{"id":"e-b7eca039219a7f53","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-6fea5aff4f44fa54","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":"28b0677de51356622004bdee49b3e32263cbcbf0992e57af7cdf296451825f68","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":629,"certificate_compressed_size":373,"conclusion_name":"a(n) = 1 if n is of the form m(m+3)/2, otherwise 0.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-6fea5aff4f44fa54","claim":"real_rooted"},{"node_id":"n-6fea5aff4f44fa54","claim":"one_signed_coefficients"},{"node_id":"n-6fea5aff4f44fa54","claim":"hadamard_kernel"}]}