{"id":"e-e258896fea087a41","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-6a690be6f27c7004","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":"ac1d307b0e69f241e575d6a4bd1e1e4736fa0aafce8e9bbebcb5831804131c10","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":647,"certificate_compressed_size":381,"conclusion_name":"veronese parent of Binomial coefficients C(n,k) with n-k even, read by rows.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-6a690be6f27c7004","claim":"real_rooted"},{"node_id":"n-6a690be6f27c7004","claim":"one_signed_coefficients"},{"node_id":"n-6a690be6f27c7004","claim":"hadamard_kernel"}]}