RESULT-CHANGING: LatticeSearch takes Le Page's class over the table's only for a length-equality class

3c001eb7a let the metric two-folds (Le Page, obliquity up to 1 deg) override the
Niggli character table wherever they found a richer class. The motivating case -
an F-cubic lattice whose degenerate shortest vectors give the table a reduced cell
it reads as I-tetragonal - is a class that equates lengths. For a class carried by
its angles alone (monoclinic, orthorhombic) the override instead promoted
pseudo-symmetric metrics the table had refused:

- a monoclinic small-molecule set (twin-composite pass): mC/mP -> oC at 0.3-0.9 deg
  obliquity; ISa 46.4 -> 16.7, R_meas 4.2 -> 4.9 %, SHELXL R1 0.049 -> 0.066
- a monoclinic protein, two in-house sets: mP -> oC at 0.2-1.0 deg; the beam-centre
  check then compared different classes at the two centres; ISa 3.6 -> 2.4,
  CC1/2 0.98 -> 0.45 on one, R_meas 68 -> 135 % on the other
- a triclinic crystal with a pseudo-I-orthorhombic metric: aP -> oI at 0.5 deg
  at the file's centre, and the run merged at a markedly lower ISa and resolution

Obliquity does not separate these from the F-cubic case (its unrefined cells
promote at up to 1 deg too), so the line is drawn on the class: Le Page's answer
is taken only where its class is tetragonal, trigonal, hexagonal or cubic. The
F-cubic set keeps F432 (ISa 7.7, R_meas 13.2 %, unchanged); the three regressions
return to their rc184 numbers.

Guard sets (open + in-house, 26) against rc186-merge: 20 identical; cytidine,
2wnn and myob_x10sa return to their rc184 numbers (differences in the third
digit); 2wnq returns to rc184's C2221 (R-free 0.547) from P21212 (0.444) - the
deposition is P21, so both fail.

The synthetic gains 3c001eb7a measured for oC/oI (monoclinic under-calls of
centred orthorhombic lattices) are given back; cF, hP, hR, tI are kept.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01HVeDQsU5a8AJUdJPgWevAK

image_analysis/lattice_search/LatticeSearch.cpp

@@ -480,10 +480,19 @@ std::optional<LatticeSearchResult> SearchCharacters(const CrystalLattice &L, dou
     // class than the table, take it - held to this call's own tolerances, so a search that grants no
     // length equality still grants none.
     //
+    // Only for a class that equates lengths (tetragonal, trigonal, hexagonal, cubic): those are the
+    // lattices whose degenerate shortest vectors give the table more than one reduced cell. A class
+    // carried by its angles alone the table reads on any of them, and where it refuses one the
+    // two-folds would grant, the angle is not there: measured on monoclinic crystals with
+    // pseudo-orthorhombic metrics (and a triclinic one with a pseudo-I-orthorhombic one), Le Page
+    // promoted at 0.2-1 deg obliquity, the constrained cell was integrated and every one merged
+    // worse (ISa 46 -> 17 on one, CC1/2 0.98 -> 0.45 on another).
+    //
     // A tetragonal or cubic cell refused only on its length equality is, on its angles alone, the
     // orthorhombic lattice of the same centring in the same basis - the class a search granting no
     // length equality has to return, as the table did for the settings it could read.
-    if (auto lp = LePageLattice(L, std::min(angle_tolerance, LATTICE_MAX_OBLIQUITY_DEG))) {
+    if (auto lp = LePageLattice(L, std::min(angle_tolerance, LATTICE_MAX_OBLIQUITY_DEG));
+        lp && ClassImposesLengthEquality(lp->system)) {
         const auto [angle, length] = ClassMetricDeparture(lp->conventional.GetUnitCell(), lp->system);
         if (length > dist_tolerance && (lp->system == gemmi::CrystalSystem::Tetragonal
                                         || lp->system == gemmi::CrystalSystem::Cubic))