A K-trivial set which is not jump traceable at certain orders

We construct a K  -trivial c.e. set which is not jump traceable at any order in o(logx).

► There is a K  -trivial set which is not jump traceable at any o(logn) order.
► The construction applies to all orders satisfying a certain summability property.
► The construction relies on the additive cost function characterization of K-triviality.