{"id":"e-7403f1e58efb6a95","operation":{"operation":"parent_provers","route":"periodic_product"},"operation_detail":"periodic_product","conclusion_id":"n-a679863398df5985","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":"e0d19c27b2d17cc7189be94e760275449f41dce0f24533efa5a58352ce4362c6","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"parent_provers","certificate_raw_size":630,"certificate_compressed_size":375,"conclusion_name":"Triangle of coefficients in expansion of (14 + x)^n.","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[],"cited_by":[{"node_id":"n-a679863398df5985","claim":"one_signed_coefficients"},{"node_id":"n-a679863398df5985","claim":"hadamard_kernel"},{"node_id":"n-a679863398df5985","claim":"real_rooted"}]}