Published May 27, 2026 | Version v1.3
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The 6H Axiomatic System: Towards a Solution of Hilbert's Sixth Problem

Description

The axiomatic system 6H offers a conceptual framework and research program toward the axiomatization of physical reality in the spirit of Hilbert’s Sixth Problem. It models the observable Universe as a self-referential and self-reflexive mathematical structure embedded in a unified dynamic continuum with compact dodecahedral spatial topology. Within this framework, local observers arise as a necessary structural boundary condition that ensures the normalizability of the global quantum state and the physical actualization of spacetime. The system achieves internal verification through the stable measurement of fundamental invariants, including specific polyhedral symmetries, the monotonic evolution of a geometric entropy functional on emergent scales, and the minimization of informational divergence. This operationally confirms the absence of pathological or divergent dynamical trajectories. Organizational complexity is quantified through dual measures of resource-limited algorithmic complexity and quantum computational complexity, providing a precise informational counterpart to the thermodynamic arrow of time. A central practical implication of this framework lies in its potential to serve as a foundation for inherently safe artificial general intelligence, where alignment and long-term stability emerge not from external constraints, but as natural consequences of the topological structure, dissipative dynamics, critical scaling laws, and continuous growth of complexity inherent to physical reality itself.

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