{"id":"e-69bbc7837aabb73c","operation":{"map":"A027465","operation":"basis_map"},"operation_detail":"A027465","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":"387cb5866eeaacc7e24f97997a3d4816cd483c66fe00c9a8590563ecfd6f2aa0","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":11670,"certificate_compressed_size":2198,"conclusion_name":"Riordan array (1, 3+3x).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-4ec583084451043e","role":"sequence","name":"basis-map coefficients of Riordan array (1, 3+3x).","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"3"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 3]"}],"cited_by":[{"node_id":"n-016d7724d51f6416","claim":"one_signed_coefficients"},{"node_id":"n-016d7724d51f6416","claim":"hadamard_kernel"},{"node_id":"n-016d7724d51f6416","claim":"real_rooted"}]}