-ing forms after a comma: reduced participle phrase or gerund?

Question

In sentences like "the results show x, leading researchers to believe..." or "..., indicating that further research must be done" or "..., proving the validity of the theory..." etc

is the -ing form after the comma a reduced form of "which is leading/indicating/proving" or is it a gerund? It seems like it shouldn't be a gerund because the rest of the sentence feels like a complement to some kind of verb phrase, but saying "which is +-ing" sounds so unnatural.

I work at an academic language support service and a student asked me why the -ing form is so prevalent after commas and what the reason is for putting it there.

It feels like those -ing forms are almost adverbial, but I'm not really sure.

Answer 1

You have there examples of a participle phrase or present-participle phrase. This type of participle phrase typically acts as an adjective, modifying the subject of the main clause it is attached to (this is even clearer if you put the participle phrase first in the sentence, which puts it next to the subject without altering the meaning).

source: grammar.com