{"id":"e-576aa1dc371fa216","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-260e022530e5976c","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":"0c2d789b3c99612f3ca0352e4950835273d9e57d58e202218658b5aa385bfc66","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1159,"certificate_compressed_size":609,"conclusion_name":"Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 3*x)^(-1/3), (-1/3)*log(1 - 3*x)). A generalized Stirling1 triangle.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-260e022530e5976c","claim":"one_signed_coefficients"},{"node_id":"n-260e022530e5976c","claim":"hadamard_kernel"},{"node_id":"n-260e022530e5976c","claim":"real_rooted"}]}