`gwstrain` STF projection subtracts only diagonal element instead of full trace

Summary

In Castro::gwstrain, the symmetric trace-free (STF) projection is documented as
STF(A^{ij}) = 1/2 A^{ij} + 1/2 A^{ji} - 1/3 delta^{ij} sum_k A^{kk}, but the implementation subtracts only dQtt(m,m) for each diagonal component. This does not remove the full trace and yields an incorrect STF tensor.

Location

• Source/driver/sum_utils.cpp:476
• Source/driver/sum_utils.cpp:486

Problem Details

Current code:

dQ(l,m) = 0.5_rt * dQtt(l,m) + 0.5_rt * dQtt(m,l);
if (l == m) {
    dQ(l,m) -= (1.0_rt / 3.0_rt) * dQtt(m,m);
}

For diagonal entries, the subtraction must use the full trace
dQtt(0,0) + dQtt(1,1) + dQtt(2,2), not the single matching diagonal element.

Impact

• Incorrect gravitational-wave quadrupole STF tensor.
• Biased h_plus / h_cross diagnostics, especially when anisotropy is significant.

Suggested Patch

diff --git a/Source/driver/sum_utils.cpp b/Source/driver/sum_utils.cpp
--- a/Source/driver/sum_utils.cpp
+++ b/Source/driver/sum_utils.cpp
@@
-            for (int l = 0; l < 3; ++l) {
+            const Real tr = dQtt(0,0) + dQtt(1,1) + dQtt(2,2);
+
+            for (int l = 0; l < 3; ++l) {
                 for (int m = 0; m < 3; ++m) {
                     dQ(l,m) = 0.5_rt * dQtt(l,m) + 0.5_rt * dQtt(m,l);
                     if (l == m) {
-                        dQ(l,m) -= (1.0_rt / 3.0_rt) * dQtt(m,m);
+                        dQ(l,m) -= (1.0_rt / 3.0_rt) * tr;
                     }
                 }
             }

Prepared by Codex

Start in Source/driver/sum_utils.cpp at lines 476 and 486, where Castro::gwstrain constructs the symmetric trace-free tensor. Compare the implementation with the documented STF formula and inspect the diagonal calculation. Done means the computed tensor removes the complete three-dimensional trace and preserves the intended h_plus and h_cross diagnostics.