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The barrel is most certainly not a serialized component.
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To my knowledge, it has never been clarified by the ATF if the "upper receiver" of an AR type firearm would be acceptable for the markings other than the serial number.
The barrel and serialized lower receiver are unambiguously acceptable.
The law defines the term "firearm frame or receiver" as "That part of a firearm which provides housing for the hammer, bolt or breechblock, and firing mechanism, and which is usually threaded at its forward portion to receive the barrel" (27 CFR § 478.11)
While either "receiver" of an AR type could meet that definition, the law is also generally precise in its wording that if it says "that part" then that means one and only one part can be considered the receiver under the legal definition. That being the case, the AR lower receiver has been defined as the "receiver" and I, personally, wouldn't want to be the test case for putting required markings on the AR upper receiver, if it ever came up.