A Universal Recoverability Basin in Coupled Overwrite–Decoder Systems

We investigate the recoverability landscape of locally coupled binary memory arrays subjected to priority-ordered overwrite and belief-propagation decoding. Recoverability is quantified by the function (\Phi(\Xi)), representing reconstruction fidelity as a function of overwrite density (\Xi). The location of the recoverability minimum, denoted (\Xi_{\rm basin}), defines the ambiguity basin of the reconstruction process. We introduce the displacement measure (\Delta = \Xi_{\rm basin} - 0.5), which quantifies deviation from the binary-symmetric-channel midpoint. Systematic simulations reveal the emergence of a stable negative recoverability basin for nonzero overwrite coupling within a finite decoder-coupling window. Across overwrite couplings (J_{\rm ow} \in [10^{-4},10^{-2}]), system sizes (N=64,128,256), and multiple independent reference configurations, the basin converges to a universal displacement (\Delta_\infty \approx -0.27) to (-0.28). The displacement exhibits high sign consistency, decreasing variance with increasing system size, and strong robustness against variations in overwrite strength. In contrast, the uncoupled system ((J_{\rm ow}=0)) remains in a disordered boundary state characterized by large fluctuations and the absence of a stable basin location. Decoder coupling plays a critical role. Stable basin formation occurs only within an intermediate decoder-coupling regime; weak coupling preserves binary-symmetric-channel behavior, while strong coupling produces a nearly flat recoverability landscape in which basin localization disappears. These results identify a robust basin-selection phenomenon arising from the interaction between structured overwrite dynamics and neighborhood-informed reconstruction. The findings establish the existence of a universal recoverability basin within the studied overwrite–decoder–belief-propagation model and provide a quantitative framework for analyzing ambiguity landscapes in coupled memory and reconstruction systems.