SOVEREIGN: A Cognitive Operating System for Self-Evolving AI Agents — Unifying Immunity, Resonance, Impedance Matching, and Compound Learning under Cognitive Entropy Theory

We present SOVEREIGN, a cognitive operating system that transforms AI agents from reactive query-answerers into self-evolving cognitive entities. The system introduces twelve contributions unified under a single mathematical framework — Cognitive Entropy: (1) Cognitive Immunity — bio-inspired failure pattern learning via antigen/antibody mechanisms with PAC learning bounds; (2) Epistemic Confidence Fields — architectural anti-hallucination using thermodynamic phase transitions; (3) Cognitive Resonance — wave interference model for multi-source evidence fusion with superlinear amplification; (4) Personality Homeostasis — PID-controlled identity stability with BIBO stability guarantees; (5) Cognitive Impedance Matching — the first application of RF impedance matching theory to AI-human communication; (6) Cognitive Flywheel — compound knowledge growth through procedural crystallization; (7) Cognitive Attention Budget — information-theoretic optimal allocation of finite context windows via water-filling; (8) Journey Engine — persistent multi-turn task graphs; (9) WisdomBench — the first longitudinal benchmark for measuring agent wisdom acquisition; (10) Cognitive Entropy — a unified metric with Piaget-inspired developmental stages; (11) Adversarial Robustness Bounds — tri-layer defense with provable damage ceiling (D ≤ 1.9%); (12) Cognitive Scaling Laws — Kaplan-style power laws predicting agent cognitive development. The system comprises 12,800+ lines of code across 14 core modules, formalizes 18 theorems with full proofs, and introduces three novel metrics: Wisdom Quotient (WQ), Generalization Ratio (GR), and Overfitting Ratio (OR).

V2: Unified author to Mian Zhang; corrected WQ formula (denominator changed from |T'| to N); empirical validation expanded to dual-model data (DeepSeek-v4-flash + Qwen-Plus, N=2,400 verified evaluations); removed unverified model references.