perf(jacobian-action): major updates to jacobian action application by removing redudant quadrature work. ~5x increase in speed

experiments/README.md

@@ -147,3 +147,42 @@ 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
 next to that target; do not add them to the ordinary test executable.
+
+## P0 preconditioning baseline
+
+The P0 diagnostic establishes the unpreconditioned reference for the complete,
+central-density-closed `n = 3` stellar equilibrium Jacobian. It uses an identity
+inverse preconditioner with FGMRES, recomputes the true residual independently,
+records every residual block, and counts and times Jacobian and preconditioner
+applications. A separate fixed-operator Arnoldi measurement acts explicitly on
+the right-preconditioned product `J M^-1`. Its singular-value ratio is a
+projected Krylov-space condition proxy, not the condition number of the full
+Jacobian. The same output records Ritz values, clustering about one,
+nonnormality, and the real extent of the projected field of values.
+
+The extended baseline preserves the fixed 40-iteration FGMRES budget used by
+the original P0 run and increases the Arnoldi dimension from 12 to 48. It writes
+the complete reported FGMRES residual history, block-relative and
+manifest-scaled final residuals, the fraction of the squared residual in each
+physics block, timings for construction/projection/preparation/direct-residual
+measurement, and separate Arnoldi operator and orthogonalization timings. Live
+progress messages delimit every expensive phase and report every fourth
+Arnoldi application. The CSV records whether it came from a Debug or Release
+build.
+
+Run the focused synthetic verification tests with:
+
+```text
+./cmake-build-debug-homebrew/tests "[preconditioning][diagnostics][unit]"
+```
+
+Run the performance and spectral measurement separately with:
+
+```text
+mpirun -np 1 ./cmake-build-release-homebrew/experiments \
+    --experiment-output preconditioning_p0_identity_extended.csv \
+    --catch2 "[preconditioning][diagnostics][baseline]"
+```
+
+Set `MEANFIELD_SINGLE_JACOBIAN_BENCHMARK=1` to stop after the initial prepared
+Jacobian timing instead of running FGMRES and Arnoldi.