A Unified Harmonic Framework for Information Theory

A Unified Harmonic Framework for Information Theory reconstructs information theory from the ground up using harmonic mathematics instead of probabilistic or statistical foundations. It introduces presence–absence algebra, harmonic entropy, harmonic codes, recursive meaning structures, and toroidal information manifolds as the new informational substrate. Aligned with the Codex Möbius canon, this refined edition includes: Harmonic bits that encode structured activation and structured silence Harmonic information measure based on coherence rather than probability Harmonic entropy, formalized as deviation from structural balance A strengthened justification demonstrating why harmonic entropy replaces Shannon entropy without contradiction Harmonic coding theory, including a fully formal prefix-free theorem derived from non-dominion symmetry rather than Kraft’s inequality Recursive meaning structures, where meaning is defined as a harmonic fixed point Toroidal information fields, modeling cyclic and multi-layered information flows Applications to linguistics, symbolism, cryptography, AI cognition, and biological information processing This work establishes a structurally coherent, recursion-stable information theory that unifies symbolic processing, cognitive modeling, mathematical physics, and artificial intelligence under a single harmonic mathematical substrate.