Analytic first-surface sampling diagnostic

Test the joint bias offset without retuning solver, saturation, bias limits, seeds or success gates. Use the same 54 sphere-scene cases: 3 layouts × visible/all-return inputs × 0,+.25,-.25 m measurement bias × ± seeds and truth start. Keep 36 perturbation trials and 18 truth-start checks separate. Parallel-plane degeneracy was checked in the preceding experiment; it is not rerun or counted in this sampler comparison. Archived bilinear results and source are hash-pinned, not rerun or included in new execution timing.

Change only depth sampling. At each candidate-transformed LiDAR point, form the continuous camera ray with z component one. Raycast the first surface of the known analytic scene from the corresponding camera origin, then add the fixed measurement offset. Compute LiDAR z minus this depth. Keep the original valid image domain (u in [0,width-1), v in [0,height-1), z>.1), unsupported penalty, point population, positive saturation and soft-L1. No point is filtered with true visibility by the sampler; all-return points behind the first camera surface retain large residuals. The favorable visible-only population is unchanged from preceding inputs.

The oracle sampler explicitly knows scene surfaces and camera origins and builds the biased measurement function using the injected offset. The optimizer sees only its residuals, never a target correction or true extrinsic. This separates interpolation from measurement geometry in a synthetic control, not a deployable estimator, independent dataset or evidence of real-data calibration accuracy. Do not mistake knowing how to generate biased measurements for estimating bias without measurements.

Seven-parameter fitting remains zero-initialized correction, ±.5 m bias bounds, original pose bounds/scales, ≤100 nfev / hard ≤800 actual calls, same support and raw/effective-robust sensitivity diagnostics. Pose recovery and joint recovery (bias error <.05 m and locally identifiable) use unchanged gates. Include every case, no retries or post-score settings changes. Record actual bias error even when a coarse joint gate passes. The analytic solver copy must have identical function definitions to the previous solver except its sampler import.

Decide from visible-only and all-return separately: whether the systematic offset shrinks, whether pose remains accurate and whether any residual occlusion bias or local degeneracy remains. The finite-difference rank check may change when image silhouette interpolation is removed; report it, do not relax rank gates. If results improve, investigate implementable discontinuity-aware sampling next rather than promoting an oracle. If they do not, retain asymmetric-objective mismatch as a live hypothesis instead of blaming bilinear interpolation by assumption.

PYTHONPATH=src:. OPENBLAS_NUM_THREADS=1 /workspace/work/p0-venv/bin/python \
  tools/evaluate_analytic_sampling.py docs/assets/analytic_sampling_20261029/plan.json \
  docs/assets/analytic_sampling_20261029/evaluation.json