{"id":"e-aa0ec4b5da096d18","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-54284d24a094e2d3","premise_count":0,"theorem":"polytool parent provers, route root_domain: every parent row P_n, n >= 0, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"65dbbe16caac241b370911733891511b686497c25c6f1eaa4d7b49580e205c04","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1160,"certificate_compressed_size":613,"conclusion_name":"Triangle read by rows, Stirling cycle numbers of order 2, T(n, n) = 1, T(n, k) = 0 if k < 0 or k > n, otherwise T(n, k) = T(n-1, k-1) + (n-1)^2*T(n-1, k), for 0 <= k <= n.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-54284d24a094e2d3","claim":"real_rooted"},{"node_id":"n-54284d24a094e2d3","claim":"one_signed_coefficients"},{"node_id":"n-54284d24a094e2d3","claim":"hadamard_kernel"}]}