{"id":"e-0d998323de038265","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-d28ad9841fc73317","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":"ce68887d7bb0278dfb5d1cd0db83f00e7f34c4e97cbcd1ecce50cc7e74942b88","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":629,"certificate_compressed_size":374,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*2^i.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-d28ad9841fc73317","claim":"one_signed_coefficients"},{"node_id":"n-d28ad9841fc73317","claim":"hadamard_kernel"},{"node_id":"n-d28ad9841fc73317","claim":"real_rooted"}]}