{"id":"e-51cb02553cf4a8ac","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-a624e5aba8e1c39e","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":"9da21b28421e2a2c1c0ba30195f71f47de31d0e0aac7e97380d5e5ccbd4bc89a","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":643,"certificate_compressed_size":383,"conclusion_name":"Triangle read by rows: T(n,k) = 2^floor(n/2)*binomial(n-1,k-1).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-a624e5aba8e1c39e","claim":"real_rooted"},{"node_id":"n-a624e5aba8e1c39e","claim":"one_signed_coefficients"},{"node_id":"n-a624e5aba8e1c39e","claim":"hadamard_kernel"}]}