HTE is a complete soft-body physics engine decoupling physics from rendering via a dual-layer architecture. A BFS spanning tree plus harmonically-selected chord subset (~35% edge reduction) drives all simulation; the original polygon mesh renders passively. Validated on NVIDIA A100 (64% less jitter vs random reduction) and ARM Cortex-X3 (15.3% lower latency). Includes emergent topology-driven destruction: unique fracture patterns per collision without pre-authored geometry. Hardware/software agnostic. Prior art disclosure. Dual license PolyForm NonCommercial 1.0.0 (algorithms) / CC BY-NC 4.0 (paper).