The Structural Origin of Macroscopic Classicality

We propose a structural criterion for macroscopic classicality formulated within a hierarchical graph framework. Physical systems are modeled as finite graphs endowed with nested rigid substructures generated through successive coarse-graining. Two structural parameters are introduced: the fraction of hierarchically rigid matter fcfcfc and the hierarchical depth D (G). We show that when fc and D (G) exceed critical thresholds, boundary-spanning structurally transmitting clusters cease to exist and the dynamically admissible macroscopic configuration space reduces to a single connected component. In this regime, macroscopic non-superposition emerges not from a modification of quantum dynamics, but from structural closure of configuration space. The framework combines combinatorial rigidity theory with percolation arguments and yields critical scaling behavior for the lifetime of macroscopic configuration branching near closure. Classicality is thereby interpreted as trivial dynamic connectivity of configuration space rather than dynamical suppression of quantum superposition. This structural perspective provides a topological mechanism for the quantum-to-classical transition while preserving microscopic quantum validity, and offers falsifiable predictions through threshold behavior and scaling relations in hierarchical matter systems.