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 ( () ), representing reconstruction fidelity as a function of overwrite density (). The location of the recoverability minimum, denoted (₁₀ₒ₈₍), defines the ambiguity basin of the reconstruction process. We introduce the displacement measure (= ₁₀ₒ₈₍ - 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 ₎ₖ 10^-4, 10^-2), system sizes (N=64, 128, 256), and multiple independent reference configurations, the basin converges to a universal displacement (_ -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 ₎ₖ=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.
Luiz PUODZIUS (Sat,) studied this question.