EUV was "invented" (demonstrated) in Japan first, though those US labs did a lot of work on the overall lithography system and reflective optics to put it into practice. The US DOE along with the manufacturers made a consortium (EUV LLC consortium) to commercialize/scale that Japanese technology because they could obviously see the promise, and Cymer is a member, as was ASML already via SVG.

Simultaneously Japan created its own initiative (EUVA), and Gigaphoton didn't rely upon the US initiative at all. And again in an alternate universe -- one where Japan isn't protectionist and Cymer wasn't out of financial runway and desperate -- we'd be talking about how ASML is really Japanese tech, etc.