{"id":"e-5234407c4fbd8679","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-ff0214c333bfdcca","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":"d17552363a39b890feaaaccc930a12082d4c8abd29936a3e1a1cdc5bc7fc10ee","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":630,"certificate_compressed_size":375,"conclusion_name":"Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k).","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-ff0214c333bfdcca","claim":"one_signed_coefficients"},{"node_id":"n-ff0214c333bfdcca","claim":"hadamard_kernel"},{"node_id":"n-ff0214c333bfdcca","claim":"real_rooted"}]}