{"id":"e-5c6f5707f5ad5120","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-efe593ca91bb62f5","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":"999f86d2d762b0781ec56741b6da9b8e787d25606c2bcdd7604ec6995478167f","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":12290,"certificate_compressed_size":2327,"conclusion_name":"shift_x_plus_one 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-efe593ca91bb62f5","claim":"one_signed_coefficients"},{"node_id":"n-efe593ca91bb62f5","claim":"hadamard_kernel"},{"node_id":"n-efe593ca91bb62f5","claim":"real_rooted"}]}