Self-collision detection has become the dominant computational bottleneck in GPU-accelerated cloth simulation, as modern parallel solvers such as XPBD have drastically reduced the cost of position updates while leaving collision resolution largely unoptimized. Existing spatial partitioning methods treat all cloth regions uniformly, saturating GPU memory bandwidth despite the fact that the vast majority of the mesh surface remains geometrically flat and collision-free at any given frame. We propose a hierarchical self-collision culling framework built upon a resolution-independent discrete curvature metric derived from the $h^2$-normalized Laplace-Beltrami operator, integrated with a discrete Kirchhoff–Love shell model combining distance and dihedral bending constraints within XPBD. Unlike prior cache-dependent acceleration strategies, our method tightly couples curvature-driven geometric pruning with a fused GPU kernel design and shows that this stateless formulation is both faster and physically more reliable. Evaluated on meshes of $512\times 512$ and $1024\times 1024$ particles, our method achieves a $5.5\%$ and $9.7\%$ FPS improvement alongside a $34.9\%$ and $28.4\%$ reduction in active collision pairs, respectively, with qualitative validation via high-fidelity rendering confirming artifact-free self-contact and strict ground-plane non-penetration. Ablation results further reveal that temporal coherence, conventionally regarded as an optimization standard, strictly degrades both performance (FPS decrease of $1.4\%p$ to $1.9\%p$) and physical accuracy (penetration depth increase of $36.1\%$ to $100.0\%$ relative to the curvature-only stage) on RTX 3070 GPU, advocating for stateless per-frame geometric evaluation as the preferred design paradigm.