docs: complete euler beam planning gates

phases/euler-beam-3d/index.json

@@ -16,7 +16,8 @@
     {
       "step": 1,
       "name": "research-evidence",
-      "status": "pending",
+      "status": "completed",
+      "summary": "3D Euler beam research evidence added",
       "allowed_paths": [
         "docs/research/euler-beam-3d-research.md"
       ]
@@ -24,7 +25,8 @@
     {
       "step": 2,
       "name": "formulation-spec",
-      "status": "pending",
+      "status": "completed",
+      "summary": "3D Euler beam formulation contract added",
       "allowed_paths": [
         "docs/formulations/euler-beam-3d-formulation.md"
       ]
@@ -32,7 +34,8 @@
     {
       "step": 3,
       "name": "numerical-review",
-      "status": "pending",
+      "status": "completed",
+      "summary": "3D Euler beam numerical review added",
       "allowed_paths": [
         "docs/numerical-reviews/euler-beam-3d-review.md"
       ]
@@ -40,7 +43,8 @@
     {
       "step": 4,
       "name": "io-reference-contract",
-      "status": "pending",
+      "status": "completed",
+      "summary": "3D Euler beam I/O and reference model contracts added",
       "allowed_paths": [
         "docs/io-definitions/euler-beam-3d-io.md",
         "docs/reference-models/euler-beam-3d-reference-models.md"
@@ -49,7 +53,8 @@
     {
       "step": 5,
       "name": "implementation-plan",
-      "status": "pending",
+      "status": "completed",
+      "summary": "3D Euler beam implementation plan added",
       "allowed_paths": [
         "docs/implementation-plans/euler-beam-3d-implementation-plan.md"
       ]
@@ -100,4 +105,4 @@
     }
   ],
   "created_at": "2026-06-12T17:44:12+0900"
-}
+}