diff --git a/myscript-iink/UIReferenceImplementation/src/main/java/com/myscript/iink/uireferenceimplementation/InputController.java b/myscript-iink/UIReferenceImplementation/src/main/java/com/myscript/iink/uireferenceimplementation/InputController.java
index d732d66..2298035 100644
--- a/myscript-iink/UIReferenceImplementation/src/main/java/com/myscript/iink/uireferenceimplementation/InputController.java
+++ b/myscript-iink/UIReferenceImplementation/src/main/java/com/myscript/iink/uireferenceimplementation/InputController.java
@@ -3,6 +3,7 @@
 package com.myscript.iink.uireferenceimplementation;
 
 import android.content.Context;
+import android.os.Build;
 import android.os.SystemClock;
 import android.util.Log;
 import android.view.GestureDetector;
@@ -188,7 +189,14 @@ else if (inputMode == INPUT_MODE_FORCE_TOUCH)
         ToolController toolController = editor.getToolController();
         PointerTool tool = toolController.getToolForType(iinkPointerType);
         if (tool == PointerTool.PEN || tool == PointerTool.HIGHLIGHTER)
-          editorView.requestUnbufferedDispatch(event);
+        {
+          // API 27/28/29 의 ViewRootImpl 은 "즉시 배치 소비"(scheduleConsumeBatchedInputImmediately)가
+          // 예약된 프레임 소비를 취소만 하고 실제로는 아무것도 소비하지 않는다. 그 결과 배치된 입력이
+          // 영영 회수되지 않아 입력 디스패치 타임아웃 ANR 이 발생한다. API 30 에서 수정됨.
+          // → trouble-shootings/myscript-iink-4.5-anr-rollback.md
+          if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.R)
+            editorView.requestUnbufferedDispatch(event);
+        }
 
         try
         {
diff --git a/myscript-iink/src/main/java/com/knowre/android/myscript/iink/jiix/Expression.kt b/myscript-iink/src/main/java/com/knowre/android/myscript/iink/jiix/Expression.kt
index 2a567dc..f7088e3 100644
--- a/myscript-iink/src/main/java/com/knowre/android/myscript/iink/jiix/Expression.kt
+++ b/myscript-iink/src/main/java/com/knowre/android/myscript/iink/jiix/Expression.kt
@@ -14,7 +14,15 @@ data class Expression(
     @SerializedName("bounding-box")
     val boundingBox: BoundingBox?,
     val symbols: List<Symbol>?,
-    val operands: List<Expression>?
+    /**
+     * iink 4.5 부터 **미해결 피연산자 자리**(예: `2+` 처럼 한쪽을 비운 입력)를
+     * 객체가 아닌 `null` 로 직렬화한다. 3.0.2 는 같은 자리를
+     * `{"type":"number","label":"?","generated":true,"error":"Unsolved"}` 객체로 내보냈다.
+     *
+     * Gson 은 Kotlin 의 non-null 제네릭을 강제하지 않아 타입 선언만으로는 막을 수 없으므로,
+     * 원소 타입을 nullable 로 선언하고 순회하는 쪽에서 걸러낸다.
+     */
+    val operands: List<Expression?>?
 )
 
 internal fun Expression.changeItem(newItem: Item): Expression =
@@ -23,6 +31,6 @@ internal fun Expression.changeItem(newItem: Item): Expression =
             if (item.id == newItem.id) newItem else item
         },
         operands = operands?.map { operand ->
-            operand.changeItem(newItem)
+            operand?.changeItem(newItem)
         }
     )
diff --git a/myscript-iink/src/main/java/com/knowre/android/myscript/iink/jiix/Jiix.kt b/myscript-iink/src/main/java/com/knowre/android/myscript/iink/jiix/Jiix.kt
index 5d89aab..d1a1162 100644
--- a/myscript-iink/src/main/java/com/knowre/android/myscript/iink/jiix/Jiix.kt
+++ b/myscript-iink/src/main/java/com/knowre/android/myscript/iink/jiix/Jiix.kt
@@ -7,7 +7,8 @@ data class Jiix(
     val id: String,
     val type: String,
     val items: List<Item>?,
-    val expressions: List<Expression>?,
+    /** 원소가 null 일 수 있는 이유는 [Expression.operands] 주석 참고. */
+    val expressions: List<Expression?>?,
     @SerializedName("bounding-box")
     val boundingBox: BoundingBox?,
     val version: String
@@ -15,7 +16,7 @@ data class Jiix(
 
 fun Jiix.isValid() =
     !expressions.isNullOrEmpty() &&
-        expressions.all { it.id != null } &&
+        expressions.all { it?.id != null } &&
         getAllItems().all { it.isValid }
 
 fun Jiix.changeItem(itemId: String, func: Item.() -> Item) =
@@ -27,6 +28,6 @@ internal fun Jiix.changeItem(newItem: Item) =
             if (item.id == newItem.id) newItem else item
         },
         expressions = expressions?.map { expression ->
-            expression.changeItem(newItem)
+            expression?.changeItem(newItem)
         }
     )
diff --git a/myscript-iink/src/main/java/com/knowre/android/myscript/iink/jiix/JiixExtension.kt b/myscript-iink/src/main/java/com/knowre/android/myscript/iink/jiix/JiixExtension.kt
index 4f4a7fc..2dc0144 100644
--- a/myscript-iink/src/main/java/com/knowre/android/myscript/iink/jiix/JiixExtension.kt
+++ b/myscript-iink/src/main/java/com/knowre/android/myscript/iink/jiix/JiixExtension.kt
@@ -8,9 +8,9 @@ import java.util.Collections
 //region Jiix
 internal fun Jiix.getAllExpressions(): List<Expression> {
     fun List<Expression>.flatten(): List<Expression> =
-        this + this.flatMap { it.operands?.flatten() ?: Collections.emptyList() }
+        this + this.flatMap { it.operands?.filterNotNull()?.flatten() ?: Collections.emptyList() }
 
-    return this.expressions?.flatten() ?: Collections.emptyList()
+    return this.expressions?.filterNotNull()?.flatten() ?: Collections.emptyList()
 }
 
 fun Jiix.getCandidates(item: Item): List<String> {