{"id":"e-711ca5eff5ba56ea","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-26633b980c3508e8","premise_count":0,"theorem":"polytool parent provers, route periodic_product: every parent row P_n, n >= 0, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"83d02709ea5825e8f249f36269fa8d4843c749b1081b3fc0e27f52c0ea62196d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":639,"certificate_compressed_size":383,"conclusion_name":"Triangle read by rows: (i,j)-th entry is binomial(i,j)*3^(i-j)*8^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-26633b980c3508e8","claim":"one_signed_coefficients"},{"node_id":"n-26633b980c3508e8","claim":"hadamard_kernel"},{"node_id":"n-26633b980c3508e8","claim":"real_rooted"}]}