Metaformal Analysis of the Law of Transition from Quantitative to Qualitative Change

The classical law of transition from quantitative to qualitative change is traditionally treated as a philosophical principle rather than a formal dynamical mechanism. In this work, we present a metaformal analysis of this transition by modeling it as a structural process governed by refinement, instability, and stabilization across critical thresholds. We show that gradual quantitative variation may lead to abrupt qualitative reorganization through crisis-like dynamics, singular consolidation, and the emergence of stable invariants. Within this framework, qualitative change is interpreted as the formation of post-critical structural invariants that persist under further refinement. These invariants act as organizational anchors and naturally give rise to constants and fixed ratios observed in nonlinear and physical systems. The proposed approach provides a unifying language connecting bifurcation theory, phase transitions, and universality, while remaining fully compatible with established mathematical and physical formalisms.