{"id":"e-1c0801c63e403da5","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-691e332e74d300f5","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":"b0d3fec4dd886219203d57982bf6941b45eb472999b70f537930c5d074e350fe","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":8972,"certificate_compressed_size":2440,"conclusion_name":"veronese_section_2_0 of Pascal-(1,7,1) array.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[{"position":0,"node_id":"n-1e2f1b7f566b371c","role":"sequence","name":"Pascal-(1,7,1) array.","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-691e332e74d300f5","claim":"real_rooted"},{"node_id":"n-691e332e74d300f5","claim":"one_signed_coefficients"},{"node_id":"n-691e332e74d300f5","claim":"hadamard_kernel"},{"node_id":"n-691e332e74d300f5","claim":"interlacing"}]}