{"id":"e-08677a836f0d08e5","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-a8bf9bc375c66ce8","premise_count":0,"theorem":"polytool parent provers, route periodic_product: every parent row P_n, n >= 1, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"24a6b619357bf7895e659d9cf140982545c4be182e1e8de59941c045e5742286","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":645,"certificate_compressed_size":377,"conclusion_name":"veronese parent of Triangle T(n,k) with diagonals T(n,n-k) = binomial(n,3k).","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-a8bf9bc375c66ce8","claim":"real_rooted"},{"node_id":"n-a8bf9bc375c66ce8","claim":"one_signed_coefficients"},{"node_id":"n-a8bf9bc375c66ce8","claim":"hadamard_kernel"}]}