{"id":"e-bf95690978550a83","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-7fd16a32c438d522","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":"c4ba7b45d9ebd1389f4ff252a186983973807f6a95cd98e68cbe51e06fbf4ef7","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1149,"certificate_compressed_size":606,"conclusion_name":"Triangle T(n,k)=Sum_{i=0..n} |stirling1(n,n-i)|*binomial(i,k), k=0..n-1.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-7fd16a32c438d522","claim":"one_signed_coefficients"},{"node_id":"n-7fd16a32c438d522","claim":"hadamard_kernel"},{"node_id":"n-7fd16a32c438d522","claim":"real_rooted"}]}