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.

number theory – solving two variables for n related to Collatz's conjecture

For this code, for each x, I want to solve all ranges of values ​​for c1 and c2 in a limited range, ie. C1 and c2 in the range of real numbers + -100 for c1 and c2 for each x, which gives "Length (stepsForEachN) == nRangeToCheck – 1". Here is the code up to now, I'm not sure how to solve both variables c1 and c2 for each x:

(*stepsForEachN output is A006577={1,7,2,5,8,16,3,19} if c1=c2=1*)
c1 = 1; 
c2 = 1;
nRangeToCheck = 10;
stepsForEachNwithIndex = {};
stepsForEachN = {};
stepsForEachNIndex = {};
maxStepsToCheck = 10000;

c1ValuesForEachN = {};

For(x = 2, x <= nRangeToCheck, x++,

 n = x;

 For(i = 1, i <= maxStepsToCheck, i++,
  If(EvenQ(n), n = Floor((n/2)*c1),
   If(OddQ(n), n = Floor((3*n + 1)*c2))

  If(n < 1.9,
   AppendTo(stepsForEachN, i);
   AppendTo(stepsForEachNIndex, x);
   AppendTo(stepsForEachNwithIndex, {x, i});
   i = maxStepsToCheck + 1
Length(stepsForEachN) == nRangeToCheck - 1

Fourier Analysis – Explicit Limits of Tao's Result on Collatz's Conjecture

A new pre-print of Terry Tao has been published recently and has yielded interesting results on the topic of Collatz's conjecture. I will not cite the precise result, but rather an equivalent formulation that Tao notes in his remark 1.4:

For all $ delta> $ 0 there is a constant $ C_ delta $ such as $ mathrm {Col_ {min}} (N) leq C_ delta $ for everyone $ N $ in a subset of $ mathbb N + 1 $ at least logarithmic density $ 1- delta $.

My question is something about the growth rate of $ C_ delta $ as $ delta to 0 $. I will ask two specific questions in this regard. The first, I imagine, could have been known before the recent Tao result.

Are there values ​​of $ delta <1 $ for which a explicit upper limit for $ C_ delta $ is known?

The second essentially asks if something explicit can be deduced from the result of Tao.

Is the function $ N mapsto C_ {1 / N} $ Upper bound by a computable function?

(Note that I do not think the answer is "obviously yes" to the mere existence of $ C_ delta $since the control of the operation of a particular value seems to be $ Sigma ^ 0_3 $ (it exists $ N_0 $ as for all $ N> N_0 $ it exists $ M $ as in $ M $ not at least $ 1- delta $ numbers below $ N $ to go downstairs $ C_ delta $) and is obviously not lower)

A new way to look at Collatz's conjecture

Firstly, it is not a proof, but a new way of looking at Collatz (which other mathematicians, hopefully, will be able to prove / counter-test). I came here to find out if what I found is valid.

Trial: (If the formulas do not appear, please download and open in Microsoft Word)

Python files:

PS I am really sorry about the way the test is informal (I do not have experience in formal writing for mathematics) and I know that it seems hasty and that I'm I could have made more generalizations, but the reason why I shared it so quickly is I believe that other mathematicians larger and more experienced than me (who are not mathematicians) can benefit from it. Plus, I know the code is not so good (and I'm sorry, I just started programming last month and my "rush" code is not so good).