{"id":"e-25f661182ec3ab36","operation":{"operation":"basis_map_theorem"},"operation_detail":null,"conclusion_id":"n-0026e6b972fa04d4","premise_count":0,"theorem":"ray basis maps: for L f = (a + b t) f + kappa (t - h) f', b > 0, kappa >= 0, and g real-rooted with every root <= h, of multiplicity m at h, T(u^k) = L^k g sends every real polynomial with all roots in S to one with all roots in (-inf, h] if and only if S lies in (-inf, a + b h + kappa m] (RealRooted rayBasisMap_maps_realRootedIn_iff; the step is Ma and Wang, EJC 15 (2008) R17, Theorem 2)","lean_route":null,"lean_declarations":[],"certificate_hash":"87744c968cee214f7cf37c0e0f3fbbb5a04000683f65c86aaa7ba1f8d4b2bc58","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"basis_map_theorem","certificate_raw_size":1996,"certificate_compressed_size":841,"conclusion_name":"Stirling2 triangle with scaled diagonals (powers of 9).","claims":[{"claim":"basis_map_preserver","input_interval":"(-inf, 9]","output_interval":"(-inf, 0]","statement":"source (-inf, a + b h + kappa m] = (-inf, 9] with m = 0, target (-inf, 0]"}],"premises":[],"cited_by":[{"node_id":"n-0026e6b972fa04d4","claim":"basis_map_preserver"}]}