This paper proposes a formal epistemological framework — the G6–Q9 model — for describing cyclic dynamics of generation, manifestation, and return in physical and biological systems. The framework distinguishes two complementary structural states (G6: centripetal potential; Q9: centrifugal manifestation) governed by two transition operators: eXopia (X) and Entropy (N). The algebraic structure is rigorously derived: X is defined as an anti-diagonal endomorphism with involutive torsion (X² = −IdV) ; N as a projection-contraction operator with VG as fixed-point subspace. The self-composition law (N ∘ X) ·A·UK = A²·UK is established as a theorem, and the Möbius topological representation as a direct algebraic consequence. Formal structural analogies are identified with six foundational formalisms of theoretical physics: the Hamiltonian, the Schrödinger equation, the Boltzmann–Shannon entropy, the Klein–Gordon field equation, the Dirac spinor structure, and the Maxwell propagation equations. The framework is applied to the internal optical system of the vertebrate eye as a physical instantiation of the abstract cycle. Submitted for peer review at Synthese (Springer Nature).
Succi et al. (2026) studied this question.