Rights to privacy are not imaginary. We purposely don't discuss a user's moderation history without their permission. Since you have given that permission, we can provide more details about moderation of your post in the thread in question, although we don't have similar permission from other users who participated in the thread.
We're repeating our explanations here, but you've asked essentially the same questions several times, and don't seem to appreciate that moderation is based on the documented form rules, applied to every post, and that everyone is responsible for their own posts, no matter what anyone else posts.
You and other users were participating in a debate about hardware. The debate was within the rules, but you were given a temporary suspension for calling another user a liar. Under the rules, posts can dispute what others say, but not call other users names or belittle their character. The violation was rather minor, and it was treated seriously only because it was the 11th case of personal insults or trolling on your record, and moderation actions escalate with repeated rule violations.
I’m not asking what would make it obvious to the other user. The other user had 5 relies from me and didn’t once acknowledge them - he just kept posting the same blatantly false claims.
If you had asked the user to provide sources, and the other user had not provided them, and you had reported the original claim and your request, the moderators would have been able to apply rule #1, as explained above. Since you didn't do these things, the rule didn't apply and wasn't considered.
im asking what it takes to make moderators understand that a user is posting disputed claims and take action on it, rather than penalising someone for saying “stop lying” when they post the same false claim over and over.
You reported that a user was making disputed claims, so the moderators knew that was your opinion. However, that's not against the rules. When you used name-calling, that had nothing to do with disputed claims, just the name-calling. It was not appropriate to look to the moderators to take your side in a technical debate.
Are you saying it’s unreasonable for me to expect a moderator would see that, and actually look at the posts the other party had been making?
The moderators look at every reported post, to see if it breaks the rules, and they often look at neighboring posts and posts quoted by a reported post, to get some context or check if others had broken rules. So it's reasonable to expect that a moderator would see other posts, including ones in your technical debate.
if you want to call “stop lying” a troll I’m not going to waste my time arguing how ridiculous it is - I’m asking why the repeated false claims that the moderator must be aware of are not deemed to break both rule 1 and 2.
False claims can be challenged by other users in a thread. The moderators are not tasked with determining what's true, even when they see posts that others (like you) claim are false. That's the case even if the moderators have personal opinions about the subject of the debate. They keep their opinions to themselves and stick to enforcing the forum rules.
See the post above for when the rule against repeatedly making the same post applies.
To clarify: I don’t have any ****s to give about being suspended.
The reason that moderators don't ban users for a first offense is to give them reminders and short suspensions as warnings that the rules will be enforced. If you don't care about suspensions, and are therefore not heeding these warnings, then further violations of the rules will likely get you banned. When users violate rules repeatedly and end up banned, they often complain that the very last violation wasn't ban-worthy, but it's the accumulation of problems that produces bans.
im asking what it takes to make moderators understand that a user is posting disputed claims and take action on it, rather than penalising someone for saying “stop lying” when they post the same false claim over and over.
The moderators didn't choose to either (A) stop a user from posting disputed claims or (B) penalize you for name-calling, as if it had to be one or the other (choosing sides). They evaluate each user's posts on their own merits. In this case, the other user's posts didn't break the rules and yours did.
if you want to call “stop lying” a troll I’m not going to waste my time arguing how ridiculous it is - I’m asking why the repeated false claims that the moderator must be aware of are not deemed to break both rule 1 and 2.
Rule #1 applies to users who fail to provide evidence of a claim after being asked to provide it. That didn't occur in this case. Asking a user to provide citations, links, etc. is not the same as simply telling them that their claim is wrong. Rule #2 applies as explained above, but since you're talking about the posts of another user we can't provide details about any moderation applied to that user without their permission.
I’m asking about why false and deliberately misleading statements are simply ignored.
The statements were not ignored. You brought them to the attention of the moderators, and expected them to decide that the claims were false (which is beyond the scope of their job) and then remove the posts (despite their not breaking the rules).