{"id":"e-252e19fd44a7da1c","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":1},"operation_detail":"r=2, j=1, shift 0","conclusion_id":"n-7e99bca717f629d0","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":"fe75f120038ca486bfaf760cab9f17aa86a8b6bc646c2fe43a47f83a101eede6","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":4442,"certificate_compressed_size":1278,"conclusion_name":"veronese_section_2_1 of Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*2^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-01cea33b6485d9cc","role":"sequence","name":"Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*2^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-7e99bca717f629d0","claim":"real_rooted"},{"node_id":"n-7e99bca717f629d0","claim":"one_signed_coefficients"},{"node_id":"n-7e99bca717f629d0","claim":"hadamard_kernel"}]}