{"id":"e-c2c3539c3b6bbd5d","operation":{"map":"A038291","operation":"basis_map"},"operation_detail":"A038291","conclusion_id":"n-016d7724d51f6416","premise_count":1,"theorem":"geometric family P_k = g(t) (a + d t)^k: T(p) = g(t) p(a + d t), so the roots of T(p) are those of g and the points (r - a)/d for the roots r of p (elementary)","lean_route":null,"lean_declarations":[],"certificate_hash":"d70bdc6b31be8aaa0665ff808deeb907d25824e0f05efa8b7c0c228f826ba2f4","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":14426,"certificate_compressed_size":2796,"conclusion_name":"Riordan array (1, 3+3x).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-767aa1cf87a969b2","role":"sequence","name":"basis-map coefficients of Riordan array (1, 3+3x).","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"9"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 9]"}],"cited_by":[{"node_id":"n-016d7724d51f6416","claim":"hadamard_kernel"},{"node_id":"n-016d7724d51f6416","claim":"real_rooted"},{"node_id":"n-016d7724d51f6416","claim":"interlacing"},{"node_id":"n-016d7724d51f6416","claim":"one_signed_coefficients"}]}