{"id":"e-7f9dd568d5b3e61f","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-b9fbfb57d9269e2f","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":"7459521a370fd56c834165b8deac52b69ae7b4616aad32986bdce813b2fc790c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1404,"certificate_compressed_size":703,"conclusion_name":"Triangle of unsigned Stirling numbers of the first kind (see A048994), read by rows, T(n,k) for 0 <= k <= n.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-b9fbfb57d9269e2f","claim":"real_rooted"},{"node_id":"n-b9fbfb57d9269e2f","claim":"one_signed_coefficients"},{"node_id":"n-b9fbfb57d9269e2f","claim":"hadamard_kernel"}]}