{"id":"e-532ccda39f04a0f0","operation":{"map":"A038303","operation":"basis_map"},"operation_detail":"A038303","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":"f6ff3b8d6ab0d4da0a06173c07812c30d8dfd364a51763d811734ab2025c5d74","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":11703,"certificate_compressed_size":2189,"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-dd0db9eabdf2db44","role":"sequence","name":"basis-map coefficients of Riordan array (1, 2+2x).","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"10"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 10]"}],"cited_by":[{"node_id":"n-f5a001953ee28e8f","claim":"one_signed_coefficients"},{"node_id":"n-f5a001953ee28e8f","claim":"hadamard_kernel"},{"node_id":"n-f5a001953ee28e8f","claim":"real_rooted"}]}