{"id":"e-71e0b3707c4ee7db","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-01cea33b6485d9cc","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":"ac8ae88f5cfaa6b2a130c2e0f03b9ae0f5f7b2dcc51a1666d5ae6181313de48b","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":629,"certificate_compressed_size":375,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*2^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-01cea33b6485d9cc","claim":"one_signed_coefficients"},{"node_id":"n-01cea33b6485d9cc","claim":"hadamard_kernel"},{"node_id":"n-01cea33b6485d9cc","claim":"real_rooted"}]}