Because you don't live with your wife, you can't apply for naturalization after only 3 years of permanent residence status. You'll have to wait 5 year from the date the you became a permanent resident.
Your address is where you actually, in fact, live; not where you receive mail.
I agree. Naturalization applications is at least two years away form you.
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The fact that you are not living together would be an issue. Probably best to wait and apply under the five year rule.
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If you want to file now, you can. You will need to prove that you are still married and that you are not living together because of short-term career goals. This happens a lot when both spouses are professionals and have difficulty finding jobs in the same locality. As long as you can show that the move is temporary, you will be fine. Will suggest you hire an attorney to help you collect the right evidence to submit.
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