Radial background: one mechanism for stills and rotation, decided per run on empty apertures (D5)

Wherever the correction is set for the whole run its curve is the frame's peak-excluded ring
background (the adaptive spot finder's, whole frame) and the ring's clip follows it - as stills have
done since integ-pal - now rotation too. One empty-aperture measurement (BackgroundAperture) decides
it for both workflows:

- The apertures' corrected difference is now taken as the integrator applies the correction: the
  clip follows the curve (each ring pixel's threshold raised by the curve's rise from the centre, in
  whole counts) as well as the kernel correction. Before, the tally clipped flat, so it measured a
  correction the engine never applies.
- Rotation measures the stencils the spot width can give it (r1 = 4, 5, 6 with the ring-area rule,
  RotationStencil) and decides on the one it gets, and separately on the pre-adaptive stencil the
  geometry pre-pass and the starvation guard return to.
- Stills: on wherever the corrected ring predicts the empty disk better (unchanged rule).
  Rotation: the frame's curve on every image only where it takes >= 10% of the apertures' mean
  square error away (ROTATION_RADIAL_MIN_GAIN); otherwise the existing per-image ice gate with the
  reflections' curve is left exactly as it was. Why a margin on rotation only: a still has no other
  correction, a sweep has one. Measured over 18 rotation sets (forced on every image): photon-counting
  sweeps gain 0.1-5% on the apertures (z 3-4) and lose ISa/anomalous signal when corrected
  (insulin, lysozyme, cytochrome c; 9yzk R-free +0.009 at 1.2%), as the earlier stills-rule trial
  found; the home-source CCD and smooth-ice runs gain 13-31%.

Result (CPU A/B vs 87684012f, 18 rotation sets): 12 .hkl byte-identical (every photon-counting
control without ice), 5uth R-free 0.210 -> 0.201 / ISa 10.4 -> 10.8, the ice set neutral; stills:
lcls242_s turns the correction on (the clip-following tally), R-free 0.2399 -> 0.2406.
No integration kernel changed; the tally is host code. Tests: BackgroundAperture_CorrectedClipFollowsTheCurve,
RadialHelps margins.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_015CeEGgpKdfkCTJb3YNMJcu
(cherry picked from commit dd3f3f2da39f5338e7dda1874bbdd535229bce98)

rugnux/rugnux_cli.cpp

@@ -255,7 +255,7 @@ void print_usage() {
     std::cout << "   --integration-high-resolution <num> High resolution limit for prediction/integration. If omitted (or 0), integration extends as far as the detector reaches" << std::endl;
     std::cout << "   --max-hkl <n>                   Predict reflections with |h|,|k|,|l| <= n. Default: derived per crystal from the refined cell (ceil(longest axis / d_min) + 1), which is the exact bound - set it only to override that" << std::endl;
     std::cout << "   --background-clip <n>           High-side clip of the background ring at mean + n*sqrt(mean) (default 4; 0 = off). This is the default background estimator - it rejects neighbour cores and zingers without the symmetric trim's Poisson skew bias. Ignored by --integrator boxsum" << std::endl;
-    std::cout << "   --background-radial[=on|off|auto] Correct the background ring for the CURVATURE of the radial background (default auto). The signal disk and the background ring are concentric, so a background linear in position cancels between them and only curvature survives - which on a smooth ice ring reaches +26 counts on a single reflection. =auto applies it per image where that image's ice score shows a smooth powder ring, which is where a radius-only background model holds; on ice made of discrete crystallite spots there is no such ring and the correction makes the bias worse. On stills the curve is taken from the spot finder's peak-excluded background of the whole frame, and =auto applies it to every image of a run where it makes the background ring predict the background of empty apertures better (measured in the pre-scan): a smooth solvent or carrier hump curves the background as much as ice does. Costs one short dot product per reflection and no extra pixel reads" << std::endl;
+    std::cout << "   --background-radial[=on|off|auto] Correct the background ring for the CURVATURE of the radial background (default auto). The signal disk and the background ring are concentric, so a background linear in position cancels between them and only curvature survives - which on a smooth ice ring reaches +26 counts on a single reflection. Where it is on, the curve is the spot finder's peak-excluded background of the whole frame, and the ring's outlier clip follows it, so a background falling steeply from the beam is not cut as outliers. =auto decides it per run in the pre-scan, on empty apertures of the pre-scan frames: on stills it is applied to every image where it makes the background ring predict the background of empty apertures better at all (a smooth solvent or carrier hump curves the background as much as ice does); on rotation data it is applied to every image where it takes at least 10% of that error away, and otherwise only to the images whose ice score shows a smooth powder ring, with the curve from the reflections' own rings (ice made of discrete crystallite spots leaves no such ring, and the correction makes the bias worse). Costs one short dot product per reflection and no extra pixel reads" << std::endl;
     std::cout << "   --background-trim <f>           Use the old symmetric trimmed mean for the background ring instead of the clip (0<=f<0.5; 0.10 was the former default). Switches --background-clip off. A symmetric trim is biased low on Poisson data and adds ~5 counts to every partial, so this is for back compatibility only; 0 = plain ring mean" << std::endl;
     std::cout << "   --overlap <txt>                 What to do where two predicted reflections share signal pixels: off|reject|exclude (default exclude). A pixel inside two signal disks belongs to the nearer centre; before this, nothing kept a neighbour's flux out of a reflection's own disk, so on a dense pattern a crowded reflection read high. exclude drops the shared PIXELS from the profile fit, which renormalises itself, so the reflection is kept; reject instead drops the whole reflection when less than --overlap-minpk of its expected profile is cleanly its own (what XDS calls MINPK). --integrator boxsum has no profile to renormalise with, so exclude does nothing there and only reject acts" << std::endl;
     std::cout << "   --overlap-minpk <f>             Least fraction of a reflection's expected profile that must be usable for the reflection to be kept (default 0.75, XDS MINPK). Governs both ways part of a profile is lost: the fraction that must be READABLE - not masked, untrusted, in a detector gap or overloaded - in every profile mode, and, under --overlap reject, the fraction that must be cleanly the reflection's own. --integrator boxsum has no profile to renormalise with, so there a signal disk with any unreadable pixel is still discarded outright and the reject fraction is by disk AREA, which cuts harder" << std::endl;
@@ -3439,7 +3439,7 @@ static int RunRugnux(int argc, char **argv, bool no_gpu) {
         logger.Info("Background ring: radial curvature correction {}",
                     radial.has_value() ? (*radial ? "on" : "off")
                                        : rotation_indexing
-                                             ? "auto (per image, where the ice score sees a smooth ring)"
+                                             ? "auto (decided in the pre-scan on empty apertures; otherwise per image, where the ice score sees a smooth ring)"
                                              : "auto (decided in the pre-scan on empty apertures; the curve from the whole frame)");
     }