chore(fem-and-beam-kernel): step 0 output

phases/fem-and-beam-kernel/index.json

@@ -5,7 +5,10 @@
     {
       "step": 0,
       "name": "quadrature-and-shape-functions",
-      "status": "pending"
+      "status": "completed",
+      "summary": "Added fixed 1D Gauss rules, Line2 shape primitives, and a validated length/2 Jacobian with invariant and invalid-input tests.",
+      "started_at": "2026-07-31T01:37:23+0900",
+      "completed_at": "2026-07-31T01:48:32+0900"
     },
     {
       "step": 1,
@@ -22,5 +25,6 @@
       "name": "timoshenko-stiffness-kernel",
       "status": "pending"
     }
-  ]
+  ],
-}
+  "created_at": "2026-07-31T01:37:23+0900"
+}