Effective Prescribed-Gradient Stability for Homogeneous Real-Stable Polynomials
Scott Schubr

The manuscript proves explicit all-fixed-degree constants for a global
prescribed-gradient coefficient reserve in the normalized homogeneous
nonnegative real-stable class. It includes a closed gradient ball,
singular boundaries, and the Hermitian mixed-discriminant corollary.
The constants are coarse and may depend on n.

The proof is analytic. The included exact checks corroborate coefficient normalizations and selected identities.

Files
  Effective_stable_polynomial_reserves.pdf  Complete manuscript.
  main.tex                                Editable manuscript source.
  verify_reserve.py                       Exact rational controls.
  build.py                                Local Tectonic build helper.
  CITATION.bib                            Citation metadata.
  SHA256SUMS                              Checksums of all other members.

Requirements and reproduction
  Python 3.10 or later; standard library only for the control program.
  Run: python verify_reserve.py
       python -O verify_reserve.py
  The JSON results should agree exactly and report PASS. They cover133
  balanced product fixtures in degrees2 through6,15 gradient-correction
  fixtures, a specialized Vamos quartic, and the negative intrinsic
  quartic example. Assertions are not used as acceptance gates.

  For the PDF, install Tectonic and run:
       python build.py --tectonic /path/to/tectonic
  Alternatively compile main.tex with a current LaTeX installation using
  the listed standard packages. The helper fixes SOURCE_DATE_EPOCH.
  A new Tectonic installation can need network access for its TeX bundle.

This is an author preprint.  The cited earlier
prescribed-gradient paper retains priority for the qualitative theorem.

AI tools assisted mathematical research, preparation and internal checking.
