refine: fit the direction of the goniometer axis, not its length

The residual applies angle_rad * |rot_vec| and rot_vec is a free three-vector, so the first pass has
been fitting a goniometer rotation SCALE nobody asked for. GoniometerAxis::Axis() then normalises it
away on write-back, and RotationIndexer scores the candidate with the normalised axis - so the cell
that won the fit is judged under a rotation model the fit did not use. Measured over 43 rotation
datasets: the length reaches 1.2%, and the fit-vs-score disagreement a median 0.124 deg and up to
6.19 deg of goniometer angle, against rocking widths of 0.05-0.36 deg. That score picks the lattice
class, which nothing later revisits.

The fitted length is not a usable measurement of anything either: on synthetic data it recovers 54%
of a known scale error, repeated first passes on one dataset disagree with each other in sign, 26 of
43 datasets disagree with themselves, and on the one dataset with a proven 1.3% stage fault it comes
out negative. It is absorbing other systematics. The rotation scale is measured properly, once, with
cross-validation and gates, in PostRefine.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EFEJG6WBQv8th4UJFNe53N

image_analysis/geom_refinement/XtalOptimizer.cpp

@@ -455,6 +455,18 @@ bool XtalOptimizerInternal(XtalOptimizerData &data,
 
             if (!data.refine_rotation_axis) {
                 problem.SetParameterBlockConstant(rot_vec);
+            } else {
+                // Only the DIRECTION of the goniometer axis is a parameter. The residual applies
+                // angle_rad * |rot_vec|, so a free three-vector also fits a rotation SCALE - which
+                // GoniometerAxis::Axis() then normalises away, leaving the candidate scored by
+                // RotationIndexer::accumulate() under a rotation model the fit did not use. Measured
+                // over the corpus, that length reached 1.2 % and the fit/score disagreement a whole
+                // degree of goniometer angle. It is not a usable measurement either: on synthetic
+                // data it recovers 54 % of a known scale error, repeated first passes on one dataset
+                // disagree with each other in SIGN, and on the one dataset with a real 1.3 % stage
+                // fault it comes out negative. The rotation scale is measured properly, once, with
+                // four gates and a jackknife, in PostRefine.
+                problem.SetManifold(rot_vec, new ceres::SphereManifold<3>);
             }
 
             if (!data.refine_unit_cell) {