{"id":"e-396a3b284da38893","operation":{"index_shift":0,"modulus":2,"operation":"veronese_section","residue":1},"operation_detail":"r=2, j=1, shift 0","conclusion_id":"n-ec6cfd69d11c8345","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":"75ab5530a5f9500e8da4d89bea5fb57ffeed7517a264055cdbbcaefd82510169","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"veronese_section","certificate_raw_size":4442,"certificate_compressed_size":1277,"conclusion_name":"veronese_section_2_1 of Triangle of coefficients in expansion of (2+3x)^n.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-5733d79f45a14084","role":"sequence","name":"Triangle of coefficients in expansion of (2+3x)^n.","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-ec6cfd69d11c8345","claim":"one_signed_coefficients"},{"node_id":"n-ec6cfd69d11c8345","claim":"hadamard_kernel"},{"node_id":"n-ec6cfd69d11c8345","claim":"real_rooted"}]}