{"id":"e-399c4cc80f25ee4f","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-b7cf68162d40a956","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":"6881a416154e4c63cd6947811af67b977a3364b169469ee3003e96397eb60130","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":630,"certificate_compressed_size":373,"conclusion_name":"Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*11^j.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-b7cf68162d40a956","claim":"hadamard_kernel"},{"node_id":"n-b7cf68162d40a956","claim":"real_rooted"},{"node_id":"n-b7cf68162d40a956","claim":"one_signed_coefficients"}]}