The paper is full of basic errors, misreadings, and fallacies.

1. "The claim P1 is circular since the first sentence of the quote already supposes that the system is ε-safe; if the system is ε-safe then it is ε-safe".

The authors unfortunately seem to have misread the statement entirely. What the original statement in the paper is saying, is that if you suppose that the system has been properly parametrized (the variables k, alpha, f, beta, etc), then the failure probability is less than ε. It's not saying that if the system is already safe, then it's safe, which would — in fact — be circular reasoning. In PBFT terms, for example, it's the same as saying the following:

Suppose that we set minimum quorum intersection at 2/3n + 1, and f < 1/3n. Then the system has a failure probability of zero.

Could a better wording than the paper's original statement of "Let the system be parametrized for an ε-safety failure under a maximum expected f number of adversarial nodes"? Likely, but it is still a misreading. The authors seem to be incentivized maliciously, and the authors are likely using this strategy for grabbing attention on social media.

2. "P2 claims that the protocols terminate with positive probability within a finite time. This a just the minimal condition of any protocol; if a protocol does never converge in finite time it is of no use. A result meaningful and worth to be published would be that the protocols terminate within O(logn) rounds with probability at least 1−ε. Such a statement is, however, in general wrong for the Snow protocols."

This is unfortunately another set of authors misunderstanding that this is in regards to the leaderless version of the Snow family. The paper provides a tight bound if f < sqrt(n). This is thanks to the CTL, which gives a really nice closed form expression. If the author requires the full expression, it is also written in the original Avalanche paper, which gives the authors the explicit DTCM formula for expected time to convergence. Unfortunately, that formula is also very large, and has really poor (if at all) closed-form expressions. However, anyone can immediately calculate the precise extinction time under linear adversarial presence etc if they so choose.

Returning to the main point: this only applies to the leaderless version of Snow protocols. People have written about liveness in Avalanche before entirely missing the point that Avalanche is a simple instantiation and the Snow family is entirely customizable. If you want to boost up liveness, no problem, introduce a tie-break mechanism. The most popular of such mechanisms is a leader. Then you can get up to n/3 Byzantine presence in effectively constant number of rounds.

Section 6

The author's set of claims in regards to falsification/conscious manipulation of statistical results falls short when very clearly we label and number all axes. Every graph has a legend, proper titles, and proper numerical and symbolic labeling of all axes in each graph. The author also makes introductory-level algebraic mistakes, such as confusing a negative exponent for a negative number:

The author claims that the right graph has negative number of rounds in the y-axis, when it's just a fractional value.

We recommend the author also do some reading on how a system designer can tradeoff liveness vs. safety: https://medium.com/p/46125eb4e7e1