{"id":"e-38b35fa9e37eb25d","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-cfc5b48d32898a3e","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":"ac5692ca100d77a482d58391e63b2a7204c24940416d3777d5a31e2eb6e23fdc","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":643,"certificate_compressed_size":384,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*9^(i-j)*11^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-cfc5b48d32898a3e","claim":"one_signed_coefficients"},{"node_id":"n-cfc5b48d32898a3e","claim":"hadamard_kernel"},{"node_id":"n-cfc5b48d32898a3e","claim":"real_rooted"}]}