>fails to understand the gumbel softmax technique

I think in this case it doesn't help that there are multiple watermarking schemes, and the easiest for people to understand is the red/green scheme by Kirchenbauer et al. (https://arxiv.org/pdf/2301.10226), which does technically distort the logits (but I'd argue only in cases where you wouldn't notice it anyway).

I wasn't aware of this gumbel softmax scheme, it seems you're referring to https://simons.berkeley.edu/talks/scott-aaronson-ut-austin-o... ? That's really clever as it doesn't even distort the logits, basically cryptographically indistinguishable from a "real" random sample unless you have the key.

The actual scheme Claude uses seems to be neither of those two though, they say it is SynthId-text which seems to be tournament sampling based.