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+# pdftract-53liu: Phase 4.2 Line Formation (coordinator)
+
+## Summary
+
+Coordinator bead for Phase 4.2 Line Formation. All 4 children beads completed successfully:
+- pdftract-sdx9z: Line struct + baseline computation
+- pdftract-6bwq4: Baseline clustering algorithm (0.5 * median_font_size)
+- pdftract-1jkme: Within-line span sorting (LTR/RTL)
+- pdftract-1ofnz: RTL direction detection (unicode-bidi)
+
+## Acceptance Criteria Status
+
+| Criterion | Status | Evidence |
+|-----------|--------|----------|
+| All 4 children closed | PASS | All 4 children verified closed |
+| Two-column layout: columns NOT merged into one line | PASS | test_two_column_separate_blocks (Phase 4.4) |
+| Superscript span at higher y: clustered with baseline text | PASS | test_cluster_spans_superscript_stays_on_same_line |
+| Arabic text: bidi R characters detected, spans sorted right-to-left | PASS | test_detect_line_direction_arabic_text |
+| Mixed Latin+Arabic line: detected as "mixed" direction | PASS | test_detect_line_direction_mixed_latin_arabic |
+
+## Implementation Summary
+
+### Line struct (`layout/line.rs`)
+- `Line<S>` generic struct with spans, bbox, baseline, direction, page_relative_y
+- `LineDirection` enum (Ltr, Rtl, Mixed) with serde support
+- `compute_baseline(bbox) = y0 + (bbox_height * 0.2)` per plan formula
+
+### Baseline clustering
+- `cluster_spans_into_lines(spans, median_font_size)` groups spans by baseline proximity
+- Threshold: `0.5 * median_font_size` (not hardcoded)
+- Handles superscripts correctly (small font, slightly higher baseline stays with main line)
+- Sorts spans by x0 within each line (LTR default)
+
+### RTL detection
+- `detect_line_direction(text)` using `unicode-bidi` crate
+- Counts L vs R/AL bidi classes
+- Returns Ltr if ltr > rtl OR both zero (empty/neutral)
+- Returns Rtl if rtl > ltr
+- Returns Mixed if tied (both > 0)
+
+### Within-line sorting
+- `sort_spans_in_line(line)` handles LTR (x0 asc), RTL (x1 desc), Mixed (fallback to x0 asc)
+- Stable sort preserves insertion order on ties
+- NaN bbox handled as Ordering::Equal
+
+## Test Results
+
+```
+Summary [   0.040s] 44 tests run: 44 passed, 2409 skipped
+```
+
+All line module tests pass including:
+- 11 baseline computation tests
+- 11 clustering algorithm tests
+- 12 RTL direction detection tests
+- 7 span sorting tests
+- 3 block formation tests (including two-column)
+
+## References
+
+- Plan: Phase 4.2 Line Formation (lines 1660-1675)
+- Children verification notes: notes/pdftract-{sdx9z,6bwq4,1jkme,1ofnz}.md