{"id":"e-a3d90d8bb42bdd7e","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-63490e7c6342a0ed","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":"1556c9552b9433d8cd9a784e4d5d4e69c19fc057f46256bbd15d01d0f49f6f4d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":4446,"certificate_compressed_size":1270,"conclusion_name":"veronese_section_2_0 of Triangle of coefficients in expansion of (1+3*x)^n.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-6a5af5e1168bb679","role":"sequence","name":"Triangle of coefficients in expansion of (1+3*x)^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-63490e7c6342a0ed","claim":"real_rooted"},{"node_id":"n-63490e7c6342a0ed","claim":"one_signed_coefficients"},{"node_id":"n-63490e7c6342a0ed","claim":"hadamard_kernel"}]}