The links in this post seem to be broken, but I wanted to add my two cents on the topic because I'm really curious about it myself...
When it comes to notating inversions with roman numerals, there seem to be no modern standard. The standard you will find in books (mostly classical music) derives from basso continuo (figured bass) notation in which a first inversion triad is a 6 chord, a second inversion triad is a 64 chord, and for 7th chords is all different - 7 65, 43, and 2.
I believe this convention is probably too old for modern practice, where you have a lot of possible "dissonances" / "tensions" in chords. For example - in Jazz a 6 chord or a 6/9 chord means something else entirely.
In Jazz Chord Symbols, a slash is used to denote the bass note. C/G would be C in second inversion (i.e. G on the bass). I've seen a couple of people (including myself) trying to adapt this approach a key-neutral tonal analysis (i.e. roman numerals) in various way.
The two ways I've encountered this being done (including the one mentioned in the post are:
a) You use an Arabic numeral to denote the degree of the chord in quesion after a slash. So V/3 in C major is G/B.
b) You use an Arabic numeral to denote the degree of the key in question. So V/7 in C major would be G/B. (Which I believe is the case in this post).
I have not encountered it a lot, but from what I've seen so far, it seems like option a is more popular.
However, I tend to agree option b because of a couple of reasons:
- It is more similar to Jazz chords, and easier to translate. To translate V/7 I need to find two scale degrees: V -> G, 7 -> B. With the other approach, You need to figure out the root key, and THEN the bass note.
- It is easier to see bass motion: I V/7 vi. The bass motion is clearly 1 7 6, so you can see it's step wise. With I V/3 vi is harder to see that kind of motion.
Auditory-wise, I feel like that I/3 and V/7, despite being the same chord type, have drastically different sounds, so it does not justify using the same symbol to show that it's the same "chord type".
This is the system I've used on OpenEar