Boundary-Absorbed A₂-Curvature Inequalities for Toeplitz–Pólya Frequency Schur Minors
Year: 2026
Type: article
Abstract: NB: Version 2 update: this version proves the finite-band cancellation identity that was stated as a conjecture in v1. Consequently, the endpoint product factorization is now unconditional. The prefix shifted-residual positivity statement remains conjectural.This preprint introduces a family of signed Schur-minor defect expressions motivated by Toeplitz/Pólya-frequency Jacobi-Trudi minors. The paper studies a boundary-absorbed global curvature mechanism on an A2-lattice strip, showing that local positivity routes are structurally inadequate: the relevant defect is not Schur-positive, its transverse second differences are not pointwise nonnegative, and fixed local endpoint absorption is too strong. The main endpoint gate is reduced by Pieri expansion to an explicit finite Schur-function expression built from three-column families. In conjugate coordinates, the local defect becomes a transverse second difference, giving an integrated A2-curvature interpretation. Under principal specialization, the paper proves a baseline hook-content skeleton theorem, a universal width-three cancellation factor, endpoint asymptotic cancellation certificates, and a positive centered content-moment identity. The endpoint product factorization is obtained conditionally on a finite-band cancellation identity. The manuscript also formulates a stronger prefix shifted-residual positivity conjecture. Exact symbolic checks are included for the endpoint product formula, finite-band identities, and prefix shifted-residual nonnegativity over the stated finite ranges. No claim about the Riemann Hypothesis is made.
Author: Dumas, Alexandre
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7159808109