{"id":"e-7643b829dc52d64b","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-37ec1285a176250d","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":"fafdf1a4d5be047a587ca15195319c42ae22de4550641c88a6bbaf21ec7a5d19","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":4470,"certificate_compressed_size":1272,"conclusion_name":"veronese_section_2_0 of Riordan array (1-x,x/(1-x)).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-7717563017cb9e5f","role":"sequence","name":"Riordan array (1-x,x/(1-x)).","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-37ec1285a176250d","claim":"real_rooted"},{"node_id":"n-37ec1285a176250d","claim":"one_signed_coefficients"},{"node_id":"n-37ec1285a176250d","claim":"hadamard_kernel"}]}