count-law interpretation. The global neighborhood and
constants are dimension-dependent and qualitative. The balanced uniqueness
theorem is a cited prior input. The proof has no computational premise.

Rebuild
  With a conventional LaTeX distribution:
    pdflatex -interaction=nonstopmode -halt-on-error main.tex
    pdflatex -interaction=nonstopmode -halt-on-error main.tex
  Alternatively:
    tectonic main.tex
  Required packages: fontenc, lmodern, amsmath, amssymb, amsthm,
  geometry, hyperref. No external bibliography database is needed.
  The compiler output is main.pdf. PDF metadata and bytes may vary with
  compiler versions and build time; the manifest identifies the supplied PDF.

Optional arithmetic reproduction (Python 3, standard library only):
    python -B verify_quartic.py
    python -B -O verify_quartic.py
  The checker evaluates the defining quartic on the Boolean cube at six
  rational parameters. Interpolation certifies the two degree-four identities.
  It does not establish real stability or nondeterminantal representability;
  those are cited mathematical inputs. No output files are created.

Integrity
  Recompute SHA-256 for the five files named in MANIFEST.sha256.json.
  A matching digest establishes byte identity, not mathematical correctness.

This is a scholarly source bundle. The paper discloses AI assistance.
