{"id":"e-896c34b831f8e9e4","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-4e096b5929fd3f2e","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":"174021893713f53dc9efd751e76061d91e240c7969192bf499bbb551f0f553ce","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":630,"certificate_compressed_size":375,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*9^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-4e096b5929fd3f2e","claim":"one_signed_coefficients"},{"node_id":"n-4e096b5929fd3f2e","claim":"hadamard_kernel"},{"node_id":"n-4e096b5929fd3f2e","claim":"real_rooted"}]}