feat(surface): major work on implementing surface constraints in a presciption agnostic manner

experiments/README.md

@@ -24,6 +24,49 @@ Run only the budget and choose its output path with:
 ./mean_field_experiments --experiment-output gravity_budget.csv --catch2 "[accuracy]"
 ```
 
+## Stellar-equilibrium null-space experiments
+
+`stellar_null_space_experiments` is a dedicated diagnostic executable rather
+than an ordinary verification or validation test. It constructs the analytic
+`n = 3` Lane-Emden seed, probes the three computational translations and three
+computational rotations, and compares the Jacobian before and after the strong
+centering-row replacement. It records total and residual-block response norms,
+the isolated centering contribution, and centered finite-difference errors.
+
+The experiment prints rank-zero progress messages while it builds the seed,
+solves its gravity field, and completes each rigid-mode case. Run it with:
+
+```text
+mpirun -np 1 ./cmake-build-debug-homebrew/stellar_null_space_experiments \
+    --experiment-output stellar_null_space.csv \
+    --catch2 "[null_space][rigid_motion]"
+```
+
+The rotation sweep includes zero rotation and a spherical-state diagnostic at
+half the Keplerian angular speed. The rotating result is an operator-symmetry
+probe, not a definitive rotating-equilibrium null-space measurement.
+
+The gravity-completed probe solves the linearized mixed gravity subsystem for
+the gravity-gradient and gravity-potential variations accompanying each rigid
+displacement. It then measures the complete equilibrium response with and
+without the centering rows:
+
+```text
+mpirun -np 1 ./cmake-build-debug-homebrew/stellar_null_space_experiments \
+    --experiment-output gravity_completed_null_space.csv \
+    --catch2 "[null_space][gravity_completed]"
+```
+
+The gravity solver prints its convergence summary, while the experiment prints
+the current mode and completed-case count. This probe prepares each rotation
+state only once and does not repeat the expensive nonlinear finite-difference
+calculations from the original rigid-motion diagnostic.
+
+A whole-Jacobian dense singular-value experiment is intentionally deferred.
+The checked-in `sandbox.smesh` is too large for a useful dense SVD, and the
+current matrix-free root operator does not provide a transpose action needed by
+a scalable smallest-singular-value method.
+
 The executable needs the same dependencies, generated module mapping, and
 configuration registration as the existing Catch2 test executable. Add
 `experiment_main.cpp` and `gravity_accuracy_budget.cpp` as a second executable