brush-paint-opt: lex-rank structural fails above bg-rate fail

Reorder tier-1 from (cov, bg, 1stk, 2stk, len) to (cov, 1stk, 2stk,
len, bg). Previous run found the comparator preferred a tiny-brush
config (bg fails 4 vs 7) over a structurally-correct one
(1stk fails 11 vs 38, len-budget fails 0 vs 104). bg-rate is an
aesthetic — wrong stroke counts and wandering paths break the
glyph's topology, so they outrank.

Mirrored in the jq sort in scripts/meta_optimize_distributed.sh.

scripts/meta_optimize_distributed.sh

@@ -108,16 +108,16 @@ if [[ "$LINES" -ne "$N" ]]; then
 fi
 
 # Lex-sort matching CorpusReport's compare_reports:
-#   tier-1: fail_coverage, fail_bg, fail_single_stroke, fail_two_stroke, fail_length_budget
+#   tier-1: fail_coverage, fail_single_stroke, fail_two_stroke, fail_length_budget, fail_bg
 #   tier-2: total_bg, total_strokes, total_unpainted_density, total_repaint, total_length
 echo "" >&2
 echo "[orch] top 5 by lex order:" >&2
 jq -s 'sort_by([
   .report.fail_coverage,
-  .report.fail_bg,
   .report.fail_single_stroke,
   .report.fail_two_stroke,
   .report.fail_length_budget,
+  .report.fail_bg,
   .report.total_bg,
   .report.total_strokes,
   .report.total_unpainted_density,
@@ -129,10 +129,10 @@ echo "" >&2
 echo "[orch] best (full JSON on stdout):" >&2
 jq -s 'sort_by([
   .report.fail_coverage,
-  .report.fail_bg,
   .report.fail_single_stroke,
   .report.fail_two_stroke,
   .report.fail_length_budget,
+  .report.fail_bg,
   .report.total_bg,
   .report.total_strokes,
   .report.total_unpainted_density,

src/brush_paint_opt.rs

@@ -253,15 +253,21 @@ pub fn run_one_start(start_idx: usize, base: &PaintParams, max_passes: u32) -> R
 //
 // Tier 1 — count of letters violating each hard criterion:
 //   1. max unpainted cluster > 0.5 × brush_area   (a feature is missing)
-//   2. bg_painted / total_swept > 5 %
+//   2. SINGLE_STROKE_LETTERS with strokes ≠ 1     (wrong topology)
-//   3. SINGLE_STROKE_LETTERS with strokes ≠ 1
+//   3. TWO_STROKE_LETTERS    with strokes ≠ 2     (wrong topology)
-//   4. TWO_STROKE_LETTERS with strokes ≠ 2
+//   4. total_length > 2 × skeleton_length          (wandering path)
-//   5. total_length > 2 × skeleton_length
+//   5. bg_painted / total_swept > 5 %             (off-glyph paint)
+//
+// Order rationale: structural correctness (cluster coverage, stroke
+// topology, path budget) ranks above aesthetic cleanliness (off-glyph
+// paint). A previous run found the comparator was preferring
+// tiny-brush configs that minimised bg paint at the cost of doubling
+// stroke counts and 5×ing path length — bg sat at the wrong tier.
 //
 // Tier 2 — corpus aggregates (smaller is better, in this order):
 //   6. total bg pixels
 //   7. total stroke count
-//   8. total density-weighted unpainted (Σ size^1.5)
+//   8. total density-weighted unpainted (exponential per-cluster)
 //   9. total repaint
 //  10. total length
 
@@ -350,11 +356,12 @@ pub fn compare_reports(a: &CorpusReport, b: &CorpusReport) -> Ordering {
         }
     }; }
     // Tier 1: count of letters failing each hard criterion.
+    // Structural fails first; bg-rate last (a soft aesthetic).
     cmp_field!(fail_coverage);
-    cmp_field!(fail_bg);
     cmp_field!(fail_single_stroke);
     cmp_field!(fail_two_stroke);
     cmp_field!(fail_length_budget);
+    cmp_field!(fail_bg);
     // Tier 2: aggregates.
     cmp_field!(total_bg);
     cmp_field!(total_strokes);