{"id":"e-4c0875826685c298","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-849de7332df28657","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":"7dd9219068c51cada605cfee28cb1e8c9899413a02a27c87d5fd88a894c766d8","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1159,"certificate_compressed_size":607,"conclusion_name":"Triangle T(n, k) read by rows: T(n, k) = Sum_{j=0..n} binomial(j, n-k) * |Stirling1(n, n-j)|.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-849de7332df28657","claim":"real_rooted"},{"node_id":"n-849de7332df28657","claim":"one_signed_coefficients"},{"node_id":"n-849de7332df28657","claim":"hadamard_kernel"}]}