{"id":"e-cb24020f7808d9ac","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-a6a633b989da1879","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":"9346e1856a97a48048b7936abe125ab6b19705a512d426375653f0d8e823cd8b","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":629,"certificate_compressed_size":376,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*5^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-a6a633b989da1879","claim":"one_signed_coefficients"},{"node_id":"n-a6a633b989da1879","claim":"hadamard_kernel"},{"node_id":"n-a6a633b989da1879","claim":"real_rooted"}]}