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However, if RDTS doubles down on their minority chaintip
I think the if is hardcoded to a block height / flag day, so this is not a question of if or even when anymore. It's a question of "what now"?
invalidating the first block of that branch
The one that applies to forking rules, yes.
I just re-read #5316 - must have been 11 years since I read that ugh - and now I think I'm confused about the mechanism. I remember that at one point the consensus was that invalidateblock would tag a block to lose to a competing block of lower weight, but now I am uncertain of where I read that.
A checkpoint is a commitment to a specific block,
invalidateblockrules out a specific block. Is it that what you mean?However, if RDTS doubles down on their minority chaintip, invalidating the first block of that branch in the chain makes your node consider all descending blocks invalid, too.