[nearby]
Initial nearest-point RMSE: 0.562084 m
After one update: 0.432199 m
Final pose: 20.000000 deg, (0.600000, -0.200000) m
Final nearest-point RMSE: 0.000000 m
Reference pose errors: 0.000000 m, 0.000000 deg
Stop: Step tolerance reached (iteration 4)

[bad-start]
Initial nearest-point RMSE: 0.695486 m
After one update: 0.466319 m
Final pose: 148.866330 deg, (0.539248, -0.601187) m
Final nearest-point RMSE: 0.366997 m
Reference pose errors: 0.405761 m, 128.866330 deg
Stop: Step tolerance reached (iteration 5)

[symmetric]
Initial nearest-point RMSE: 0.000000 m
After one update: 0.000000 m
Final pose: -160.000000 deg, (0.600000, -0.200000) m
Final nearest-point RMSE: 0.000000 m
Reference pose errors: 0.000000 m, 180.000000 deg
Stop: Step tolerance reached (iteration 1)

Checks passed: fixed-pair fit, composition, ties, degeneracy, and all three cases.