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You could put this captcha in a location that wouldn't be very visible for a human, but if the LLM is looking at the HTML he would find this form.

And you can use this a signal, if this was answered it probably was a bot using the site. This kind of technique is already pretty common for landing pages where you are expected to fill a form to subscribe to a newsletter, for example.

Does hiding things from humans with display:none or visibility:0 work against bots. Don’t they look at the styling? Even stacked elements should be discernible.

If something is not NOT human, then it is human. :)

Ha! So basically to get in to a site protected by it, you need to _fail_ the HATCHA.

irrefutable logic

It might be useful if you wanted a bot to access something but not someone passing by casually. You could use it to store information. It wouldn't be encrypted exactly...