{"id":"e-ce8b1eb4dfdacda9","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-a6e4c21559f1b253","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":"28caaec43f4fc15a9f0c8cea69af8f8f02862f1a8c2cd457b262c816771f23b5","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":11666,"certificate_compressed_size":2201,"conclusion_name":"basis_map_A013611 of Riordan array (1, 3+x).","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-5d39164c4108e043","role":"sequence","name":"Riordan array (1, 3+x).","uses":{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-a6e4c21559f1b253","claim":"real_rooted"},{"node_id":"n-a6e4c21559f1b253","claim":"one_signed_coefficients"},{"node_id":"n-a6e4c21559f1b253","claim":"hadamard_kernel"}]}