I can't understand how it is possible that when such ceasefires are agreed there isn't a designated third party who has the signatures of both parties and can say, and prove, if it's been violated.

There is a designated third party Pakistan and they say Lebanon is part of the ceasefire.

They say it, but can they prove it? Because everyone seems to be saying a different thing. Shouldn't Pakistan be able to say "this is the document, these are the terms, these are the signatures, case closed"?

Pakistan are the mediators, why would they lie about the explicit terms of the agreement? They would immediately loose all trust if they did.

I'm not saying they're lying, I am just wondering why they don't seem to have a definitive proof of what they say- they say one thing and the US "disagrees"- why can't any of the parties just show the fucking document?

So if both sides do not agree to that request it’s not part of the ceasefire, pretty simple.

If both sides don't agree on the terms of a ceasefire you don't have a ceasefire.

1. The version of the ceasefire that you are got third hand from Twitter or American news outlets are not accurate.

2. Iranians can't read.

Which do you think is more likely?

Most likely not. I've seen Iranian sources claim that the 10 point plan is violated[1]. However I (1) do not know about Iran's government structure and (2) I can only trust other sources that I believe are trustworthy.

However I think assuming that Israel violating the ceasefire (as they have done multiple times in the past) is more reasonable than assuming a country with a ~400B GDP (similar to Hong Kong, Portugal) has leaders that "can't read".

[1] https://x.com/mb_ghalibaf/status/2041943537386958858