A direct empirical proof of dark matter is presented through weak lensing observations of the galaxy cluster 1E0657-558 (z = 0.296), a unique cluster merger. The study shows that the gravitational potential does not trace the distribution of the plasma (the dominant baryonic mass component), but rather the distribution of galaxies. This spatial offset between the total mass and the baryonic mass peaks is significant at 8σ and cannot be explained by altering the gravitational force law, thus proving the existence of dark matter. The cluster merger causes the collisionless galaxies and the fluid-like X-ray emitting plasma to spatially separate. The gravitational lensing maps reveal that the gravitational potential traces the distribution of galaxies, not the plasma. This separation is due to the different behaviors of galaxies (collisionless) and plasma (subject to ram pressure) during the merger. The observed offset between the centers of the total mass and the baryonic mass peaks is consistent with the presence of dark matter, which is collisionless and thus not affected by the plasma's ram pressure. The study uses a combination of ground-based and HST/ACS images to create gravitational lensing maps. The results show that the gravitational potential is significantly offset from the baryonic mass peaks, with the total mass center being offset by ~2σ from the baryonic mass peaks. The plasma mass is estimated to be about 14% of the observed κ in the main cluster and 10% in the subcluster, consistent with the X-ray plasma contributing a significant fraction of the total mass. The analysis of the cluster's mass components shows that the total mass of the subcluster is greater at the plasma peak than at the brightest cluster galaxy (BCG), but the lensing mass center is near the BCG. The baryonic mass difference between these positions would be even greater if the non-peaked plasma component between the shock front and the subcluster were excluded. For the main cluster, a similar effect is observed, although the baryonic mass difference is smaller. The study concludes that the observed lensing signal cannot be explained by alternative gravity models, as these models fail to reproduce the observed mass distribution. The results provide strong evidence for the existence of dark matter, as the gravitational potential does not trace the baryonic mass distribution, indicating the presence of unseen matter. The findings support the dark matter hypothesis and highlight the importance of gravitational lensing in detecting dark matter in galaxy clusters.A direct empirical proof of dark matter is presented through weak lensing observations of the galaxy cluster 1E0657-558 (z = 0.296), a unique cluster merger. The study shows that the gravitational potential does not trace the distribution of the plasma (the dominant baryonic mass component), but rather the distribution of galaxies. This spatial offset between the total mass and the baryonic mass peaks is significant at 8σ and cannot be explained by altering the gravitational force law, thus proving the existence of dark matter. The cluster merger causes the collisionless galaxies and the fluid-like X-ray emitting plasma to spatially separate. The gravitational lensing maps reveal that the gravitational potential traces the distribution of galaxies, not the plasma. This separation is due to the different behaviors of galaxies (collisionless) and plasma (subject to ram pressure) during the merger. The observed offset between the centers of the total mass and the baryonic mass peaks is consistent with the presence of dark matter, which is collisionless and thus not affected by the plasma's ram pressure. The study uses a combination of ground-based and HST/ACS images to create gravitational lensing maps. The results show that the gravitational potential is significantly offset from the baryonic mass peaks, with the total mass center being offset by ~2σ from the baryonic mass peaks. The plasma mass is estimated to be about 14% of the observed κ in the main cluster and 10% in the subcluster, consistent with the X-ray plasma contributing a significant fraction of the total mass. The analysis of the cluster's mass components shows that the total mass of the subcluster is greater at the plasma peak than at the brightest cluster galaxy (BCG), but the lensing mass center is near the BCG. The baryonic mass difference between these positions would be even greater if the non-peaked plasma component between the shock front and the subcluster were excluded. For the main cluster, a similar effect is observed, although the baryonic mass difference is smaller. The study concludes that the observed lensing signal cannot be explained by alternative gravity models, as these models fail to reproduce the observed mass distribution. The results provide strong evidence for the existence of dark matter, as the gravitational potential does not trace the baryonic mass distribution, indicating the presence of unseen matter. The findings support the dark matter hypothesis and highlight the importance of gravitational lensing in detecting dark matter in galaxy clusters.