How do you know if your hypothesis has proven?

If you have over 50% of visitors signing up, you're on to something (there's definitely a pain, and it looks like you may have figured out a solution).

If you have less than 5% of visitors signing up, the pain may not be that strong, and / or your solution isn't what people think they need.

It will likely be somewhere in between, which means your hypothesis isn't conclusive. This doesn't mean you don't have a valid startup concept - it just means that its unclear that there's a market already aware they need your product.

If it's higher than 10% conversion, consider iterating on your messaging - describing the pain and even try some other solutions to the problem (different than your initial idea for a product). This is an opportunity to learn what people think they want BEFORE you've spent months developing a product.