{"id":"e-0a35d6a32dc0856a","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-a93042cd70c4761e","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":"d9d8bcb8772e4fe2ca60467d6c42465be8b49b7b7e344d80ef0167ed08bc4a05","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":642,"certificate_compressed_size":386,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*4^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-a93042cd70c4761e","claim":"one_signed_coefficients"},{"node_id":"n-a93042cd70c4761e","claim":"hadamard_kernel"},{"node_id":"n-a93042cd70c4761e","claim":"real_rooted"}]}