If an LPR travels IN and OUT of USA at every 180th day during the 2 year reentry period, does that preserve continuous residency?
There is no such thing as a two year reentry period. You can obtain a reentry permit that allows you to remain outside the US for up to two years under certain circumstances. It is not necessary to return every 180 days if you have that permit. If you don't have that permit, you can return every 180 days, but after the 2nd or 3rd time a CBP officer may decide to revoke your green card because you do not actually reside in the U.S. You should consult with an immigration lawyer to make sure you understand this very important area of law before you lose your green card.
It sounds like your are interested in Naturalization. There are many other factors to preserving residency than just your physical presence in the US. The 6 months you are suggesting is the general presumption of continuous residency where someone is abroad so long as they return within the 6 months. This is just one factor of many that goes to preserving continuos residency for the purposes of Naturalization.
You should contact an attorney to have all factors analyzed so that you do not inadvertently overlook ways to preserve continuos residency.
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