天叢雲剣 Kusanagi Core Ver.3.0.0: Apparent Scaling without Criticality in Interference-Induced XOR Persistence

Abstract

We investigate persistence dynamics in a finite two-dimensional binary lattice governed by local XOR interactions. The system exhibits heavy-tailed persistence distributions that resemble power-law behavior over intermediate scales. However, systematic finite-size analysis reveals the absence of a consistent scaling regime.

The characteristic cutoff scale, quantified by the 99th percentile persistence time T₉₉(L), shows clear non-monotonic dependence on system size: it increases up to intermediate sizes (L ≈ 128–256) and subsequently decreases. All measurements are obtained with zero censoring, excluding finite-time truncation as a source of this behavior.

Furthermore, effective scaling exponents defined via T_q(L) ∼ L^{z(q)} depend strongly on the quantile level q and remain approximately zero or negative, indicating the absence of a universal scaling exponent.

These results demonstrate that heavy-tailed persistence can arise without true criticality. Instead, the observed behavior originates from interference-induced restructuring inherent to XOR dynamics, providing a concrete counterexample to the common identification of heavy-tailed statistics with scale-invariant critical phenomena.