Double-Helix Active Geometry: LiDAR-Anchored Multi-View Depth with Selective Abstention

arXiv:2607.02561v1 Announce Type: new Abstract: Consumer depth sensors such as the LiDAR scanner on recent iPhones provide metric range, but their useful range is short and their returns are sparse. We present DH-Active, a lightweight, training-free geometry back-end that treats the sensor as a metric ruler rather than the sole source of depth. Near-field returns anchor the metric relative pose of two views through PnP; visually trackable samples without a valid depth return are then triangulated under that pose. A parallax/reprojection gate abstains wherever the geometry is ill-conditioned, leaving an explicit hole and a selective score instead of forcing an estimate. The measured core front end, including spiral sampling, sparse back-projection, and hole taxonomy but excluding preprocessing and multi-view recovery, runs at 1.11 ms median latency on CPU (OpenCV using 14 threads), about 38 times faster than a DINOv2-L visual branch on GPU in our timing setup. Across two iPhone captures and the public TUM RGB-D and ARKitScenes benchmarks, held-out depth is recovered at 1.4 to 6.7 percent median relative error. In a controlled ARKitScenes protocol that uses only returns within 2 m to set scale and an independent laser scan as ground truth, DH-Active achieves 64.2 percent scene-median coverage of evaluable far-field candidates at 13.4 percent scene-median relative error; direct triangulation from the device trajectory is not usable. We also report the alternatives that failed in our tests: single-frame defocus, classical focus-stack depth, defocus-LiDAR fusion, point-to-point ICP over a good visual-inertial track, and attention-to-holes resampling. A 1.26 B learned model remains more accurate after oracle scale alignment. The contribution here is narrower: metric sparse depth, explicit abstention, zero learned parameters, and near-millisecond CPU cost.