18 USC 1542:
Whoever willfully and knowingly makes any false statement in an application for passport with intent to induce or secure the issuance of a passport under the authority of the United States, either for his own use or the use of another, contrary to the laws regulating the issuance of passports or the rules prescribed pursuant to such laws; or
Whoever willfully and knowingly uses or attempts to use, or furnishes to another for use any passport the issue of which was secured in any way by reason of any false statement—
Shall be fined under this title, imprisoned not more than 25 years (if the offense was committed to facilitate an act of international terrorism (as defined in section 2331 of this title)), 20 years (if the offense was committed to facilitate a drug trafficking crime (as defined in section 929(a) of this title)), 10 years (in the case of the first or second such offense, if the offense was not committed to facilitate such an act of international terrorism or a drug trafficking crime), or 15 years (in the case of any other offense), or both.
18 USC 1425:
(a) Whoever knowingly procures or attempts to procure, contrary to law, the naturalization of any person, or documentary or other evidence of naturalization or of citizenship; or
(b) Whoever, whether for himself or another person not entitled thereto, knowingly issues, procures or obtains or applies for or otherwise attempts to procure or obtain naturalization, or citizenship, or a declaration of intention to become a citizen, or a certificate of arrival or any certificate or evidence of nationalization or citizenship, documentary or otherwise, or duplicates or copies of any of the foregoing— Shall be fined under this title or imprisoned not more than 25 years (if the offense was committed to facilitate an act of international terrorism (as defined in section 2331 of this title)), 20 years (if the offense was committed to facilitate a drug trafficking crime (as defined in section 929(a) of this title)), 10 years (in the case of the first or second such offense, if the offense was not committed to facilitate such an act of international terrorism or a drug trafficking crime), or 15 years (in the case of any other offense), or both.
Neither section addresses false statements explicitly, but courts have found that 1425 has a materiality requirement, namely that immaterial false statements do not violate the statute (see US v. Alferahin).
Is it safe to say that a similar analysis would apply to section 1542? Has any court ruled explicitly on this question?