Bragg integration: drop the 2% sigma floor and carry the background variance

Two changes to the same variance chain; they are in one commit because the second
exists to remove an assumption the first was breaking, and separating them leaves a
tree that is correct only by luck.

The reported sigma was floored at 2% of the intensity, a per-partial I/sigma cap of
50. It applied only to the box-sum seed, never to the profile fit, so the shipped
default was unaffected - but the combine back-derives each partial's non-signal
variance as sigma^2 - I, and a floored sigma makes that quantity mean nothing. It
then read corr^2 * (0.0004 I^2 - I), which is not a background variance. Measured on
--integrator boxsum: the reported sigma understated the true scatter by up to 16x at
I ~ 21000 counts per partial, and pooled_I amplified a 1 ct/px background drift into
an 11.5% intensity error on the strongest reflections.

What the floor stood in for - that at high intensity the error is systematic rather
than counting - is already carried downstream, twice: the fitted b in
v = a*sigma^2 + (b*I)^2, measured from the data rather than assumed, and
SigmaWithSystematicFloor on the merged sigma. The floor was that idea applied one
level too early with a hardcoded b of 0.02. It arrived without a test or a setter and
was unreachable from the CLI, the API and the config.

The merge now takes the non-signal variance the integrator actually measured instead
of inverting sigma^2 = I + N. That identity is exact for a box sum once the floor is
gone and was never exact for a profile fit, whose sigma^2 = 1/den + (wsum/den)^2 *
bkg_var is formed against a fitted intensity. The value is carried through
BraggFitResult, Reflection and Obs, both engines, both merges, and the process-file
round trip; files written before this change are read with the term absent, which is
what they had.

Battery, 37 crystals, paired: space groups unchanged, reflection sets unchanged,
median delta zero on R_meas and CC1/2. --integrator boxsum on the reference crystal
goes ISa 8.9 -> 20.2 with a 0.947 -> 1.032.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

writer/HDF5DataFilePluginReflection.cpp

@@ -16,7 +16,8 @@ void HDF5DataFilePluginReflection::Write(const DataMessage &msg, uint64_t image_
 
     std::vector<int32_t> h, k, l;
     std::vector<float> I, sigma, d, lp;
-    std::vector<float> image, phi, pred_x, pred_y, obs_x, obs_y, bkg, partiality, zeta, scale_factor;
+    std::vector<float> image, phi, pred_x, pred_y, obs_x, obs_y, bkg, var_bkg, partiality, zeta,
+            scale_factor;
 
     h.reserve(msg.reflections.size());
     k.reserve(msg.reflections.size());
@@ -29,6 +30,7 @@ void HDF5DataFilePluginReflection::Write(const DataMessage &msg, uint64_t image_
     obs_x.reserve(msg.reflections.size());
     obs_y.reserve(msg.reflections.size());
     bkg.reserve(msg.reflections.size());
+    var_bkg.reserve(msg.reflections.size());
     lp.reserve(msg.reflections.size());
     partiality.reserve(msg.reflections.size());
     image.reserve(msg.reflections.size());
@@ -49,6 +51,7 @@ void HDF5DataFilePluginReflection::Write(const DataMessage &msg, uint64_t image_
         obs_x.emplace_back(refl.observed_x);
         obs_y.emplace_back(refl.observed_y);
         bkg.emplace_back(refl.bkg);
+        var_bkg.emplace_back(refl.var_bkg);
         lp.emplace_back(1.0/refl.rlp);
         partiality.emplace_back(refl.partiality);
         phi.emplace_back(refl.delta_phi_deg);
@@ -71,6 +74,7 @@ void HDF5DataFilePluginReflection::Write(const DataMessage &msg, uint64_t image_
     image_group.SaveVector("int_sum", I);
     image_group.SaveVector("int_err", sigma);
     image_group.SaveVector("background_mean", bkg);
+    image_group.SaveVector("background_variance", var_bkg);
     image_group.SaveVector("observed_frame", image);
     image_group.SaveVector("lp", lp);
     image_group.SaveVector("partiality", partiality);