{"id":"e-342cfe46a0a2cd4c","operation":{"map":"A013611","operation":"basis_map"},"operation_detail":"A013611","conclusion_id":"n-550f42ea21954e22","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":"0c8ada4bb8f665a02a661b3b6c55e7dd4190aeef3d793cd3aaf309fc71be6248","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map","certificate_raw_size":10659,"certificate_compressed_size":2350,"conclusion_name":"basis_map_A013611 of (3,1) Pascal triangle.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"unordered"}],"premises":[{"position":0,"node_id":"n-92128fbba2409faa","role":"sequence","name":"(3,1) Pascal triangle.","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-550f42ea21954e22","claim":"real_rooted"},{"node_id":"n-550f42ea21954e22","claim":"one_signed_coefficients"},{"node_id":"n-550f42ea21954e22","claim":"hadamard_kernel"},{"node_id":"n-550f42ea21954e22","claim":"interlacing"}]}