{"id":"e-6127b6ec6dbac6db","operation":{"map":"A007318","operation":"basis_map"},"operation_detail":"A007318","conclusion_id":"n-b29f2814dc39e975","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":"96ed0fb730c0830c14d7c8b2a80d6100e193b3726fc5256a2d448732ac5a2856","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":13318,"certificate_compressed_size":2507,"conclusion_name":"shift_x_plus_one of theta_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-5118548b67eae4b6","role":"sequence","name":"theta_plus_one of 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-b29f2814dc39e975","claim":"one_signed_coefficients"},{"node_id":"n-b29f2814dc39e975","claim":"hadamard_kernel"},{"node_id":"n-b29f2814dc39e975","claim":"real_rooted"}]}