The Mathematical Foundations of Reflexive Reality (MFRR) framework proves that a physically real universe must be reflexive—its law, its description, and its execution must be three aspects of the same internal mechanism. This condition, Perfect Self-Containment (PSC), eliminates the need for external laws or meta-rules and forces a specific mathematical structure that unifies logic, computation, quantum mechanics, gravitation, and cosmology. MFRR is built on a suite of seventeen closure theorems which prove that any universe that can exist self-consistently and computably must implement: Transputation (PT)—a lawful, non-computable adjudication process that resolves logical degeneracies (Choice Points) internal to the universe. Forced as the unique internal adjudicator under closed-choice conditions, machine-proved in a companion Lean development (zero sorry; Strong Transputational Universality, STU). Reflexive Landauer Bound—every act of adjudication carries a quantifiable energetic cost exceeding the classical bound, linking information, energy, and geometry. Fisher Information Geometry—the natural geometry of distinguishability, whose curvature governs adjudication density and whose stress-energy sources a physical field. Self-Referential Renormalization Group (SRRG)—a reflexive gradient flow on theory space whose unique stable fixed point is the Standard Model gauge structure, established via the Two-Layer PSC Theorem. Information Profit Principle—a universal...