{"id":"e-4a3fbc77a3e37655","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":1},"operation_detail":"r=2, j=1, shift 0","conclusion_id":"n-373413a99f5cc9e6","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":"dd33a5f4f74523b807c68adc05b30a3091fffbf493d6e8968371bf82c885276e","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":4444,"certificate_compressed_size":1270,"conclusion_name":"veronese_section_2_1 of Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-3dcaebc50e901d48","role":"sequence","name":"Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-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-373413a99f5cc9e6","claim":"real_rooted"},{"node_id":"n-373413a99f5cc9e6","claim":"one_signed_coefficients"},{"node_id":"n-373413a99f5cc9e6","claim":"hadamard_kernel"}]}