{"id":"e-6956732375ae53ac","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":1},"operation_detail":"r=2, j=1, shift 0","conclusion_id":"n-0698904a58ac3702","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":"71ad55bb304efd7dde1e1a0027e5af0b6d8d3c135d84f34a4402cada642d76a9","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":8694,"certificate_compressed_size":2327,"conclusion_name":"veronese_section_2_1 of Triangle read by rows: T(n, k) = binomial(2n, 2k).","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[{"position":0,"node_id":"n-f7935c36a3c0ec8c","role":"sequence","name":"Triangle read by rows: T(n, k) = binomial(2n, 2k).","uses":{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-0698904a58ac3702","claim":"real_rooted"},{"node_id":"n-0698904a58ac3702","claim":"one_signed_coefficients"},{"node_id":"n-0698904a58ac3702","claim":"hadamard_kernel"},{"node_id":"n-0698904a58ac3702","claim":"interlacing"}]}