I proposed and rigorously proved the Zizhu 2-Core Rank Scaling Theorem, which characterizes the asymptotic behavior of the rank of the incidence matrix of the 2-core for Erdős--Rényi random graphs in the critical window. The theorem shows that the rank scales as \ (ₚ (N^2/3) \) and converges to a non-degenerate limiting distribution. Through the mapping from random graphs to graph states, this result is interpreted as Wang's Quantum Rank Collation Phenomenon---a statistical law governing the number of irreducible stabilizer constraints in random stabilizer states after entanglement stripping. The study demonstrates that the influence of local entanglement clusters is limited, while the algebraic complexity of global entanglement exhibits a highly predictable \ (N^2/3\) scaling in the critical window, establishing a direct link between the core structure of random graphs and the scaling of quantum entanglement.
ZiZhu Wang (Sun,) studied this question.