The computable-subfield characterization of random infinite extensions

Let $K$ be an infinite extension of ${\mathbb Q}$ with no computable subfields of infinite degree over ${\mathbb Q}$.

Computable-subfield characterization. Then $K$ is random.

This conjecture proposes a characterization of random infinite extensions of ${\mathbb Q}$ through the absence of computable subfields of infinite degree. The supplied text does not establish the claim or indicate whether it is resolved.