feat(core): 일체기초 footings for 2·3주형 with per-footing pile grid

- Columns closer than one footing length (10400) share a 일체기초 whose
  length is the outer-column distance + 10400, centred between them (spec §4.6).
- Pile grid is computed from each footing's length (rows across 8150,
  pile count along the length from (length − 1400) / 2250 + 1).
- Blinding concrete follows each combined footing.

Co-Authored-By: Claude Haiku 5.5 <noreply@anthropic.com>

tests/validate-and-foundation.test.ts

@@ -106,3 +106,27 @@ describe('bearing and block checks (spec §10 W03, W04)', () => {
     expect(issues.map((i) => i.code)).toContain('W04');
   });
 });
+
+describe('일체기초 (spec §4.6)', () => {
+  it('2주형 L 12000: columns 7200 apart share one footing of 17600 with 4 × 8 piles', () => {
+    const m = buildPier({ ...loadP1(), type: '2주형', columnCount: 2, copingLengthMm: 12000, foundationType: '말뚝기초' });
+    expect(m.footings).toHaveLength(1);
+    expect(m.footings[0].length).toBeCloseTo(17.6, 6);
+    expect(m.footings[0].s).toBeCloseTo(6.0, 6);
+    expect(m.blindings[0].length).toBeCloseTo(17.8, 6);
+    expect(m.piles).toHaveLength(32);
+    expect(m.derived.pileLayout).toBe('7@2314 × 3@2250 = 32본');
+  });
+
+  it('3주형 L 12000: three columns 3600 apart share one footing', () => {
+    const m = buildPier({ ...loadP1(), type: '3주형', columnCount: 3, copingLengthMm: 12000, foundationType: '직접기초' });
+    expect(m.footings).toHaveLength(1);
+    expect(m.footings[0].length).toBeCloseTo(17.6, 6);
+  });
+
+  it('2주형 with columns 18000 apart: separate footings of 10400', () => {
+    const m = buildPier({ ...loadP1(), type: '2주형', columnCount: 2, copingLengthMm: 30000, foundationType: '직접기초' });
+    expect(m.footings).toHaveLength(2);
+    expect(m.footings.every((f) => Math.abs(f.length - 10.4) < 1e-9)).toBe(true);
+  });
+});