Question about possible issues in GPATH documentation (expressions for s and z)

[lyndonlsmeng]

Dear PLUMED developers and users,

I am writing to ask about a possible issue in the GPATH documentation, specifically in the page:
https://www.plumed.org/doc-master/user-doc/html/GPATH/
It seems that the expressions for s and z in this documentation may not be correct.

For s:
The formula in the documentation appears to differ from the one given in the reference:
G. Díaz Leines and B. Ensing, "Path Finding on High-Dimensional Free Energy Landscapes", Physical Review Letters 109 (2012).
Path Finding on High-Dimensional Free Energy Landscapes | Phys. Rev. Lett.
and the derivation of the path collective variable can be found in:
SuppInfo.pdf
From the theoretical point of view, it seems unlikely that the correct result can be obtained using only two points (as in the documentation) on the circle.

For z:
The formula seems to have a similar issue, a v3 was write as v2 .
Additionally, there may be a dimensional inconsistency: it looks like there could be an extra square under the square root.

I want to ensure:
Are these discrepancies only an issue in the documentation, or are they also present in the actual source code of PLUMED?

Thank you so much for your help!