shall be set as shall be necessary to comply with this provision. The procedures with respect to notice of such a hearing and the conduct thereof, and in respect to appeals shall follow the then established general procedures and rules of practice of the Department of the Interior in respect to contests or protests affecting public lands of the United States. If, pursuant to such a hearing the final decision rendered in the matter shall affirm the validity and effectiveness of any mining claimant’s so asserted right or interest under the mining claim, then no subsequent proceedings under this section shall have any force or effect upon the so-affirmed right or interest of such mining claimant under such mining claim. If at any time prior to a hearing the department or agency requesting publication of notice and any person filing a verified statement pursuant to such notice shall so stipulate, then to the extent so stipulated, but only to such extent, no hearing shall be held with respect to rights asserted under that verified statement, and to the extent defined by the stipulation the rights asserted under that verified statement shall be deemed to be unaffected by that particular published notice.