Ummmm...I'm thinkin' the tree would have stopped growing when someone made a door out of it.
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The date the wood was cut can’t be determined, IOW, the RC dates of the rings can (at best) be wiggle-matched against any established data (because there’s annual fluctuations in RC production and absorption) — unless there happens to be an outer ring with the bark attached. Then the year the wood was cut can be determined within the appropriate range of error.
A somewhat younger door was found in Greece some years back — it was still being used as a door, but apparently had been borrowed from an older derelict structure, and before that from an earlier derelict, etc, such that the RC date on the wood was (if memory serves) something like 2000 BC. Again, without a bark layer, it’s not possible to know when the wood was cut. :’)