{"id":"e-5d982f8f22366510","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-081b3f700db2d097","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":"35ad2ccd007eaf2fd11f9c0201ab34c48ca3d8f2a9fee993716716bd2afe8308","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":4446,"certificate_compressed_size":1272,"conclusion_name":"veronese_section_2_0 of Cube of lower triangular normalized binomial matrix.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-8d887bfc40d036b9","role":"sequence","name":"Cube of lower triangular normalized binomial matrix.","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-081b3f700db2d097","claim":"real_rooted"},{"node_id":"n-081b3f700db2d097","claim":"one_signed_coefficients"},{"node_id":"n-081b3f700db2d097","claim":"hadamard_kernel"}]}