Structural Calculus is a deterministic mathematical framework for defining, analyzing, and verifying structure, coherence, and recursion in informational, physical, and computational fields. The axiomatic foundation is the identity Existence = Coherence = Recursion (E=C=R): a structure exists if and only if it is recursion-closed and exceeds a domain coherence threshold. This work formalizes admissible spaces, operators, the structural derivative and integral, and proves a Structural Fundamental Theorem of Calculus. It states well-posed evolution laws, negative-entropy monotonicity, provides a worked non-reducibility example, implementation semantics, and a mapping to the MSPV verification methodology.