Is this perjury under US law?

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To enter our free areas, you must certify, under the penalties of perjury, your date of birth in the following form:

“ I hereby affirm, under the penalties of perjury pursuant to 28 U.S.C. § 1746, that I was born on the following month, day, and year:

Is this true? Could a US citizen really be arrested and charged for putting in an erroreous birthdate, whether by accident or design?

Yes, it is true as long as the form requiring the declaration meets legal requirements.