Add resident GPU ICP transforms and centered moment reductions

CHANGELOG.md

@@ -21,6 +21,14 @@ removed no sooner than the next major (see `docs/API_STABILITY.md`).
 
 ### Changed
 
+- Extend `register-icp-gpu` with explicit `align_with_gpu_reduction`: retain
+  original source/target on GPU, transform, match and reduce centered moments
+  on device, then download a fixed 176-byte result per evaluation. CPU Horn
+  pose solving and convergence remain; post-update moments are reused for the
+  next update and final fitness. Ordinary CPU/correspondence paths retain their
+  math and trimming support. The new route requires untrimmed ICP and documents
+  f32 matching/reduction/conditioning differences and full-call measurements.
+
 - Add opt-in `filter-mls-gpu` smoothing for constant, linear and quadratic
   surfaces. Reusable input-bound radius rows feed GPU weighted frames and
   polynomial fits in three passes; explicit upload/download receipts and

README.md

@@ -644,6 +644,14 @@ The target KD-tree is uploaded once and reused for update/fitness queries;
 the result contains the ICP trace and transfer accounting. Pose estimation
 remains on CPU. See [measurements and limits](notes/2026-10-12_gpu_icp_correspondences.md).
 
+`IcpRegistration::align_with_gpu_reduction(&runtime, &source, &target)` under
+the same feature retains both clouds on GPU and also runs coordinate transforms,
+centroid/cross-covariance and fitness reductions on device. Each evaluation
+downloads only 176 bytes of moments/status; CPU pose solving and convergence
+remain. This route requires untrimmed ICP and uses f32 device math, which can
+differ near match gates and degenerate geometry. See
+[resident ICP measurements](notes/2026-10-13_gpu_icp_reduction.md).
+
 GICP exposes the same explicit correspondence entry point under
 `register-gicp-gpu`; configured radius covariances run on the supplied runtime
 and share the transfer receipt. Its Hessian/gradient accumulation and pose