The 6H Axiomatic System: Towards a Solution of Hilbert's Sixth Problem

The axiomatic system 6H presents a conceptual roadmap toward a complete axiomatic formulation of physical reality, treating the observable Universe as a self-referential and self-reflexive mathematical structure wherein local observers constitute an indispensable structural element. The evolution of this structure enables operational internal verification of its integrity, completeness, and consistency, thereby shifting the focus from formal syntactic proof to physical semantic coherence. Self-reflexive verification is embedded within the system not as a derivable consequence, but as a fundamental boundary condition, wherein the internal observer ensures the normalizability of solutions and the physical actualization of the continuum. Verification is attained when the system configuration permits the stable measurement of fundamental invariants, thereby unambiguously confirming the absence of pathological or divergent dynamical branches. A key practical significance of this framework lies in establishing an architectural foundation for genuinely safe artificial general intelligence (AGI), whose mechanisms of stability and alignment are not imposed as external software constraints, but emerge naturally from fundamental principles embedded within the topology, evolutionary dynamics, and hierarchical organization of physical reality itself.