This work was conducted without institutional funding, grants, or corporate sponsorship. The complete dual-layer architecture and simulation algorithms are fully disclosed in this paper — nothing is held back — so that the scientific community can verify, reproduce, and build upon them freely for research purposes. Independent research of this kind is sustained entirely by fair agreements with the organizations that benefit from it. If this framework creates value inside your company — whether in game engine development, real-time physics middleware, VR/AR simulation, or VFX pipelines — I ask that you honor the noncommercial terms and reach out for a fair arrangement. These agreements are what make the next discovery possible. I have chosen full disclosure over patents, and an honest request over legal pressure. Reaching a fair arrangement is straightforward and far less costly than the alternatives. I trust that rendering engineers, game developers, and organizations who benefit from open technical work will recognize the fairness of this exchange. To reach an agreement: lctrnc1@gmail.com | andrespirolo@gmail.com

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).