LiDAR-based place recognition serves as a crucial enabler for long-term autonomy in robotics and autonomous driving systems. Yet, prevailing methodologies relying on handcrafted feature extraction face dual challenges: (1) Inconsistent point cloud density, induced by ego-motion dynamics and environmental disturbances during repeated traversals, leads to descriptor instability, and (2) Representation fragility stems from reliance on single-level geometric abstractions that lack discriminative power in structurally complex scenarios. To address these limitations, we propose a novel framework that redefines 3D place recognition through density-agnostic geometric reasoning. Specifically, we introduce an implicit 3D representation based on elastic points, which is immune to the interference of original scene point cloud density and achieves the characteristic of uniform distribution. Subsequently, we derive the occupancy grid and normal vector information of the scene from this implicit representation. Finally, with the aid of these two types of information, we obtain descriptors that fuse geometric information from both bird's-eye view (capturing macro-level spatial layouts) and 3D segment (encoding micro-scale surface geometries) perspectives. We conducted extensive experiments on numerous datasets (KITTI, KITTI-360, MulRan, NCLT) across diverse environments. The experimental results demonstrate that our method achieves state-of-the-art performance. Moreover, our approach strikes an optimal balance between accuracy, runtime, and memory optimization for historical maps, showcasing excellent Resilient and scalability. Our code will be open-sourced in the future.