V01.01 — Mirror Theory I: A Minimal Computational Theory of Recursive Observerhood

This paper develops a minimal computational theory of recursive observerhood. It asks what structural organisation must exist before the term observer can be used as a formal computational predicate. The proposed foundation consists of four primitive assumptions: distinguishability, dynamics, viability and bounded computational capacity. Symbols, representation, selfhood and observerhood are not introduced as primitives, but are treated as structures to be derived from persistence, compression, prediction and viability-constrained model selection. The central result is an information-theoretic theorem: where future viability depends on compressed internal state, and where the reliability of the internal model carries additional information about future viability, architectures maintaining compressed recursive self-models achieve strictly lower optimal predictive risk under log loss than architectures lacking those variables. This release forms part of the Theory Arc of Mirror Programme, Volume I: Observerhood.