feat(core): haunch-and-Level-300 coping underside, steel pile 609.6, W03/W04 checks

- Multi-column coping (2·3주형): underside between columns drops 300 below
  Level with 300 × 300 haunches (spec §4.5, Q3 추천안).
- Steel pipe pile diameter 609.6 mm (spec §4.5, Q5 추천안).
- Direct foundation keeps the 100 mm blinding concrete (Q4 추천안, test added).
- W03: bearing centre closer than half a block width to a step boundary.
- W04: block footprint outside the coping plan.

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

src/core/geometry.ts

@@ -6,6 +6,8 @@ export const DIM = {
   copingH1: 1.0,
   copingH2: 1.5,
   levelWidth: 2.1,
+  /** Multi-column coping: underside between columns sits this far below Level, with 45° haunches of the same size (spec §4.5, Q3 추천안). */
+  haunch: 0.3,
   padThickness: 0.05,
   padSize: 1.0,
   blockSize: 1.2,
@@ -14,7 +16,8 @@ export const DIM = {
   footingH: 2.0,
   blindingMargin: 0.2,
   blindingT: 0.1,
-  pileDiameter: 0.6,
+  /** 강관 609.6 × 12 (spec §4.5 강관 type, Q5 추천안 적용). */
+  pileDiameter: 0.6096,
   pileEnd: 0.7,
   pileSpacing: 2.25,
   /** Front/back EL difference below this is treated as no lateral step (spec §4.3, Q2). */
@@ -204,12 +207,24 @@ export function buildPier(input: PierInput): PierModel {
   const levelEnd = Math.max(...colS) + DIM.levelWidth / 2;
   if (levelStart < 0 || levelEnd > L) throw new Error('코핑 길이가 Level 구간보다 짧습니다.');
 
+  // Underside from the right end to the left end. Between columns (2·3주형) it drops 300 below Level with 300 × 300 haunches (spec §4.5, Q3).
+  const underside: [number, number][] = [[L, endBottom]];
+  const levelZones = [...colS].sort((a, b) => b - a).map((s) => [s - DIM.levelWidth / 2, s + DIM.levelWidth / 2] as const);
+  levelZones.forEach(([zoneStart, zoneEnd], k) => {
+    underside.push([zoneEnd, levelBottom], [zoneStart, levelBottom]);
+    const next = levelZones[k + 1];
+    if (!next) return;
+    const gap = zoneStart - next[1];
+    if (gap <= 2 * DIM.haunch) throw new Error('기둥 사이 간격이 헌치(300 × 2)보다 좁아 코핑 하면을 만들 수 없습니다.');
+    const lowerEl = levelBottom - DIM.haunch;
+    underside.push([zoneStart - DIM.haunch, lowerEl], [next[1] + DIM.haunch, lowerEl], [next[1], levelBottom]);
+  });
+
   const profile: [number, number][] = [[0, endBottom]];
   for (const seg of segments) {
     profile.push([seg.s0, seg.top], [seg.s1, seg.top]);
   }
-  profile.push([L, endBottom], [levelEnd, levelBottom], [levelStart, levelBottom], [0, endBottom]);
-  profile.pop(); // the last point repeats the first one
+  profile.push(...underside);
 
   const footingTop = input.foundationType === '현장타설말뚝' ? input.footingBottomEl : input.footingBottomEl + DIM.footingH;
   const columns: ColumnModel[] = colS.map((s) => ({