{"id":"e-c09624445104be48","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-e655e253465c7aff","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":"b64c806b8c93819c02b090c6e2c26edf3b59e0080aaadd14048072a71be56ffa","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":655,"certificate_compressed_size":383,"conclusion_name":"veronese parent of Binomial coefficients C(n,k) with n-k odd, read by rows.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-e655e253465c7aff","claim":"real_rooted"},{"node_id":"n-e655e253465c7aff","claim":"one_signed_coefficients"},{"node_id":"n-e655e253465c7aff","claim":"hadamard_kernel"}]}