3D Gaussian Splatting (3DGS) has become a state-of-the-art framework for real-time, high-fidelity novel view synthesis. However, its substantial storage requirements and inherently unstructured representation pose challenges for deployment in streaming and resource-constrained environments. Existing Level-of-Detail (LOD) strategies, particularly those based on bottom-up construction, often introduce redundancy or lead to fidelity degradation. To overcome these limitations, we propose Iterative Gaussian Synopsis, a novel framework for compact and progressive rendering through a top-down "unfolding" scheme. Our approach begins with a full-resolution 3DGS model and iteratively derives coarser LODs using an adaptive, learnable mask-based pruning mechanism. This process constructs a multi-level hierarchy that preserves visual quality while improving efficiency. We integrate hierarchical spatial grids, which capture the global scene structure, with a shared Anchor Codebook that models localized details. This combination produces a compact yet expressive feature representation, designed to minimize redundancy and support efficient, level-specific adaptation. The unfolding mechanism promotes inter-layer reusability and requires only minimal data overhead for progressive refinement. Experiments show that our method maintains high rendering quality across all LODs while achieving substantial storage reduction. These results demonstrate the practicality and scalability of our approach for real-time 3DGS rendering in bandwidth- and memory-constrained scenarios.