The Supreme Court has issued a decision construing when a person procures naturalization in a manner contrary to law.  Specifically, the Court held that the false statement must have some causal connection to the approval of the naturalization application.  "The statute it passed, most naturally read, strips a person of citizenship not when she committed any illegal act during the naturalization process, but only when that act played some role in her naturalization."  

"If the facts the defendant misrepresented are themselves disqualifying, the jury can make quick work of that inquiry. In such a case, there is an obvious causal link between the defendant’s lie and her procurement of citizenship. To take an example: An applicant for citizenship must be physically present in the United States for more than half of the five-year period preceding her application."  

"But that is not the only time a jury can find that a defendant’s lie had the requisite bearing on a naturalization decision. For even if the true facts lying behind a false statement would not in and of themselves justify denial of citizenship, they could have led to the discovery of other facts which would do so . . .  a person whose lies throw investigators off a trail leading to disqualifying facts gets her citizenship by means of those lies—no less than if she had denied the damning facts at the very end of the trail."

"When relying on such an investigation-based theory, the Government must make a two-part showing to meet its burden. As an initial matter, the Government has to prove that the misrepresented fact was sufficiently relevant to one or another naturalization criterion that it would have prompted reasonable officials, seeking only evidence concerning citizenship qualifications, to undertake further investigation.  If that much is true, the inquiry turns to the prospect that such an investigation would have borne disqualifying fruit. As to that second link in the causal chain, the Government need not show definitively that its investigation would have unearthed a disqualifying fact (though, of course, it may). Rather, the Government need only establish that the investigation would predictably have disclosed some legal disqualification. If that is so, the defendant’s misrepresentation contributed to the citizenship award in the way we think § 1425(a) requires."

The full text of Maslenjak v. United States can be found here: