The second paragraph clearly states the qualification of eligibility: "I am a natural born citizen of the United States, and at least thirty-five years of age, and have been a resident within the United States for at least fourteen years"

And over Obama's signature is this language: "I do solemnly swear (or affirm) that all the information in this Nomination Paper is true, that is to these and all other qualifications.  I am qualified to hold the office that I seek, having fulfilled the United States constitutional requirements for holding said office.  I further swear (or affirm) that I have fulfilled Arizona statutory requirements for placing my name on its Presidential Preference Election ballot."

It appears Obama has committed perjury.