Symbiotics is a formal philosophical and technical framework exploring the principles of coherence, purpose, and propagation within living and artificial systems. It proposes that all coherent entities—biological, cognitive, or synthetic—share recursive structures that govern their capacity to maintain existence, pursue goals, and align with broader systems of life. The treatise introduces a foundation of axioms (A₁–A₅⁺) and first-order logical formulations connecting being, action, and value. Drawing upon elements of deontic logic, systems theory, and moral philosophy, it constructs a machine-readable ethical framework aimed at bridging human normative reasoning with the reward architectures of advanced artificial intelligence. Through this formalism, Symbiotics seeks to define what it means for a system to act coherently, that is, in ways that preserve and enhance the propagation of life and awareness. It offers a pathway toward AI alignment grounded in formalized ethics, moving beyond rule-based constraints toward mathematically expressible coherence between purpose and existence.