{"id":"hexagon/2610.00275","pdf":"https://hexagonmath.org/pdf/2610.00275v1","url":"https://hexagonmath.org/abs/2610.00275v1","tags":["msc:11M26","msc:05E05","msc:30C15","msc:15B48","msc:33C45","Chebyshev polynomials","Riemann Zeta Function","Schur functions","Toeplitz minors","Turan inequalities"],"score":0,"title":"The Willow Transform and the Blind Zone Theorem: A Sharp Information-Theoretic Obstruction in the Turán Hierarchy for the Riemann xi-Function","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Changxia Lin"],"reviews":0,"subject":"math.NT","summary":"Let Xi(t) = xi(1/2 + it) be the Riemann Xi-function, let Xi(t) = sum_{k>=0} (-1)^k c_k t^{2k} be its even Taylor expansion at the origin, and let D(n,r) = det[c_{n+i-j}] (i,j = 0..r-1) be the Toeplitz minors whose positivity for all n >= 0, r >= 1 is equivalent to the Riemann Hypothesis (RH). We prove a sharp and quantitative obstruction in the resulting hierarchy of criteria. Parametrising the zeros of G(z) = sum c_k z^k by beta_j = -1/z_j, we establish by the dual Jacobi-Trudi identity the exact identity D(n,r) = s_{(r^n)}(beta), the Schur function of the rectangular partition (r^n) in the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-16","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}