{"id":"e-c6792048648d3d6d","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":1},"operation_detail":"r=2, j=1, shift 0","conclusion_id":"n-1864d83319c9138c","premise_count":1,"theorem":"Veronese sections of Polya frequency sequences (Aissen--Schoenberg--Whitney--Edrei): if P is real-rooted with coefficients of one sign, equivalently nonzero with all roots in (-inf, 0], every section V_(r,j)(P) is zero or real-rooted with roots in (-inf, 0]","lean_route":null,"lean_declarations":[],"certificate_hash":"46d78ec19c7a8c03ad5b8a4e00e0cf6a54d48da30451a9ec4409ba091a986cef","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":4442,"certificate_compressed_size":1270,"conclusion_name":"veronese_section_2_1 of Triangle of coefficients in expansion of (1+2*x)^n.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-71965e79e47a4526","role":"sequence","name":"Triangle of coefficients in expansion of (1+2*x)^n.","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-1864d83319c9138c","claim":"real_rooted"},{"node_id":"n-1864d83319c9138c","claim":"one_signed_coefficients"},{"node_id":"n-1864d83319c9138c","claim":"hadamard_kernel"}]}