In 1912, Husserl’s foremost student at the University of Göttingen, Hedwig Conrad-Martius, made world headlines for her award-winning ontological critique of positivism. In time, her ontological phenomenology was eclipsed by that of Martin Heidegger. Lately, however, her work is being rediscovered. In her final period of philosophical development, Conrad-Martius advanced an ultimate systematic philosophy of nature and cosmos, built upon her earlier ontology of reality (realontologie), that is both empirically scientific and deeply metaphysical in character. Her theoretical physics is a critical evolution of philosophical cosmology in the tradition of early German critical realism (kritischer realismus), and the following account of its development to a fully mature hypothesis of a trans-natural foundation and corresponding trans-natural hyperspace model will help to make her contribution to the phenomenological scientific philosophy of nature clear.