In an ideal world the combination of genus and specific epithet should map to one concept.
That world doesn't exist, as long as taxonomists will declare one name to be a heterotypic synonym of another.
The type specimen of the name "Centropyge fisheri" was collected in Hawaii.
The type specimen of the name "Centropyge flavicauda" was collected at Macclesfield Banks, China Sea.
Some treatments regard these as distinct species. Some regard them as synonyms. The name with priority is C. fisheri.
Thus, the combination of genus and specific epithet "Centropyge fisheri" can therefore refer to at least two different concepts: one (sensu stricto) is the set of organisms in Hawaii; the other (sensu lato) is the set of organisms in Hawaii and the China Sea (and places in-between).
As long as there are heterotypic synonyms in the world (i.e., as long as taxonomists disagree...), there ideal world will never exist.
And, of course, this doesn't even take into account homonyms.
I believe that was Linnaeus's original intent.
Only because he was a creationist.
Unfortunately the current system seems to have strayed from this original
goal.
Only because taxonomists insist on believing in evolution, and have differing opinions about how best to apply names to aggregations of organisms in nature (lumpers v. splitters).
The GNI needs some additional parts to make sense of these. I will leave it to others to describe those additional parts.
I assume you mean GNUB? Or something else?
"Valid" names would include properly formed synonyms so Felis concolor would return Felis concolor Linnaeus 1771.
Careful with the use of the word "valid". It means two entirely different things to botaniststs and zoologists, and neither of them mean it in the same way you are using it.
Aloha, Rich