The petition shall be filed by the proponents, or by any person or persons authorized, in writing, by the proponents. All sections of the petition shall be filed at one time. When the petition is presented for filing, the secretary shall determine the total number of signatures affixed to the petition. If, from this examination, the secretary determines that the petition has been signed by at least 5 percent of the registered voters in the district, then the secretary shall accept the petition for filing. The petition shall be deemed as filed on that date. Any sections of the petition not so filed shall be void for all purposes.