{"id":"e-facb0d3b0416b76b","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-d938c1937a93c4df","premise_count":0,"theorem":"polytool parent provers, route root_domain: every parent row P_n, n >= 1, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"d2aa886033ecf60b4dde545e05c1ce6bd91a117b291af40c6f72c06614792fc6","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1362,"certificate_compressed_size":640,"conclusion_name":"Triangle of numbers T(n,k) = k!*Stirling2(n,k) read by rows (n >= 1, 1 <= k <= n).","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-d938c1937a93c4df","claim":"hadamard_kernel"},{"node_id":"n-d938c1937a93c4df","claim":"real_rooted"},{"node_id":"n-d938c1937a93c4df","claim":"one_signed_coefficients"}]}