mps-pointops: Numerically Specified Point-Cloud Operators and Adaptive Spatial Search on Apple Silicon

Preprint, version 1. This manuscript has not undergone peer review. Point-cloud learning pipelines depend on sampling, neighbor selection, and indexed reductions whose CUDA-oriented extension paths can impede execution on Apple Silicon. We present mps-pointops, an open-source implementation of point-cloud operators using Metal through PyTorch's MPS backend, with dense and ragged interfaces and explicitly scoped compatibility adapters. The system combines persistent farthest-point sampling, streaming nearest-neighbor selection, an order-preserving SIMD Ball Query scan, differentiable geometric operators, and an opt-in Morton-ordered bounding-volume hierarchy. We formalize the distinction between geometric definitions and floating-point selection contracts, derive the prefix invariant that preserves first-match order, and state the arithmetic assumptions needed for conservative pruning. An audit of source-pinned records preserved with version 1.0.0 finds that the SIMD scan reduces a sorted 100,000-point Ball Query fixture from 21.43 to 2.91 ms on an M5 Pro. For one million references and 65,536 queries, explicit BVH search reduces synchronized public kNN latency from 879.4 to 173.3 ms for a uniform fixture, but regresses from 863.6 to 1,293.2 ms for coincident points. Physical M1 records show analogous distribution dependence and a pronounced concentrated-gradient penalty in Chamfer backward. These historical measurements support bounded dispatch policies, not universal GPU superiority. The artifact includes raw records, source hashes, differential checks, counterexamples, and qualified memory/timeline measurements; remaining numerical edge cases and hardware coverage are explicitly identified. Files: manuscript PDF, matching LaTeX source, and a reproducibility supplement containing the evidence registry and scripts described in Appendix C. The separately archived software artifact is mps-pointops v1.0.0, https://doi.org/10.5281/zenodo.23107348. Code: https://github.com/gamzerA/mps-pointops. The manuscript documents known numerical edge cases and the scope of historical measurements. Author contributions: YeYoung Lee conceived and directed the research, determined the methodology and experimental design, personally reviewed the Python and Metal code and intermediate results, debugged and corrected implementation errors during that review, repeatedly revised the mathematical derivations and numerical contracts, directed the manuscript's scientific content, interpretation, structure, figures, and tables, interpreted the evidence, and made all final scientific and editorial decisions. AI tools were used under the author's instructions and continuous technical review, as specified in the manuscript. Correction (2026-10-03): the author-contribution and AI-use statements and obsolete draft-status wording were corrected. Scientific results, equations, figures, and benchmark evidence are unchanged.