The page says
reply> Anubis uses a Proof-of-Work scheme in the vein of Hashcash
And if you look up Hashcash on Wikipedia you get https://en.wikipedia.org/wiki/Hashcash which explains how Hashcash works in a fairly straightforward manner (unlike most math pages).
Oh fun so now we're effectively draining users' phone and laptop batteries now just to prove that they have batteries and somehow that's a proxy for them being human
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