{"id":"e-969b818b29eb86a6","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":0},"operation_detail":"r=2, j=0, shift 0","conclusion_id":"n-d94eb58321d693e7","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":"5afbbb62740d98fd8c0ca8f71888d56dc194b678fb9eaacd421b560a4e2f9eab","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":4447,"certificate_compressed_size":1267,"conclusion_name":"veronese_section_2_0 of basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-74c1e94669ff21ff","role":"sequence","name":"basis-map coefficients of Riordan array (1+2x,x(1+x)). shifted by x -> -x + 0","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-d94eb58321d693e7","claim":"real_rooted"},{"node_id":"n-d94eb58321d693e7","claim":"one_signed_coefficients"},{"node_id":"n-d94eb58321d693e7","claim":"hadamard_kernel"}]}