diff --git a/phases/equation-and-linear-solve/index.json b/phases/equation-and-linear-solve/index.json
index cb3e420..65a065b 100644
--- a/phases/equation-and-linear-solve/index.json
+++ b/phases/equation-and-linear-solve/index.json
@@ -27,5 +27,6 @@
       "completed_at": "2026-07-31T16:16:28+0900"
     }
   ],
-  "created_at": "2026-07-31T15:19:35+0900"
+  "created_at": "2026-07-31T15:19:35+0900",
+  "completed_at": "2026-07-31T16:16:28+0900"
 }
\ No newline at end of file
diff --git a/phases/index.json b/phases/index.json
index 8ed475f..f3dc335 100644
--- a/phases/index.json
+++ b/phases/index.json
@@ -17,7 +17,8 @@
     },
     {
       "dir": "equation-and-linear-solve",
-      "status": "pending"
+      "status": "completed",
+      "completed_at": "2026-07-31T16:16:28+0900"
     },
     {
       "dir": "results-and-pipeline",
@@ -44,4 +45,4 @@
       "status": "pending"
     }
   ]
-}
+}
\ No newline at end of file