## Does the paper "Proof of Collatz's Conjecture" by Agelos Kratimenos contain valid proof?

The document "Proof of Collatz's conjecture" (link arXiv) by Agelos Kratimenos was submitted to arXiv a few days ago (4 Nov. 2019).

Is it really a valid proof?

I mean, I know that arXiv is a prestigious newspaper. Do they have peer reviews before an article is accepted? Or are submissions possible without that?

It would be amazing if it was really a proof of Collatz's conjecture.

## Is there a "superior Segal conjecture"?

Segal's conjecture describes the double Spanier-Whitehead $$D Sigma ^ infty_ + BG$$ it's safe $$G$$. Is there a similar description of $$D Sigma ^ infty_ + K (G, n)$$ when $$n geq 2$$ when $$G$$ is finished (and abelian)?

Remarks:

• I would be happy to understand the case of cyclic groups $$G = C_p$$.

• $$K (G, n)$$ can be modeled by an abelian topological group, but I'm not sure that this falls under the guise of other generalizations known to the Segal conjecture, although $$G = mathbb Z$$ and $$n = 2$$ there is a known decomposition (see Ravenel). For $$G = mathbb Z ^ n$$ and $$n = 2$$ there is that too.

• Let me remind you that Segal's conjecture (proven by Carlsson) says that when $$G$$ is finished, the double Spanier-Whitehead $$D Sigma ^ infty_ + BG$$ is a certain completion of $$vee _ {(H) subseteq G} Sigma ^ infty_ + BW_G (H)$$ or $$(H) subseteq G$$ ranges on subgroup conjugation classes and $$W_G (H) = N_G (H) / H$$ is the Weyl group of $$H$$ in $$G$$. In particular, when $$G = C_p$$ he says that

$$D Sigma ^ infty_ + BC_p = mathbb S vee ( Sigma ^ infty_ + BC_p) ^ { coin} _p$$

or $$mathbb S$$ is the spectrum of the sphere (corresponding to the subgroup $$C_p subseteq C_p$$; the other term is the trivial subgroup $$0 subseteq C_p$$) and $$(-) ^ wedge_p$$ is $$p$$-completion.