{"id":"e-249b7eaa76a03e97","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-39194b37db596ae8","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":"436744f60cc84ecf31a8c182daf4c398f85a9603e100d241d686b9c53036220c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":625,"certificate_compressed_size":370,"conclusion_name":"a(n) = 1 if n is a triangular number, otherwise 0.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-39194b37db596ae8","claim":"real_rooted"},{"node_id":"n-39194b37db596ae8","claim":"one_signed_coefficients"},{"node_id":"n-39194b37db596ae8","claim":"hadamard_kernel"}]}