This deposit contains the complete manuscript, figures, and validated experimental results supporting this pre-print, which investigates gravitational structure displacement in merging galaxy clusters within the Lattice Field Medium (LFM) framework. Observations of spatial offsets between baryonic matter and gravitational lensing centers in merging clusters are commonly interpreted as evidence for collisionless dark matter. This work tests an alternative, falsifiable prediction: that gravitational structure is transported via a χ-mediated wave field with finite propagation and relaxation timescales, leading to bounded, phase-dependent displacement during non-equilibrium mergers. Using two independent numerical experiment suites, the study validates five claims:(1) gravitational displacement follows a bounded, phase-dependent transport law;(2) a strict, parameter-free upper bound on offset magnitude emerges directly from dynamics;(3) observed offsets exhibit correct causal directionality;(4) displacement evolves predictably with merger phase; and(5) χ-hysteresis uniquely reproduces all observed behaviors, while alternative mechanisms fail. Across twelve merging clusters with published observational inputs, all observed offsets fall below the predicted bound, with no violations and no per-cluster tuning. Control and null cases are explicitly included. The results demonstrate that collisionless dark matter is not uniquely required to explain merger offset observations, while remaining agnostic about cosmological evidence for dark matter beyond merger-scale dynamics. This repository is self-contained and includes: The final manuscript All figures referenced in the paper Full numerical results supporting Claims C1–C5 Clear evidence paths linking each claim to specific result files No additional simulations are required to reproduce the reported results.