The pdf at [0] clearly says that while they believe it could not be made without "high-precision modern machinery", that is only a belief. They are aware of that flaw writing:
"To address the question of whether or not such manufacturing accuracy is possible by hand, we will need to expand the analysis to include both modern and ancient objects that are known to have been hand-made."
I read [2]. It comes across as post-hoc numerology - looking for patterns on the assumption they are present. It is also missing a way to perform the same analysis on other objects - are all such vessels using R(n)? Can you find similar patterns in "ancient objects that are known to have been hand-made"?
There's also a complete lack of discussion of known archeology. With a bit of searching I found a picture of an Egyptian making stone vases by hand ca. 1504–1425 B.C at https://academic.oup.com/occmed/article/72/9/595/6966500?log... .
"Ahh, but the object scanned is from pre-dynastic or early dynastic Egypt more than a thousand years previous" I imagine you saying.
Digging some more I found "Artists and Patrons in Predynastic and Early Dynastic Egypt" at https://www.jstor.org/stable/44325730?seq=8
> The first assemblage to my mind unquestionably connected with [stone-working] is not funerary; Room 12 in House Group 89 in the early Old Kingdom town at Hierakonpolis was a vasegrinder's workshop. Quibell and Green found one quartzite and two sandstone drills, as well as the benches and stands used by the cutters and the remains of their abrasives
It cites page 17 of https://archive.org/details/hierakonpolis00petrgoog/page/n26... under the section "Vase Grinder's Workshop".
> Round the room ran a bench of beaten earth 0.8 m. (2½ feet) above the floor. This bench projects considerably in the W. angle and to a lesser degree in the S. angle. The upper parts of these projections have cup-like hollows in which were vase borers such as are shown on Pl. LXII. That marked .1. was of chert. It stood with working surface upwards in the depression in the bench ; under it was a quantity of sand that had been used as the abrading material. On the top of the borer were two rough pieces of chert. Near to it (marked 2) was an oblong corn grinder. The borer marked 3 on the drawing was of diorite. Both sides had been used as working surfaces. Little or no sand was found in the socket or depression in the bench.
> From the fact of the bench being 0.8 m. above the floor, it seems as if the workmen must have stood to their task ; the squatting position is, however, that represented on the reliefs, when the operation of vase making is represented.
Why can we find a room where stone vase grinders worked, and depictions of them making vases by hand, if at that time they had access to machine-made vases?
Given there were clearly hand-made stone vases, what are the odds that the first vase analyzed happens to be machine made?
How do you distinguish between hand-made and machine-made vases?