This paper introduces HyperAgents, a novel framework for creating self-referential AI systems capable of autonomous, open-ended improvement across any computable task. Unlike previous models that rely on rigid, human-designed rules for self-modification, these agents integrate task-solving logic and meta-level improvement mechanisms into a single editable program. This architecture enables metacognitive self-modification, allowing the AI to refine not only its answers but also the very process it uses to upgrade itself. By extending the Darwin Gödel Machine (DGM-H), the system demonstrates the ability to evolve sophisticated features like persistent memory and performance tracking without manual engineering. Experiments across diverse fields—including robotics, coding, and mathematical grading—show that these improvements are highly effective, transferable between different domains, and capable of compounding over time. Ultimately, the research suggests a path toward self-accelerating AI that can independently enhance its own problem-solving architecture while maintaining safety through sandboxed environments.