{"id":"e-6e85c0971e84e272","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-1bf99ad40f056d33","premise_count":0,"theorem":"polytool parent provers, route periodic_product: every parent row P_n, n >= 1, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"a255c82e31cb1ef8353e88ce0872bae56bbedf0340818b927ea1beab1379b680","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":629,"certificate_compressed_size":372,"conclusion_name":"basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-1bf99ad40f056d33","claim":"real_rooted"},{"node_id":"n-1bf99ad40f056d33","claim":"one_signed_coefficients"},{"node_id":"n-1bf99ad40f056d33","claim":"hadamard_kernel"}]}