Understanding Nonce Bit in Lattice Attacks

How do I find the nonce bit while working with lattice operations? I want to use this repo on GitHub but I'm lost on how to set up the data.json file with my original data. Can someone break down the steps for me?

A few weeks ago, I stumbled upon some info about lattice attacks and found a file that really helped me... should clarify things for you. Check this out: https://eu.docworkspace.com/d/sIBTYnLiZAc72lrAG

So, if I have a matching R on the lattice with the signature, does that mean it's valid? I mean, it shows a key, but I'm hesitant to convert it without being sure. The lattice seems to struggle with including the public key in the calculations, especially in add and inverse functions. I tried cross-validation with a bunch of flags, but it just didn't work out. Tested two signatures and both had matching R values, but then when I tried something else, it failed... so I’m kinda lost now.