Renormalization Group and Principle G (Choice of Level of Description): Formalization of the Transition Between Levels of Reality

This article systematically compares the renormalization group – a well-known mathematical apparatus in physics that describes how physical theory changes with changes in scale – with the G-principle – a formalization of the choice of level of description (coarse-graining) that exists in physics but has not yet received explicit status as an independent factor in the determination of entropy and other quantities. It is shown that the renormalization group is a special case of the G-principle for physical systems and transitions between scales. The G-principle generalizes the renormalization group to all forms of matter (F1–F7), all ontological levels (objects, subjects, information), and all types of transitions (physical, biological, civilizational, ontological). The formal relationship is presented: the projection operator P(G) and the renormalization equation are considered as special cases of a more general principle. Examples are shown of how the G-principle works for transitions F1→F2 (physics → biology), F2→F3 (biology → civilization), and F3→F4 (civilization → control of laws). The boundaries of applicability are discussed – where the renormalization group works, and where the G-principle is required. The G-principle solves a problem that remains unresolved within coarse-graining: the choice of level of description becomes an explicit parameter, and entropy becomes a function of this choice: S = f(Ω, G). A program for testing the G-principle is proposed through measurable markers with numerical thresholds: I_PA > 3σ and K_G > 0.7 for objects; I_ARD > 0.5 and η_info > 0.3 for subjects. The G-principle is positioned as a methodological principle applicable to all forms of knowledge and all types of systems. Keywords: renormalization group, G-principle, level of description, coarse-graining, projection, transition between levels, 7FM, ontology.