{"id":"e-d03002d6b7efed5a","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-6a79351bf6797e1b","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":"8ba194c09183f4cff5414938a125c1cdb0f4a362a75c86044f4a230a7e07ef9c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":8706,"certificate_compressed_size":2329,"conclusion_name":"veronese_section_2_0 of Triangle of even numbered entries of odd numbered rows of Pascal's triangle A007318.","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-ba8de4e02acfb6ca","role":"sequence","name":"Triangle of even numbered entries of odd numbered rows of Pascal's triangle A007318.","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-6a79351bf6797e1b","claim":"real_rooted"},{"node_id":"n-6a79351bf6797e1b","claim":"one_signed_coefficients"},{"node_id":"n-6a79351bf6797e1b","claim":"hadamard_kernel"},{"node_id":"n-6a79351bf6797e1b","claim":"interlacing"}]}