{"id":"e-763de8a298cf812d","operation":{"map":"A038243","operation":"basis_map"},"operation_detail":"A038243","conclusion_id":"n-f5a001953ee28e8f","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":"0358c294c80649627e60f3f71130e9a3feb0676f1c7065059217239dc00e8085","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":11679,"certificate_compressed_size":2195,"conclusion_name":"Riordan array (1, 2+2x).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-af83e10a056d6f29","role":"sequence","name":"basis-map coefficients of Riordan array (1, 2+2x).","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"5"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 5]"}],"cited_by":[{"node_id":"n-f5a001953ee28e8f","claim":"one_signed_coefficients"},{"node_id":"n-f5a001953ee28e8f","claim":"hadamard_kernel"},{"node_id":"n-f5a001953ee28e8f","claim":"real_rooted"}]}