arXiv:2601.00705v4 Announce Type: replace-cross Abstract: Gaussian Splatting enables high-fidelity differentiable SLAM by representing scenes as anisotropic Gaussian primitives. Most systems rely on residual-driven densification, which couples refinement with representation growth: accuracy saturates at a moderate primitive count, yet memory grows throughout the trajectory, degrading throughput. We introduce TopoGS-SLAM, a stationary-sampling formulation that decouples refinement from capacity through coverage-triggered Gaussian initialization and bounded-topology optimization, turning mapping into a bounded-dimensional problem with stable scaling. On standard indoor benchmarks, TopoGS-SLAM matches or surpasses densification-based pipelines in localization and reconstruction accuracy while substantially improving memory scalability and throughput, showing that iterative topology mutation is not required for accurate Gaussian SLAM in bounded-area static indoor scenes with sufficient multi-view coverage. Additional details and resources are available at this URL: https://breeze1124.github.io/rgs-slam-project-page/