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You can get verification from CMP if you want. There is a $25 search fee whether they find it or not (they will). However, and in my opinion, I don't think it's necessasry. Your rifle is a rebuild which most are today. The only thing a CMP letter will show is that they sold it because there won't be any other provenance regarding originality or "correctness." It's not a "Collector" or "Correct Grade" rifle.
It really doesn't matter where it came from unless you are curious, the rifle stands on its own for what it is regardless.
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If you send their research division a check for $25, the will check their records. If they find any record of it, they will send you a letter on CMP letterhead stating when it was sold and the grade it was when sold.