{"id":"e-649505c4b0b03bd9","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":1},"operation_detail":"r=2, j=1, shift 0","conclusion_id":"n-6195babe43991cd3","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":"3aeb479c8e3690dd89ba8e1bf99006767631d1e4507916d0a3648b4bcc6f82d6","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":5948,"certificate_compressed_size":1823,"conclusion_name":"veronese_section_2_1 of Triangle read by rows: row n consists of n zeros followed by n!.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-fbb4b9430d9de872","role":"sequence","name":"Triangle read by rows: row n consists of n zeros followed by 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-6195babe43991cd3","claim":"real_rooted"},{"node_id":"n-6195babe43991cd3","claim":"one_signed_coefficients"},{"node_id":"n-6195babe43991cd3","claim":"hadamard_kernel"}]}