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Question: is there a way i can make sure that my broadcast transaction in the mempool won't be replaced by anybody? (someone may have the same private key i have)
Or is it still a race like you said?
There's no way to do that.
Take note that there's no single Bitcoin mempool, each node has their own mempool.
So since each node has their own mempool, they have the control to accept the replacement or not.
In a scenario when someone broadcast a replacement to your transaction with priority fee,
it a matter of which will propagate to reach a miners mempool that could get it included to the next block.
BTW, question like this deserves a new topic since it's not related to the topic,
If the main reason is you want to reach a certain user, you may use @username to mention them, most users respond to that.