rugnux: decide whether there is a lattice on distinct reflections, against every wrong angle

The first pass's last gate - is the lattice this crystal's at all - compared the validation spots
on the lattice with the median of five displaced-spindle-angle nulls, against the null's binomial
noise floored at one spot. On the two in-house no-crystal controls it is fed a handful of genuine
stray reflections from something rotating with the sample (the same detector positions, a pair
symmetric about the beam 198 frames apart, in both sweeps, offset by the 15-frame start difference),
plus one reflection near the spindle axis that stays in diffraction for ~46 frames. With the
decisions taken from the first part of the sweep the 60 validation frames are 3 deg apart instead
of 6, so that one reflection is counted on three validation frames, and the gate passed on
4 spots of 151 (null median 0) and 7 of 72, where the whole-sweep flow had seen 3 and 3.

Now the evidence unit is the distinct Miller index - a reflection on several validation frames
is one piece of evidence - and the test uses every displaced angle's count: with no crystal the
recorded angles are one of six exchangeable arrangements, so the gate is the binomial tail of the
recorded arrangement's share at p = 1/6, at the same 0.001 significance (SPOT_BUDGET_SIGNIFICANCE_Z).
No threshold is added; the median and the one-spot floor go from the gate. The comparisons between
lattices (ValidationEvidencePrefers) are unchanged.

  no-crystal control 1: 4 distinct vs 2 over 5 wrong angles, tail 0.009 -> no lattice (was P 1)
  no-crystal control 2: 5 distinct vs 2, tail 0.002 -> no lattice (was P 1)
p.mtz md5 identical to rc175 7c9a6c7d1 (GPU) on 5nw5, 5reo, 7atg, 8v4o, 9qw8, 9rci, 5ky6,
insu_I_x06da_low_isa, myob_x06da_powder_2; cytidine and myob_x06da_split pass. The weakest real
lattice in the open/in-house/private battery logs has 117 spots against a null of 0.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01SVmAWnzCmRKAXVUCdc4iNi

tests/RotationScaleWalkTest.cpp

@@ -134,3 +134,16 @@ TEST_CASE("ChooseLogScaleSmoothing_SmoothsNoiseFollowsSignal", "[RotationScale]"
     CHECK(wave[47] == Catch::Approx(step[47]).margin(0.01));
     CHECK(l_wave < l_noise);
 }
+
+TEST_CASE("ValidationEvidenceBeatsChance_ExchangeableArrangements", "[RotationScale]") {
+    // Four reflections taken at the recorded angles and none at any wrong one: (1/6)^4 < 0.001.
+    CHECK(ValidationEvidenceBeatsChance({.reflections = 4, .reflections_by_chance = 0}));
+    CHECK_FALSE(ValidationEvidenceBeatsChance({.reflections = 3, .reflections_by_chance = 0}));
+    // The same four with two more spread over the wrong angles is what chance does once in ~100.
+    CHECK_FALSE(ValidationEvidenceBeatsChance({.reflections = 4, .reflections_by_chance = 2}));
+    CHECK_FALSE(ValidationEvidenceBeatsChance({}));
+    // A real lattice: thousands against a handful.
+    CHECK(ValidationEvidenceBeatsChance({.reflections = 3000, .reflections_by_chance = 250}));
+    // As many at the recorded angles as at an average wrong one is no lattice.
+    CHECK_FALSE(ValidationEvidenceBeatsChance({.reflections = 100, .reflections_by_chance = 500}));
+}