A licence number is not a credential
What a register entry proves, what it does not, and why that gap decides the whole project.
A licence reference is public text printed on websites, email footers and contracts. Reading one proves that the number exists. Quoting one proves nothing, because quoting is free and anyone can do it.
A public register closes a different gap than the one that matters here. It answers whether a licence is current and who holds it. It does not answer whether the person in front of you, or the key signing a document, is that holder.
Levels 0 to 2 of the ladder all live inside that gap. They make the claim permanent, attributable and expensive to contradict. None of them binds the number to the key.
Only the body that issued the licence can close it, by recording a key against a licence and publishing the pair. That is tier C of RVW-5, it is open problem OP-1, and it is the thing that decides whether the rest of this work matters or stays a careful way of being wrong.