fix: preserve tied connection placements and show card rarity

src/routes/analysis/+page.svelte

@@ -511,7 +511,9 @@
     const socket = member
       ? (boardSummary.models as Record<string, { groupId: string; x: number; y: number }[]>)[member.positionGroupId]?.find((position) => position.groupId === socketId)
       : null;
-    return (socket?.x ?? 0) < 0;
+    if (!member || !socket || socket.x === 0) return false;
+    const positions = (boardSummary.models as Record<string, { groupId: string; x: number; y: number }[]>)[member.positionGroupId] ?? [];
+    return positions.some((position) => position.groupId.startsWith('B-') && position.x * socket.x > 0);
   }
 
   function totalActivationRateUp(context: ReturnType<typeof connectionScoreContext>): number {
@@ -600,6 +602,7 @@
       await new Promise<void>((resolve) => requestAnimationFrame(() => resolve()));
       const optimized = optimizeBoardConnectionCards(boardSummary, effectiveMemberBoards, candidateCards, {
         currentPlacements: boardCards,
+        preservePlacementOnTie: () => true,
         placementWeight: (card, memberId, socketId) => placementMetrics(card, memberId, socketId).score,
         placementPriorityWeight: (card, memberId, socketId) => isBlueConnectionSocket(memberId, socketId)
           ? placementMetrics(card, memberId, socketId).activationRateUp
@@ -983,7 +986,7 @@
 
       <section class="connection-optimizer" aria-labelledby="connection-optimizer-title">
         <div class="connection-optimizer-heading">
-          <div><h3 id="connection-optimizer-title">연결 카드 최적화</h3><p>활성 노드는 유지하며, 파란색 영역은 액티브 발동률을 먼저 최대화한 뒤 예상 점수를 비교합니다.</p></div>
+          <div><h3 id="connection-optimizer-title">연결 카드 최적화</h3><p>활성 노드는 유지하며, 파란색 영역은 액티브 발동률 UP 합계를 먼저 최대화한 뒤 예상 점수를 비교합니다. 발동률 UP 합계와 예상 점수가 같으면 기존 연결 카드 배치를 우선 유지합니다.</p></div>
           <div class="connection-optimizer-actions">
             {#if connectionOptimizationSnapshot}<button type="button" disabled={running || connectionOptimizationRunning} on:click={undoConnectionOptimization}>직전 배치 복원</button>{/if}
             <button type="button" class="primary" disabled={running || connectionOptimizationRunning} on:click={optimizeConnectionPlacements}>{connectionOptimizationRunning ? '배치 탐색 중…' : '보유 카드로 최적화'}</button>
@@ -1009,7 +1012,7 @@
                   {@const member = boardMembers.find((item) => item.id === assignment.memberId)}
                   {@const previousCard = assignment.previousCardId ? allCardById.get(assignment.previousCardId) : null}
                   {@const card = assignment.cardId ? allCardById.get(assignment.cardId) : null}
-                  <span><small>{member?.name ?? assignment.memberId} · {connectionSocketName(assignment.memberId, assignment.socketId)}</small><strong>{previousCard ? cardLabel(previousCard) : '비어 있음'} → {card ? cardLabel(card) : '배치 해제'}</strong></span>
+                  <span><small>{member?.name ?? assignment.memberId} · {connectionSocketName(assignment.memberId, assignment.socketId)}</small><strong>{previousCard ? `${previousCard.rarity}★ ${cardLabel(previousCard)}` : '비어 있음'} → {card ? `${card.rarity}★ ${cardLabel(card)}` : '배치 해제'}</strong></span>
                 {/each}
               </div>
               <button type="button" class="apply-connection" on:click={applyConnectionOptimization}>변경 배치를 적용하고 다시 분석</button>
@@ -1197,7 +1200,7 @@
   .connection-assignment-list { display: grid; grid-template-columns: repeat(auto-fit, minmax(240px, 1fr)); gap: 6px; max-height: 240px; overflow-y: auto; }
   .connection-assignment-list > span { display: grid; gap: 3px; padding: 8px 10px; border: 1px solid #304038; border-radius: 7px; background: #121915; }
   .connection-assignment-list small { color: #819287; font-size: 11px; }
-  .connection-assignment-list strong { overflow: hidden; color: #dbe7df; font-size: 12px; text-overflow: ellipsis; white-space: nowrap; }
+  .connection-assignment-list strong { color: #dbe7df; font-size: 12px; overflow-wrap: anywhere; }
   .connection-no-changes { margin: 0; padding: 10px 12px; border-radius: 8px; color: #a9cdb6; background: #18271d; font-size: 13px; font-weight: 750; }
   .connection-proposal .apply-connection { justify-self: end; }
   .empty { color: #858f9f; font-size: 14px; line-height: 1.65; }