We propose that the G–X–Q–N cycle — generative potential, torsion, stable form, return — constitutes the minimal algebraic structure necessary for any generative cyclic process. The principle instantiated by the cycle is pre-energetic: N in stasis is the absence of energy; energy does not exist in the principle but emerges from it as the first manifestation of the cycle. The G–X–Q–N cycle is the structure anterior to physical categories — it does not describe them from within but precedes them and makes them possible. The structure was not constructed to fit specific phenomena: it was recognized through comparative morphological observation of biological, physical, and cognitive systems, formalized algebraically by convergence, and verified in six independent instantiations — the ocular lens, sensory transduction, synaptic memory, traumatic pathology, Alzheimer's disease, and collective memory. Cross-domain convergence was not sought: it emerged. We demonstrate that no simpler structure satisfies the four necessary constraints of any generative cyclic process. We propose three formal criteria for identifying new instantiations of the principle in unexplored domains. The framework is not in competition with Prigogine's thermodynamics, Friston's active inference, or Kauffman's self-organization — it includes them as particular cases of specific regimes of the complete cycle, providing the unifying structure that each of these approaches approximates without reaching.
Succi et al. (Sat,) studied this question.