{"id":"e-bbffc3f85cdc52e2","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-5a70a6e97131d437","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":"b33fdb2d8c656579ea0e41c3d105c31b9cd68c4f56666d7d9ff6bf972976c883","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":659,"certificate_compressed_size":391,"conclusion_name":"Triangle of Sulanke numbers: T(n,k) = T(n,k-1) + a(n-1,k) for n+k even and a(n,k) = a(n,k-1) + 2*a(n-1,k) for n+k odd.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-5a70a6e97131d437","claim":"real_rooted"},{"node_id":"n-5a70a6e97131d437","claim":"one_signed_coefficients"},{"node_id":"n-5a70a6e97131d437","claim":"hadamard_kernel"}]}