{"id":"e-2999c7a8514fa399","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-06693716ec45c56f","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":"5ff416f65b682b0c80f1a20d1011cd0a083bf8c5f59771cdc09df889f2ed754f","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":7107,"certificate_compressed_size":2101,"conclusion_name":"veronese_section_2_0 of 3n + 1 preceded by n zeros.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-ccc86c3dcf2ac685","role":"sequence","name":"3n + 1 preceded by n zeros.","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-06693716ec45c56f","claim":"real_rooted"},{"node_id":"n-06693716ec45c56f","claim":"one_signed_coefficients"},{"node_id":"n-06693716ec45c56f","claim":"hadamard_kernel"}]}