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New wood grows from the cambium layer between the old wood and the bark.
In the spring, when moisture is plentiful, the tree devotes its energy to producing new growth cells.
The contrast between these smaller old cells and next year's larger new cells is enough to establish a ring, thus making counting possible.
So the carbon ‘date’ is used to constrain just which match is acceptable.
Consequently, the calibration is a circular process and the tree ring chronology extension is also a circular process that is dependent on assumptions about the carbon dating system.
There are many points in a given sequence where a sequence from a new piece of wood matches well (note that even two trees growing next to each other will not have recognized that ring pattern matches are not unique.
The best match (using statistical tests) is often rejected in favour of a less exact match because the best match is deemed to be ‘incorrect’ (particularly if it is too far away from the carbon-14 ‘age’).
It is clear that dendrochronology is not a clear-cut, objective dating method despite the extravagant claims of some of its advocates.