{"id":"e-f0c12876ab8620d1","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-9e472291b944d56e","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":"6140b7c0ae411373dc575f8f4fa98a64f34c0a4f85f42a873d5714118db018e9","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":631,"certificate_compressed_size":376,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*12^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-9e472291b944d56e","claim":"one_signed_coefficients"},{"node_id":"n-9e472291b944d56e","claim":"hadamard_kernel"},{"node_id":"n-9e472291b944d56e","claim":"real_rooted"}]}