{"id":"e-267d8a8f48506a34","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":1},"operation_detail":"r=2, j=1, shift 0","conclusion_id":"n-ab55e05a7226d6fc","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":"6253e98e900ed93b003d1efdcef9de3c71d84bf06057361b662d87a59bfc8b53","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":4248,"certificate_compressed_size":1240,"conclusion_name":"veronese_section_2_1 of Riordan array ((1+x)^3,x).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-e1d160f3b707da31","role":"sequence","name":"Riordan array ((1+x)^3,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-ab55e05a7226d6fc","claim":"real_rooted"},{"node_id":"n-ab55e05a7226d6fc","claim":"one_signed_coefficients"},{"node_id":"n-ab55e05a7226d6fc","claim":"hadamard_kernel"}]}