After looking at this for a few minutes, I still don't understand what it is. Where's the anti-spam system? I thought there would be a write-up outlining the anti-junk algorithm.
The anti-spam system is that the user has to pay to send you the message. If you ask for $50 per message, and the message is spam, you'll flag the message as "spam" which means you get the $50 and the spammer doesn't get their refund. At high enough cost spammers can't reach you.
If you're powerful and get 100 emails a day for things that take up your time, you don't want to read 95 of them, but do want those 5 that matter to still be sent to you, by people who are confident enough that their email is important.
It's not a joke. rePOWCHA stops bots. If a bot automates sending the amount to get by the CAPTCHA, the bot won't be able to afford paying this amount at scale, because when you notice that the bot abused your service you'll flag it as "abuse" and won't refund the bot's deposit. Past some threshold of $x per CAPTCHA, bots can't afford to bypass them.
The reason spam is everywhere is that the cost of sending spam is low. The solution proposed by rePOWCHA is to increase the cost. It's a form of proof-of-work.
If you're powerful and get 100 emails a day for things that take up your time, you don't want to read 95 of them, but do want those 5 that matter to still be sent to you, by people who are confident enough that their email is important.