{"id":"e-a3c37a89023e80b3","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-170caf7aaf900871","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":"e08038f130231d440eb6dea4d4069c1ee32b55ed982037b260b0e0ecd5477bc8","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":12290,"certificate_compressed_size":2334,"conclusion_name":"basis_map_A013609 of 3n + 1 preceded by n zeros.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-ccc86c3dcf2ac685","role":"sequence","name":"3n + 1 preceded by n zeros.","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]"}],"cited_by":[{"node_id":"n-170caf7aaf900871","claim":"one_signed_coefficients"},{"node_id":"n-170caf7aaf900871","claim":"hadamard_kernel"},{"node_id":"n-170caf7aaf900871","claim":"real_rooted"}]}