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>

image_analysis/scale_merge/Merge.cpp

@@ -82,7 +82,7 @@ void MergeOnTheFly::AddImage(const IntegrationOutcome &outcome, int64_t image_id
             continue;
         auto hkl = generator(r);
         auto hkl_key = hkl.pack();
-        sigma_corr = CorrectedSigma(I_corr, sigma_corr, r.image_scale_corr, hkl_key);
+        sigma_corr = CorrectedSigma(I_corr, sigma_corr, r.image_scale_corr, r.var_bkg, hkl_key);
 
         // Robust outlier rejection: drop this observation if it sits more than
         // reject_nsigma error-model sigmas from the reflection's median. Needs the active
@@ -121,6 +121,7 @@ void MergeOnTheFly::AddImage(const IntegrationOutcome &outcome, int64_t image_id
 }
 
 float MergeOnTheFly::CorrectedSigma(float I_corr, float sigma_corr, float image_scale_corr,
+                                    float var_bkg,
                                     uint64_t hkl_key) const {
     if (!error_model_active)
         return sigma_corr;
@@ -144,8 +145,7 @@ float MergeOnTheFly::CorrectedSigma(float I_corr, float sigma_corr, float image_
     // observations this correction exists to stop being mistreated.
     double a_var = static_cast<double>(sigma_corr) * sigma_corr;
     if (scaling_settings.GetExpectedVarianceMerge()) {
-        const double bkg_var = std::max(0.0, a_var - static_cast<double>(image_scale_corr)
-                                                     * std::max(0.0, static_cast<double>(I_corr)));
+        const double bkg_var = static_cast<double>(image_scale_corr) * image_scale_corr * var_bkg;
         const double base = bkg_var + static_cast<double>(image_scale_corr) * std::max(0.0, I_for_b);
         if (base > 0.0)
             a_var = base;