Emotion-Gradient Metacognitive RSI (Part I): Theoretical Foundations and Single-Agent Architecture

We present the Emotion-Gradient Metacognitive Recursive Self-Improvement (EG-MRSI) framework, a novel architecture that integrates introspective metacognition, emotion-based intrinsic motivation, and recursive self-modification into a unified theoretical system. The framework is explicitly capable of overwriting its own learning algorithm under formally bounded risk. Building upon the Noise-to-Meaning RSI (N2M-RSI) foundation, EG-MRSI introduces a differentiable intrinsic reward function driven by confidence, error, novelty, and cumulative success. This signal regulates both a metacognitive mapping and a self-modification operator constrained by provable safety mechanisms. We formally define the initial agent configuration, emotion-gradient dynamics, and RSI trigger conditions, and derive a reinforcement-compatible optimization objective that guides the agent's development trajectory. Meaning Density and Meaning Conversion Efficiency are introduced as quantifiable metrics of semantic learning, closing the gap between internal structure and predictive informativeness. This Part I paper establishes the single-agent theoretical foundations of EG-MRSI. Future parts will extend this framework to include safety certificates and rollback protocols (Part II), collective intelligence mechanisms (Part III), and feasibility constraints including thermodynamic and computational limits (Part IV). Together, the EG-MRSI series provides a rigorous, extensible foundation for open-ended and safe AGI.

When Your Own Output Becomes Your Training Data: Noise-to-Meaning Loops and a Formal RSI Trigger

We present Noise-to-Meaning Recursive Self-Improvement (N2M-RSI), a minimal formal model showing that once an AI agent feeds its own outputs back as inputs and crosses an explicit information-integration threshold, its internal complexity will grow without bound under our assumptions. The framework unifies earlier ideas on self-prompting large language models, G\"odelian self-reference, and AutoML, yet remains implementation-agnostic. The model furthermore scales naturally to interacting swarms of agents, hinting at super-linear effects once communication among instances is permitted. For safety reasons, we omit system-specific implementation details and release only a brief, model-agnostic toy prototype in Appendix C.