{"id":"e-0e7ef206328a472c","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-7e353d0275e3ebc5","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":"a7c8082624890e9e7967519b84316dd4d399123c4a1b5f5ba41198fd03f2d36c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":637,"certificate_compressed_size":379,"conclusion_name":"Triangle read by rows: T(n,0) = 0 for n >= 0; T(n,2*k+1) = A152842(2*n,2*(n-k)) and T(n,2*k) = A152842(2*n,2*(n-k)+1) for n >= k > 0.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-7e353d0275e3ebc5","claim":"real_rooted"},{"node_id":"n-7e353d0275e3ebc5","claim":"one_signed_coefficients"},{"node_id":"n-7e353d0275e3ebc5","claim":"hadamard_kernel"}]}