{"id":"e-0a4154652e7b3f7f","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-4172472abe953cea","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":"330d38b07090a27100ab22e7da89c52ffe74454e6459263e355cb02c40aa4155","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":1159,"certificate_compressed_size":610,"conclusion_name":"Triangle read by rows: T(n, k) is the Sheffer triangle ((1 - 4*x)^(-1/4), (-1/4)*log(1 - 4*x)). A generalized Stirling1 triangle.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-4172472abe953cea","claim":"one_signed_coefficients"},{"node_id":"n-4172472abe953cea","claim":"hadamard_kernel"},{"node_id":"n-4172472abe953cea","claim":"real_rooted"}]}