{"id":"e-e4ffd1425a5524fc","operation":{"map":"A038327","operation":"basis_map"},"operation_detail":"A038327","conclusion_id":"n-5d39164c4108e043","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":"bc7817a6f36213ae580d96855e4a3db8cc1ef07e081379ef0f363e684a40a077","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":11704,"certificate_compressed_size":2211,"conclusion_name":"Riordan array (1, 3+x).","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-7f91c094943cee63","role":"sequence","name":"basis-map coefficients of Riordan array (1, 3+x).","uses":{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"12"}}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 12]"}],"cited_by":[{"node_id":"n-5d39164c4108e043","claim":"one_signed_coefficients"},{"node_id":"n-5d39164c4108e043","claim":"hadamard_kernel"},{"node_id":"n-5d39164c4108e043","claim":"real_rooted"}]}