Monocular outdoor navigation requires robust camera motion estimation and a dense, navigable map, where 3D Gaussian Splatting SLAM serves this task through an explicit differentiable parameterization and closed-form projection. However, typically, the geometry is recovered by associating 2D pixels with 3D points, so a modular SLAM system absorbs tracking error into the map, leading to cascading degradation. To address these gaps, we present SG^2SLAM, which couples streaming spatial geometry with a ray-conditioned 3DGS kernel. Streaming spatial geometry replaces the per- frame cross-dimensional correspondence with a chunk-level metric prior that supervises tracking and mapping from one source. A ray-conditioned kernel extends each primitive with a viewing-direction subspace that senses the monocular camera viewpoints. The joint optimization over spatial geometry and poses ensures a globally consistent map and trajectory outcome. Experiments on the KITTI and Waymo Open datasets show that our SG^2SLAM surpasses the per-frame association baselines in the monocular outdoor navigation task. Code will be made publicly available upon acceptance.
A photorealistic 3D view tells a teleoperator where a robot is, but not what the scene contains, how well each object has been observed, or how to turn pointing and speech into robot action. CognitiveReality turns a robot's RGB-D stream into a live, semantically indexed Gaussian-TSDF map shared by an operator in virtual reality and a tool-using language agent. One mapper binary serves any platform through configuration alone: it ingests poses from robot SLAM, joint kinematics, motion capture or an inline visual tracker, bridges localization outages with a shadow tracker and keyframe-anchored PnP, and maintains open-vocabulary instance identities with per-object quality at 2 Hz. Speech and controller rays are grounded against persistent scene objects through validated typed tools and operator-confirmed robot actions. In the controlled agent evaluation, the deployed local Qwen3-VL-8B router reaches 81.24\% tool exact match, while merge-aware replay correctly redirects 101 absorbed object identifiers. On robot data CognitiveReality exceeds a Gaussian-plus-SDF baseline by 2-8 dB; pose error through 5-40 s SLAM outages stays within 1-8 cm. Deployed live on two quadrupeds, the agent executed 26 of 30 navigation requests and 20 of 20 re-observation requests, raising object quality by 2-5 dB.