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I couldn't find any general explanations about TIPS adjustment, but here's a place to explore what is happening with specific TIPS:

As best I can figure out, the adjustments seem to be made daily, and they now have numbers through February, using December data. What I don't know if what the starting CPI-U is, since it can't be the day of issue (data is behind). At any rate, with TIPS we aren't dealing with 6-month periods for the inflation adjustment to principal (I think). Presumably, previously 6-months does apply for coupon payments (i.e., the new principal on which the coupon payment is made is the 6-month adjustment).
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