Do you have an approach in mind?
Alas, no. Perhaps it is impossible for someone who has a halting oracle to convince someone without a halting oracle that they have a halting oracle, even in universes whose physics allows halting oracles.
Alas, no. Perhaps it is impossible for someone who has a halting oracle to convince someone without a halting oracle that they have a halting oracle, even in universes whose physics allows halting oracles.