{"id":"e-d82c9b48e4b31a6b","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-b30e7a5b4198051a","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":"50c92cd11c82745cd226eff6f5cf3c2d06e6efe799693091d6d9f5393995ecfb","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":633,"certificate_compressed_size":376,"conclusion_name":"Triangle read by rows, T(n,k) = GegenbauerC(m,-n,-3/2) where m = k if k<n else 2*n-k, for n>=0 and 0<=k<=2n.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-b30e7a5b4198051a","claim":"real_rooted"},{"node_id":"n-b30e7a5b4198051a","claim":"one_signed_coefficients"},{"node_id":"n-b30e7a5b4198051a","claim":"hadamard_kernel"}]}