fix: mark specs as unreachable when infeasible alongside achieved specs

determineStatuses() was marking specs as 'achievable' based solely on
per-specialization upper bounds, ignoring credit sharing with achieved
specs. Now performs an LP feasibility check to verify the spec can
actually be achieved alongside the current achieved set.

app/src/solver/__tests__/optimizer.test.ts

@@ -109,6 +109,37 @@ describe('determineStatuses', () => {
     // Most specs only have 1 qualifying course in spr1 (2.5 credits < 9)
     expect(statuses['FIN']).toBe('unreachable');
   });
+
+  it('marks spec as unreachable when infeasible alongside achieved specs due to credit sharing', () => {
+    // Bug scenario: CRF+STR achieved, LCM has 10 credit upper bound but
+    // shared courses (spr3, fall3) are consumed by CRF/STR
+    const selectedCourses = [
+      'spr1-collaboration',              // LCM, MGT
+      'spr2-financial-services',         // BNK, CRF, FIN, FIM
+      'spr3-mergers-acquisitions',       // CRF, FIN, LCM, STR(S1)
+      'spr4-foundations-entrepreneurship', // ENT, MGT, STR(S1)
+      'spr5-corporate-finance',          // CRF, FIN
+      'sum1-global-immersion',           // GLB
+      'sum2-business-drivers',           // STR(S1)
+      'sum3-valuation',                  // BNK, CRF, FIN, FIM
+      'fall1-managing-change',           // LCM, MGT, STR(S2)
+      'fall2-decision-models',           // MGT, MTO
+      'fall3-corporate-governance',      // LCM, MGT, SBI, STR(S1)
+      'fall4-game-theory',               // MGT, STR(S1)
+    ];
+
+    // Baseline: LCM is achievable when no specs are achieved (upper bound alone)
+    const statusesBaseline = determineStatuses(selectedCourses, [], []);
+    expect(statusesBaseline['LCM']).toBe('achievable');
+
+    // Core bug scenario: CRF+STR achieved (without MGT), LCM should still be unreachable
+    const statusesWithoutMgt = determineStatuses(selectedCourses, [], ['CRF', 'STR']);
+    expect(statusesWithoutMgt['LCM']).toBe('unreachable');
+
+    // LCM upper bound is 10 (>= 9) but infeasible alongside CRF+STR+MGT
+    const statusesWithMgt = determineStatuses(selectedCourses, [], ['CRF', 'STR', 'MGT']);
+    expect(statusesWithMgt['LCM']).toBe('unreachable');
+  });
 });
 
 describe('optimize (integration)', () => {

app/src/solver/optimizer.ts

@@ -178,7 +178,20 @@ export function determineStatuses(
       continue;
     }
 
-    statuses[spec.id] = 'achievable';
+    // Verify spec is actually feasible alongside already-achieved specs,
+    // but only when all course slots are committed (no open sets remain).
+    // With open sets, the user can still pick different courses, so LP
+    // feasibility over selected courses alone would give false negatives.
+    if (openSetSet.size === 0) {
+      const testSet = [...achieved, spec.id];
+      const filteredCourseIds = excludedCourseIds
+        ? selectedCourseIds.filter((id) => !excludedCourseIds.has(id))
+        : selectedCourseIds;
+      const feasResult = checkWithS2(filteredCourseIds, testSet);
+      statuses[spec.id] = feasResult.feasible ? 'achievable' : 'unreachable';
+    } else {
+      statuses[spec.id] = 'achievable';
+    }
   }
 
   return statuses;