{"id":"e-aa930f654032c3a1","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":1},"operation_detail":"r=2, j=1, shift 0","conclusion_id":"n-1ad29a573524b2ae","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":"e37fac97f55a114adb2cf3d49fba19572b62327401e034b09de5072c86defa54","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":6699,"certificate_compressed_size":1928,"conclusion_name":"veronese_section_2_1 of Riordan array (1, 3+x).","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-5d39164c4108e043","role":"sequence","name":"Riordan array (1, 3+x).","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-1ad29a573524b2ae","claim":"real_rooted"},{"node_id":"n-1ad29a573524b2ae","claim":"one_signed_coefficients"},{"node_id":"n-1ad29a573524b2ae","claim":"hadamard_kernel"}]}