{"id":"e-6fdf1329e5e61ed8","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":1},"operation_detail":"r=2, j=1, shift 0","conclusion_id":"n-1f922d5ae3a4fc22","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":"ce1e96040c94cbbf6f3cf18b11b7b9e392a94b5951f8849fc59a9f4da9c89f7a","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":4462,"certificate_compressed_size":1267,"conclusion_name":"veronese_section_2_1 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-1f922d5ae3a4fc22","claim":"real_rooted"},{"node_id":"n-1f922d5ae3a4fc22","claim":"one_signed_coefficients"},{"node_id":"n-1f922d5ae3a4fc22","claim":"hadamard_kernel"}]}