This doesn't match my experience, and no dictionary I've checked says the past participle depends on the context; only that "proven" and "proved" can both be used (in any context). See e.g. https://en.wiktionary.org/wiki/proven#Verb

I'm not a mathematician though, so maybe this is a genuine semantic convention that neither I nor my dictionary are aware of. Maybe it's just that some mathematical style guides say to prefer "proved", for consistency, not that it really depends on the context?