{"id":"e-c5656743efdffc45","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-108b34f10b7468f4","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":"0f3a55fd6bec37727664bb0c541ec56e30abe3c1c6ba6e877df7669fb314b1d2","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":639,"certificate_compressed_size":383,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*3^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-108b34f10b7468f4","claim":"one_signed_coefficients"},{"node_id":"n-108b34f10b7468f4","claim":"hadamard_kernel"},{"node_id":"n-108b34f10b7468f4","claim":"real_rooted"}]}