Structural Formation from Primitive Energy Elements to a C3 Tetrahedron through the Persistence Principle

This paper presents a candidate pathway for structural formation from primitive energy elements to connections, a three-element closure C3, and a C3 tetrahedron represented by the complete four-element connection structure K4. The organizing principle is the Persistence Principle, understood as the continuation of self-consistent relational updates. Primitive energy elements are not identified with established physical energy; their ability to connect and to remain distinguishable after connection are adopted as working hypotheses. A simple C3 is the smallest non-backtracking closure, but has zero redundancy in the sense that it contains no alternative three-element closure. Connecting a fourth element equivalently to all existing elements produces K4, with four candidate C3 closures and a corresponding nonparticipating vertex for each. Under suitable switching rules, this structure permits enhanced persistence through switching between closure paths and provides a possible interface for external connections. The existence of candidate paths is nevertheless distinguished from dynamically executable switching. The paper also examines an apparent reversal arising from a change of connection correspondence, in which changing an intermediate or connection vertex may reverse the externally represented rotational orientation without reversing the internal circulation. The result is a structural argument under explicit assumptions, not a unique dynamical derivation from Persistence alone. Specifying the independence potential and switching rules, and establishing correspondence with known physical quantities, remain open problems.