{"id":"e-6bd8c236b8a4d918","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-2f02b2035f8f4541","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":"6961726fe8f6b4bef87f7d8618ba09e7b951dae125a858cd56c404412c44d056","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":630,"certificate_compressed_size":375,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*8^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-2f02b2035f8f4541","claim":"one_signed_coefficients"},{"node_id":"n-2f02b2035f8f4541","claim":"hadamard_kernel"},{"node_id":"n-2f02b2035f8f4541","claim":"real_rooted"}]}