Lattice search: gate the type-boundary retry on the boundary, not on the metric tolerance

The retry added in the previous commit was unreachable - character 44 fits any cell, so the match
always succeeds and "nothing fits" arrives as a triclinic answer, not as no answer. Retry on a
triclinic answer instead, and only replace it when the second attempt finds a real class.

That makes the gate matter, and the angle tolerance is the wrong one to use for it. It says how far
a metric may sit from an ideal one and still be called it; the question here is whether the two
Niggli types are interchangeable at all, which they are only when the reduced beta is 90. Two
degrees off the boundary is a real type-1 cell, and presenting it in the obtuse setting promotes a
general triclinic lattice to C-centred monoclinic on residuals of about two degrees - which is what
happened to the triclinic case in the unit tests. Half a degree separates that from the crystal this
was found on, which sits 0.07 degrees from the boundary and matches on 0.006 to 0.135.

With the retry reachable and gated, that crystal's lattice comes out C-centred monoclinic from the
first pass at every geometry tried, including the one where its cell reduces to the acute setting
and the run used to merge in P1.

image_analysis/lattice_search/LatticeSearch.cpp

@@ -8,6 +8,15 @@
 #include <cmath>
 #include <optional>
 
+// How close the reduced beta has to be to 90 degrees for the two Niggli types to be genuinely
+// interchangeable (see the retry at the end of LatticeSearch). Not the angle tolerance: that is how
+// far a metric may sit from an ideal one and still be called it, which is far too generous here - a
+// cell 2 degrees off the boundary is a real type-1 cell, and presenting it in the obtuse setting
+// promotes a general triclinic lattice to C-centred monoclinic on residuals of ~2 degrees. Measured:
+// the crystal this was found on sits 0.07 degrees from the boundary and matches on 0.006 to 0.135;
+// the triclinic cell that must not be promoted sits 2.0 degrees from it.
+constexpr double NIGGLI_TYPE_BOUNDARY_DEG = 0.5;
+
 struct NiggliClass {
     int number;
     int type;
@@ -352,10 +361,12 @@ LatticeSearchResult LatticeSearch(const CrystalLattice &L, double dist_tolerance
         return std::nullopt;
     };
 
-    if (auto found = match(L_niggli, D, E, F))
+    // Character 44 fits any cell, so a match is always found - "nothing fits" is reported as triclinic.
+    auto found = match(L_niggli, D, E, F);
+    if (found && found->system != gemmi::CrystalSystem::Triclinic)
         return *found;
 
-    // A reduced cell whose beta is 90 to within the angle tolerance sits ON the boundary between the two
+    // A reduced cell whose beta is 90 to within NIGGLI_TYPE_BOUNDARY_DEG sits ON the boundary between the two
     // Niggli types: the same lattice reduces to an all-acute cell or an all-obtuse one according to the
     // last digits of whatever refinement produced it. The type-1 characters are skipped for such a cell
     // (just above) and the type-2 ones are stated for the obtuse setting, so an acute cell can match none
@@ -363,12 +374,16 @@ LatticeSearchResult LatticeSearch(const CrystalLattice &L, double dist_tolerance
     // and c keeps the lattice and beta and turns alpha and gamma into their supplements. Measured on a
     // C-centred monoclinic crystal whose reduced beta sits 0.07 deg from 90: its centring was read or
     // missed according to the sign of that 0.07 deg, and with it the space group of the whole run.
-    if (L_niggli.GetUnitCell().beta >= 90 - angle_tolerance && D > 0 && E > 0 && F > 0) {
+    if (L_niggli.GetUnitCell().beta >= 90 - NIGGLI_TYPE_BOUNDARY_DEG && D > 0 && E > 0 && F > 0) {
         const gemmi::Mat33 obtuse(-1, 0, 0, 0, 1, 0, 0, 0, -1);
-        if (auto found = match(L_niggli.Multiply(obtuse), -D, E, -F))
-            return *found;
+        const auto flipped = match(L_niggli.Multiply(obtuse), -D, E, -F);
+        if (flipped && flipped->system != gemmi::CrystalSystem::Triclinic)
+            return *flipped;
     }
 
+    if (found)
+        return *found;
+
     return LatticeSearchResult{
         .niggli_class = 44,
         .primitive_reduced = L_niggli,