The highness–tracing correspondence for computable limit ordinals

Let $\alpha$ be a computable limit ordinal, possibly with additional closure properties such as closure under addition. For an oracle $A$, let $\operatorname{High}(\text{\rm \textsf{MLR}},\alpha-\text{\rm \textsf{Demuth}})$ denote the class of oracles that make every Martin-Löf random real $\alpha$-Demuth random, and let $A$ be $\alpha$-c.a. tracing when it traces every $\alpha$-c.a. function with the corresponding $A$-c.e. bounds. The highness–tracing conjecture.

$$A\in\operatorname{High}(\text{\rm \textsf{MLR}},\alpha-\text{\rm \textsf{Demuth}})\quad\Longleftrightarrow\quad A\text{ is }\alpha\text{-c.a. tracing}.$$

This is proposed as an extension of the known correspondences between highness for pairs of randomness notions and tracing properties, including the cases of $\omega$-c.a. tracing and $\Delta^0_2$ tracing. The required closure properties of $\alpha$ and the equivalence in this intermediate setting are not established here.