
https://en.wikipedia.org/wiki/Bussard_ramjet
Must be theoretically capable of operating indefinitely with no other fuel source required. (e.g. an onboard nuclear reactor or beamed energy.) Must be capable of operating with the existing interstellar medium, no prelaunched fuel required.
Resolves once we're technologically advanced enough to know the answer with high confidence.
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A 2021 study found that, while feasible in principle, the practical construction of a useful Bussard ramjet would be beyond even a civilization of Kardashev type II.
Robert Zubrin and Dana Andrews analyzed one hypothetical version of the Bussard ramjet design in 1988. They determined that their version of the ramjet would be unable to accelerate into the solar wind.
https://en.wikipedia.org/wiki/Bussard_ramjet#Feasibility
Wondering if the question is missing specification: "that can perform some useful task".
This is now a "Kardashev type II before 2199" market.