{"id":"e-f6f2e37f93f1c1e6","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-eba9e40af29eafd3","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":"5401d54350b4fa88c2ff9e29f8dba1014f8df29e81e20a02182dea0a3062922d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":8581,"certificate_compressed_size":2358,"conclusion_name":"veronese_section_2_0 of Triangle read by rows: n-th row = unsigned coefficients of the characteristic polynomials of an n X n matrix with 2's on the diagonal and 1's elsewhere.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-801895951aa20f29","role":"sequence","name":"Triangle read by rows: n-th row = unsigned coefficients of the characteristic polynomials of an n X n matrix with 2's on the diagonal and 1's elsewhere.","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-eba9e40af29eafd3","claim":"real_rooted"},{"node_id":"n-eba9e40af29eafd3","claim":"one_signed_coefficients"},{"node_id":"n-eba9e40af29eafd3","claim":"hadamard_kernel"}]}