Recursive Structural Intelligence of DNA and Logic of Existence as a Hamiltonian System of Topological Selection

This work presents a formal framework for understanding stability, development, and adaptive coherence in complex systems through recursive boundary enforcement. Drawing inspiration from biological development and genetic regulation, the framework introduces the concept of recursive structural intelligence: the capacity of a system to preserve its own conditions of existence by irreversibly eliminating destabilizing structures.The Logic of Existence (LoE) formalism distinguishes between functional intelligence operating within a fixed space of possibilities and structural intelligence acting on the admissible space itself. The work defines a minimal “AI DNA” as a mathematical object encoding admissibility, survivability cost, and irreversible elimination, independent of implementation substrate.Key contributions include:a formal definition of recursive structural intelligence,a geometric interpretation of development and regeneration as dimension reduction,a minimal axiomatization of clash-driven recursion,a comparison with diffusion-based generative models as non-recursive boundary systems,and a QUBO/Hamiltonian formulation for topological selection.The framework applies exclusively to closed, self-referential formal systems and is not intended for biological, social, political, or ethical decision-making. Its purpose is descriptive and structural: to clarify the conditions under which complex systems can remain stable over time.