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Continuation question about nonce randomness and verification of the randomness by signing parties

Original: Can a signer recover their own signature's nonce `k`? Note that under normal circumstances it is infeasible to randomly generate the same nonce, so either a non-random nonce has to have ...
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Random Number In R Value , what is it actually, is it the same as Nonce in the blocks

I wonder about the random number in R value ... if i am right , the R value is First part of the script signature which is combined of two parts (r,s) r = Gk (elliptic curve scalar multiplication) Or ...