{"id":"e-08ecf9f1e7a97c44","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-29d7c5a1e19b9d74","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":"6ee90d39a1e40d2cf8cb6a50b7716248b7a3a8fbfea0590514d7a71f276e7637","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":645,"certificate_compressed_size":386,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*12^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-29d7c5a1e19b9d74","claim":"one_signed_coefficients"},{"node_id":"n-29d7c5a1e19b9d74","claim":"hadamard_kernel"},{"node_id":"n-29d7c5a1e19b9d74","claim":"real_rooted"}]}