Neusis construction of the 11-gon?

Question

Wikipedia tells me that the 11-gon was found to be neusis constructible in 2014, and the link given doesn't seem to be a crank, but the actual method is behind a paywall. (Interestingly, the page itself states positively that the 41-gon and 61-gon are not neusis constructible, which I would think would follow.) While looking for more details, I stumbled upon these lecture notes that purport to prove that any neusis-constructible length can be found in a Galois extension of $\Bbb Q$ of dimension $2^a3^b$, which would seemingly preclude the edge of an 11-gon. So I was just wondering, who is right? If the lecture notes linked are wrong, where are they wrong? If the lecture notes are right, how did the error in Benjamin and Snyder get to such a high level, and if anyone is familiar with their work, what was it?

Answer 1

You can find some good slides of one of the author about this here

My understanding is this:

Unmarked ruler - usual theory, only some extensions of degree $2^n$ can be done.

Marked Ruler but **only allowed to use marks on lines **, only some extensions of degree $2^n3^m$ can be done.

But, if one allows the use of the marks between circles, or between a line and a circle, more is possible.

I think they prove that with marks allowed between a lines or between a line and a circle (but not between two circles) they can do a construction if and only if the intermediate degrees are up to degree 6. That means that some extensions of the form $2^n3^m5^k$ are doable.