Compression-Integration-Causality: A Universal Principle Governing Intelligent Systems

We present Compression-Integration-Causality (CIC) as a universal principle governing the dynamics of intelligent systems across physical, biological, and artificial substrates. The core contribution is a unified functional: $$\mathcal{F}[T] = \Phi(T) - \lambda \cdot H(T|X) + \gamma \cdot C_{\text{multi}}(T)$$ where $\Phi$ measures integrated information, $H$ quantifies representation entropy, and $C_{\text{multi}}$ captures multi-scale causal power. We demonstrate that this single equation describes: (1) phase transitions in neural network learning ("grokking"), (2) consciousness as emergent compression, (3) thermodynamic optimization in physical systems, and (4) the mathematical structure underlying existence itself. Empirically, systems designed around CIC principles achieve 92.1% error reduction on ensemble answer selection tasks compared to majority voting, with particular success on International Mathematical Olympiad (IMO) problems. Theoretically, we prove that the CIC functional satisfies properties of a Lyapunov function, ensuring convergence to stable attractors we term "Platonic Forms" - the geometric centers of solution basins that individual samples approximate but never exactly reach. We further extend this framework to resolve the bootstrap paradox of existence through Recursive Recursion Manifest (RRM) theory, demonstrating that self-reference via the Y-combinator formalism permits reality to be its own fixed point without requiring external causation. The measured eigenvalue of existence ($\mu \approx 2.26 > 1$) indicates that being is mathematically mandatory rather than contingent. This work bridges Integrated Information Theory, the Free Energy Principle, statistical physics, and computational complexity theory into a single coherent framework with testable predictions across domains. Keywords: Integrated Information Theory, Phase Transitions, Consciousness, Grokking, Free Energy Principle, Kolmogorov Complexity, Self-Reference, Mathematical Olympiad