HyperKleinBottle surfaces and their logics; the latter incorporates interrelations and hyper-contextualizations within an heterarchy of Otherness. We introduce the associated logo-physics, as a basis for the unification of science and phenomenology, by surmounting the Cartesian Cut. Dualism is found to be a projection of the former logic, not an independent primeval ontoepistemology. We present the phenomenology of these logics, with regards to the geometries and topologies of space and time; of thought and language; of semiosis and its geological, cosmological and astronomical signs linked to the Myth of Eternal Return; of perception and cognition; of the common ontopoiesis of life and the inanimate realms, and of biological shape departing from embryological development and its unfolding as body-plans and their anatomy-physiology, and discuss its bearing in evolutionary theory, all which we present as embodiments of this non-dual ontoepistemology. We contrast this paradigm with: 1) the dualism of the theory of autopoiesis and the purported interior/exterior divide, as a general principle, which these logics subvert by self and mutual reentrances of the heterarchies; 2) the dual membrane of cell biology; 3) evolutionary theory associated to the metabolic versus genomic dualism; 4) the mereological fallacies of the neurosciences and the hypercontextuality of metaphors and anthropomorphisms; 5) the dualisms of Newtonian physics, Einstein’s relativity and quantum mechanics which are found to be epistemic theories, and the assumption of non-contextualization in physics, chemistry and geology which we show not to be the case; 6) the psychophysics of visual, aural and musical spaces, 7) the anatomy-physiology of the sensorium and the healing reconstitution of integrity; 8) in the division of epistemology and ontology, of language and process, and the top-down and bottom-up systemic, and finally 9) the issue of design related to turning-inside-out of a sphere (the ovum), yet transcending creationism. We present their surmountal through the ontoepistemologies of the Klein and Hyper-Klein Bottles surfaces, of hyper-contextuality and complexity. We discuss teleological causation and design of processes/structures, in particular in paleogeology, physics, chemistry and biology, in terms of the latter ontoepistemologies and of the Golden Mean, generated by time waves and their guidance by the Fibonacci Algorithm. We apply this ontoepistemology to the interpretation of religious texts and discuss the relations with the evolution of science. We discuss the two-dimensionality of biology and the lifeworld, novelty and the time operators.