{"id":"e-5e5f630c1e2baa8a","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-f48bed27dbc29c5f","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":"04b7ca59a6c8fe10d32be1f3cb196df3e41794a24a943ba6018ec165a4f8e67f","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":637,"certificate_compressed_size":377,"conclusion_name":"The truncated (4,4,1)-Pascal triangle, given by 4*C(n-2, k) + 4*C(n-2, k-1) + C(n-2, k-2) for n>=2.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-f48bed27dbc29c5f","claim":"one_signed_coefficients"},{"node_id":"n-f48bed27dbc29c5f","claim":"hadamard_kernel"},{"node_id":"n-f48bed27dbc29c5f","claim":"real_rooted"}]}