This treatise presents a comprehensive derivation of ontology and the demarcation of Gradientology as a post-metaphysical science of necessity. Through systematic critique of eight major ontological systems—from substance ontology to process philosophy—we demonstrate the insufficiency of contingent approaches. The framework establishes that existence is derivable from first principles through relational-triadic computation, resolving the "why something rather than nothing" question as a logical necessity rather than contingent fact. Gradientology mathematizes process philosophy, operationalizes relational ontology, and provides falsifiable computational imperatives that bridge the modal gap between logical necessity and physical instantiation. The treatise further engages with anticipated critiques from both philosophical and scientific domains, demonstrating how Gradientology saturates the space of contingent critique through derivational necessity rather than empirical accommodation.