bibkey: brandenhuh2020lorentzian authors: Petter Brändén, June Huh year: 2020 title: Lorentzian polynomials doi: 10.4007/annals.2020.192.3.4 url: https://arxiv.org/abs/1902.03719v8 claim: Reciprocal-factorial generating polynomials of M-convex supports are Lorentzian, with positive-orthant root concavity and Hessian signature restrictions. strata_touched:

• D5/S3/Resource/SimplexCoverageHessian
• D5/S3/Resource/SimplexCoveragePolynomial license: citation-only triage: anchor

Lorentzian polynomials

The journal article is in Annals of Mathematics 192, issue 3, pages 821–891. The source version used for the concavity-transfer route is arXiv:1902.03719v8.

Mathematical interfaces

Section 2.2 gives the exchange condition for M-convex supports. Theorem 3.10, implication (7) to (4), concerns normalized generating polynomials with reciprocal-factorial coefficients. Theorem 2.30 and Proposition 2.33 supply the positive-orthant log/root-concavity context. Polynomial support conditions, nonzero evaluation, homogeneity, and degree hypotheses must be verified by a consumer; a support-indicator polynomial is not the same normalized polynomial.

Formal reuse boundary

The matrix component in D5/S3/Resource/SimplexCoverageHessian uses Mathlib’s finite real Hermitian eigenbasis and a maximum-ratio argument. It does not import a formal Lorentzian theorem, establish the represented-span polynomial induction, or settle a simplex optimizer conjecture. The citation is published mathematical context, not kernel evidence or an independent open-problem result.

D5/S3/Resource/SimplexCoveragePolynomial supplies the actual represented coefficients and contractions, degree-two Hessian classification and reverse inequality, positive-evaluation rank criterion, derivative-positive support connectivity and rank/span zero obstructions. The higher-degree normalized Hessian induction and the analytic and sampling bridges remain open.