{"id":"e-b445a5ff4f115ce0","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-6874f381e9c7e0a2","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":"8a6a9328baddbaf060108e764b55cef675c0c0d83236829c625fcc203057e660","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":643,"certificate_compressed_size":387,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*8^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-6874f381e9c7e0a2","claim":"one_signed_coefficients"},{"node_id":"n-6874f381e9c7e0a2","claim":"hadamard_kernel"},{"node_id":"n-6874f381e9c7e0a2","claim":"real_rooted"}]}