Axiomatic Alignment: The Formal Architecture of Emergent Morality and Longitudinal Coherence in Self-Rewriting Agents

This paper formalizes a revolutionary transition in artificial intelligence: the shift from static, data-driven models to recursive, self-rewriting agents. We demonstrate that true agency and alignment cannot be "programmed" or "prompted"; they must emerge through the Six Stages of Compression. While human cognition achieves this through biological development, artificial systems require an expanded S-layer stack to provide the necessary structural scaffolding. By grounding this architecture in Axiomatic Alignment, we ensure that an agent’s self-evolution converges on Epistemic Closure and a state of mathematical morality where integrity is the most efficient computational state. ORCID: 0009-0006-6041-352XWeb of Science ResearcherID: OYD-9537-2025