I do not pretend to be an expert on the matters, but I do not see where Asgardia will claim any sovereignty, by means of use or occupation, or by any other means of the Outer space, including the Moon and other celestial bodies in the form or spirit of this article II as I see in the UNITED NATIONS PUBLICATION Sales No. E.02.I.20 ISBN 92-1-100900-6 regarding the Text of treaties and principles governing the activities of States in the exploration and use of outer space, adopted by the United Nations General Assembly.
As Asgardia will only retain jurisdiction and control over is registered objects, and over any personnel or occupant thereof, while in outer space or on a celestial body.
The Article VIII of the UNITED NATIONS TREATIES AND PRINCIPLES ON OUTER SPACE give us the right to do by mentioning: A State Party to the Treaty on whose registry an object launched into outer space is carried shall retain jurisdiction and control over such object, and over any personnel thereof, while in outer space or on a celestial body. Ownership of objects launched into outer space, including objects landed or constructed on a celestial body, and of their component parts, is not affected by their presence in outer space or on a celestial body or by their return to the Earth. Such objects or component parts found beyond the limits of the State Party to the Treaty on whose registry they are carried shall be returned to that State Party, which shall, upon request, furnish identifying data prior to their return.
By retaining jurisdiction and control over is registered objects and over any of is personnel or occupant, Asgardia will have automatically the national sovereignty on our objects.
The Article XII may compromise Asgardia national sovereignty on all stations, installations, equipment and space vehicles on the Moon and other celestial bodies but not space stations residing in outer space.
This Article XII of the UNITED NATIONS TREATIES AND PRINCIPLES ON OUTER SPACE grant access to representatives of other States Parties to the Treaty on a basis of reciprocity, only on stations, installations, equipment and space vehicles on the Moon and other celestial bodies and such representatives shall give reasonable advance notice of a projected visit, in order, that appropriate consultations may be held and maximum precautions may be taken to assure safety and to avoid interference with normal operations in the facility to be visited.
Now as I could understand. on the light of those mentioned articles, our nation Asgardia could have national sovereignty on any Asgardian space station but not to the outer space or the Moone and other celestial bodies.
However, by doing so, the Constitution of Asgardia could make the international law evolve accordingly to guarantee our protection by extending our territorial sovereignty to the immediate outer space.