diff --git a/.auto-claude/specs/001-conceptual-explanations/build-progress.txt b/.auto-claude/specs/001-conceptual-explanations/build-progress.txt
index 762f08a..f441608 100644
--- a/.auto-claude/specs/001-conceptual-explanations/build-progress.txt
+++ b/.auto-claude/specs/001-conceptual-explanations/build-progress.txt
@@ -122,3 +122,49 @@ Implementation details:
 
 Committed: 0e39cff
 Status: ✓ Completed
+
+
+=== 2026-01-11 - Subtask 2.3 Completed ===
+Modified renderer.js renderLesson() function to populate the concept section.
+
+Implementation details:
+- Added logic to populate concept section elements in renderLesson() function
+- Get references to concept DOM elements by ID:
+  * concept-section (details element)
+  * concept-explanation (explanation text container)
+  * concept-diagram (optional diagram container)
+  * concept-container-vs-item (optional Flexbox/Grid distinction)
+- Conditional rendering based on lesson.concept existence:
+  * Show concept section when lesson.concept exists with explanation
+  * Hide concept section when concept is not defined
+- Field population:
+  * explanation: uses textContent (safe for user content, required field)
+  * diagram: uses innerHTML (supports SVG markup, optional field)
+  * containerVsItem: uses textContent (safe for user content, optional field)
+- Clear optional fields when not present to prevent stale data from previous lessons
+- Follows existing code patterns in renderer.js
+- Proper null checks for all DOM elements
+
+Committed: e21bca1
+Status: ✓ Completed
+
+
+=== 2026-01-11 - Subtask 2.4 Completed ===
+Added 'whyThisWorks' translation key for the concept section heading.
+
+Implementation details:
+- Added translation key to src/i18n.js for all 6 supported languages
+- Translations added:
+  * en (English): "Why This Works"
+  * de (German): "Warum das funktioniert"
+  * pl (Polish): "Dlaczego to działa"
+  * es (Spanish): "Por qué funciona"
+  * ar (Arabic): "لماذا يعمل هذا"
+  * uk (Ukrainian): "Чому це працює"
+- Translation key matches the data-i18n attribute in the concept section summary element
+- Follows existing i18n.js structure and patterns
+- Placed in "Instructions" comment section for consistency
+- Phase 2 (UI Components) is now complete - all 4 subtasks finished
+
+Committed: 3c08b45
+Status: ✓ Completed
diff --git a/.auto-claude/specs/001-conceptual-explanations/implementation_plan.json b/.auto-claude/specs/001-conceptual-explanations/implementation_plan.json
index bca8e35..298f69c 100644
--- a/.auto-claude/specs/001-conceptual-explanations/implementation_plan.json
+++ b/.auto-claude/specs/001-conceptual-explanations/implementation_plan.json
@@ -43,15 +43,17 @@
           "id": "2.3",
           "title": "Update renderer to display concepts",
           "description": "Modify renderer.js renderLesson() to populate the concept section with explanation text and optional diagram. Handle case when concept is not defined.",
-          "status": "pending",
-          "notes": ""
+          "status": "completed",
+          "notes": "Successfully modified renderer.js renderLesson() function to populate the concept section. Implementation includes:\n- Populate concept explanation text (required field) using textContent\n- Populate optional diagram field using innerHTML (to support SVG markup)\n- Populate optional containerVsItem field using textContent\n- Show concept section when lesson.concept exists with explanation\n- Hide concept section when concept is not defined\n- Clear optional fields to prevent stale data from previous lessons\nCommitted: e21bca1",
+          "updated_at": "2026-01-11T03:38:59.760229+00:00"
         },
         {
           "id": "2.4",
           "title": "Add i18n keys for concept UI",
           "description": "Add translation keys for 'Why This Works' heading and any other UI text in i18n.js for all supported languages.",
-          "status": "pending",
-          "notes": ""
+          "status": "completed",
+          "notes": "Successfully added 'whyThisWorks' translation key to i18n.js for all 6 supported languages:\n- en: \"Why This Works\"\n- de: \"Warum das funktioniert\"\n- pl: \"Dlaczego to dzia\u0142a\"\n- es: \"Por qu\u00e9 funciona\"\n- ar: \"\u0644\u0645\u0627\u0630\u0627 \u064a\u0639\u0645\u0644 \u0647\u0630\u0627\"\n- uk: \"\u0427\u043e\u043c\u0443 \u0446\u0435 \u043f\u0440\u0430\u0446\u044e\u0454\"\n\nThe translation key is used by the concept section summary element with data-i18n=\"whyThisWorks\". All translations maintain consistency with the existing patterns in i18n.js.\n\nCommitted: 3c08b45",
+          "updated_at": "2026-01-11T03:40:28.748935+00:00"
         }
       ]
     },
@@ -217,5 +219,5 @@
   },
   "created_at": "2025-01-11T00:00:00Z",
   "updated_at": "2025-01-11T00:00:00Z",
-  "last_updated": "2026-01-11T03:35:41.967508+00:00"
+  "last_updated": "2026-01-11T03:40:28.748942+00:00"
 }
\ No newline at end of file