{"id":"e-052cfd8551fd4fcd","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":"01a2a6b1073f9d5cb1464d4ae77c1939a049463178e1eaa7dec1fdc631820777","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1223,"certificate_compressed_size":597,"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":"one_signed_coefficients"},{"node_id":"n-d938c1937a93c4df","claim":"hadamard_kernel"},{"node_id":"n-d938c1937a93c4df","claim":"real_rooted"}]}