> Yes but that doesn't answer the question of how they got so close to nvidia.

Talent pool and market conditions. China was already cultivating a talent pool for decades, with limited success. But it had no market. Nobody, including Chinese, wanted to buy Chinese stuff. Without customers, they lacked practice to further develop their qualities. The sanctions gave them a captive market. That allowed them to get more practice to get better.

> But why wouldn't the west discover that same branch but now for EUV?

DUV and EUV are very different. They will have different branches. The point however is not whether the west can reach valuable branches or not. It's that western commentators have a tendency to paint Chinese efforts as futile, a dead end. For the Chinese, this is about survival. This is why western commentators keep being surprised by Chinese progress: they expected the Chinese to achieve nothing. From the Chinese perspective, any progress is better than none, but no progress is ever enough.