Demonstrate in a laboratory the triple-alpha fusion process, yielding carbon-12. This seems difficult bordering on impossible. Maybe Farnsworth fusor.
This is, anthropically, the most important nuclear reaction in the universe.
Ironically, getting the ionized helium nuclei needed as input is extremely easy: alpha particle.
Vaguely inspired by the 21 cm hydrogen line , which is very common astronomically but had never been observed in the lab and even initially seemed impossible to see in a lab because of the rarity of the "forbidden" atomic transition. However, hydrogen masers have since replicated astronomical observations.
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