{"id":"e-4fdd1b3030c1c25c","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-c11cb6bca0e3e7dc","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":"2e86ac7ed8d8151674a6e6d436c1cbd3f2b43ae06f5fd4d4aa68aab49bebac20","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":640,"certificate_compressed_size":384,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*6^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-c11cb6bca0e3e7dc","claim":"one_signed_coefficients"},{"node_id":"n-c11cb6bca0e3e7dc","claim":"hadamard_kernel"},{"node_id":"n-c11cb6bca0e3e7dc","claim":"real_rooted"}]}