{"id":"e-4d02ac33f5b2fbc9","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-ea2139b8dbf6bf8d","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":"5c3bd295408c4be71cfe79410d65d0f4e5e15078c08c1fffe66e8717b4a8a220","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":643,"certificate_compressed_size":381,"conclusion_name":"Interpolation operator: Triangle with an even number of zeros in each line followed by 1 or 2 ones.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-ea2139b8dbf6bf8d","claim":"real_rooted"},{"node_id":"n-ea2139b8dbf6bf8d","claim":"one_signed_coefficients"},{"node_id":"n-ea2139b8dbf6bf8d","claim":"hadamard_kernel"}]}