The Mathematical Foundations of Self-Referential Systems:From Computability to Transfinite Dynamics

Draft monograph (version 0.1.0) developing a unified mathematical treatment of self-referential systems from computability and logic through transfinite and field-theoretic structure. Part I formalizes Recursive Representation Theory (RRT); Part II introduces the Self-Referential Renormalization Group (SRRG); later parts connect information geometry, topology, computational limits, transputation (beyond standard computation), and the Self-Computation Principle, with applied discussion toward physics, biology, and AI-relevant settings. This deposit is the peer-review-oriented draft labeled "Pre-Publication Edition — In Preparation for Peer Review"; the archival publication date reflects the first public release (2025-09-05).