{"id":"e-4fd32b1a93a66d21","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-5fccad4e67ef9278","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":"55ee55fe0f03462ea851c43b42d85a58c59030c1afe0b50a1af950c9b2c87857","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":4446,"certificate_compressed_size":1279,"conclusion_name":"veronese_section_2_0 of Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*2^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-01cea33b6485d9cc","role":"sequence","name":"Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*2^j.","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-5fccad4e67ef9278","claim":"real_rooted"},{"node_id":"n-5fccad4e67ef9278","claim":"one_signed_coefficients"},{"node_id":"n-5fccad4e67ef9278","claim":"hadamard_kernel"}]}