arXiv:2611.13528v1 Announce Type: new Abstract: Photorealistic and metrically consistent world representations are a primary requirement for LiDAR--inertial--visual SLAM systems that serve robots over continuous operation. 3D Gaussian splatting makes such representations attainable by supplying an explicit, renderable, and queryable scene model. We present GEMOR-GS (Global Extrinsic-calibration-refined Mapping and Online Relocalization for 3D Gaussian-Splatting SLAM) to make the Gaussian map geometrically accurate, globally refined, and re-enterable, providing a better appearance for robot perception and decision-making. To improve the 3DGS map, the LiDAR--camera extrinsic is first estimated offline by direct-method alignment over dedicated calibration segments and reused by all following online and offline processes. Under the calibrated geometry, keyframe poses and Gaussian parameters are refined alternately under a gated differentiable-rendering and LiDAR--projection objective. The final global reconstruction is then rebuilt from the refined keyframe schema with all online constraints lifted. For the robot SLAM lifecycle, the method recovers the pose from the 3DGS map after tracking loss through an XFeat bypass map, RANSAC-PnP coarse localization, and Gaussian RGB-D warp refinement. Experiments on one self-collected and five public sequences quantify each element: the offline reconstruction wins all paired keyframes against the online map by 14.3--19.9 dB, improves PSNR by approximately 9 dB over Gaussian-LIC2, and achieves 86--100% held-out relocalization success tied to extrinsic quality. The results show that GEMOR-GS improves the geometric accuracy, appearance fidelity, and re-enterability of the 3DGS map, serving as a dependable robot world model for SLAM and downstream tasks.