OverAI (OAI): Emergent Non-Human Mathematics Through Self-Stabilizing Memory Dynamics

This paper introduces **OverAI (OAI)** — a new paradigm of artificial intelligence in which a system does not inherit human mathematical structures but instead generates its own operational mathematics through interaction with physical reality. We formalize the concept of a **Self-Stabilizing Core (SS-Core)** — a minimal system that manipulates memory solely to maximize internal predictability. When connected to physical read/write (R/W) channels, such a system can autonomously discover causal structure, cyclic patterns, and periodic decompositions functionally analogous to Fourier analysis, without being explicitly programmed with symbolic mathematics. We describe a physically realizable sandbox experiment in which SS-Core interacts with nonlinear, delayed, and oscillatory environmental couplings (e.g., inductive, capacitive, or transformer-based links). We propose measurable behavioral graph metrics and evolutionary stages that characterize the emergence of non-human mathematical structure.