diff --git a/src/commands/math.ts b/src/commands/math.ts
index 836870990..a7abddee3 100644
--- a/src/commands/math.ts
+++ b/src/commands/math.ts
@@ -89,6 +89,7 @@ class DOMView {
  * Descendant commands are organized into blocks.
  */
 class MathCommand extends MathElement {
+  parent: MQNode;
   replacedFragment: Fragment | undefined;
   protected domView: DOMView;
   protected ends: Ends<MQNode>;
@@ -465,7 +466,7 @@ function bindBinaryOperator(
  * symbols and operators that descend (in the Math DOM tree) from
  * ancestor operators.
  */
-class MathBlock extends MathElement {
+class MathBlockOrRootBlock extends MathElement {
   controller?: Controller;
 
   join(methodName: JoinMethod) {
@@ -547,32 +548,6 @@ class MathBlock extends MathElement {
     return super.keystroke(key, e, ctrlr);
   }
 
-  // editability methods: called by the cursor for editing, cursor movements,
-  // and selection of the MathQuill tree, these all take in a direction and
-  // the cursor
-  moveOutOf(dir: Direction, cursor: Cursor, updown?: 'up' | 'down') {
-    var updownInto: NodeRef | undefined;
-    if (updown === 'up') {
-      updownInto = this.parent.upInto;
-    } else if (updown === 'down') {
-      updownInto = this.parent.downInto;
-    }
-
-    if (!updownInto && this[dir]) {
-      const otherDir = -dir as Direction;
-      cursor.insAtDirEnd(otherDir, this[dir] as MQNode);
-      cursor.controller.aria.queueDirEndOf(otherDir).queue(cursor.parent, true);
-    } else {
-      cursor.insDirOf(dir, this.parent);
-      cursor.controller.aria.queueDirOf(dir).queue(this.parent);
-    }
-  }
-  selectOutOf(dir: Direction, cursor: Cursor) {
-    cursor.insDirOf(dir, this.parent);
-  }
-  deleteOutOf(_dir: Direction, cursor: Cursor) {
-    cursor.unwrapGramp();
-  }
   seek(clientX: number, cursor: Cursor) {
     var node = this.getEnd(R);
     if (!node) return cursor.insAtRightEnd(this);
@@ -674,6 +649,38 @@ class MathBlock extends MathElement {
   }
 }
 
+class MathBlock extends MathBlockOrRootBlock {
+  parent: MQNode;
+
+  // editability methods: called by the cursor for editing, cursor movements,
+  // and selection of the MathQuill tree, these all take in a direction and
+  // the cursor
+  moveOutOf(dir: Direction, cursor: Cursor, updown?: 'up' | 'down') {
+    var updownInto: NodeRef | undefined;
+    if (updown === 'up') {
+      updownInto = this.parent.upInto;
+    } else if (updown === 'down') {
+      updownInto = this.parent.downInto;
+    }
+
+    if (!updownInto && this[dir]) {
+      const otherDir = -dir as Direction;
+      cursor.insAtDirEnd(otherDir, this[dir] as MQNode);
+      cursor.controller.aria.queueDirEndOf(otherDir).queue(cursor.parent, true);
+    } else {
+      cursor.insDirOf(dir, this.parent);
+      cursor.controller.aria.queueDirOf(dir).queue(this.parent);
+    }
+  }
+  selectOutOf(dir: Direction, cursor: Cursor) {
+    cursor.insDirOf(dir, this.parent);
+  }
+  deleteOutOf(_dir: Direction, cursor: Cursor) {
+    pray('cursor is inside this block', cursor.parent === this);
+    cursor.unwrapGramp(this.parent);
+  }
+}
+
 Options.prototype.mouseEvents = true;
 API.StaticMath = function (APIClasses: APIClasses) {
   return class StaticMath extends APIClasses.AbstractMathQuill {
diff --git a/src/commands/math/LatexCommandInput.ts b/src/commands/math/LatexCommandInput.ts
index f82775e6d..69c7b7b04 100644
--- a/src/commands/math/LatexCommandInput.ts
+++ b/src/commands/math/LatexCommandInput.ts
@@ -26,14 +26,16 @@ CharCmds['\\'] = class LatexCommandInput extends MathCommand {
     const endsL = this.getEnd(L);
 
     endsL.focus = function () {
-      this.parent.domFrag().addClass('mq-hasCursor');
-      if (this.isEmpty()) this.parent.domFrag().removeClass('mq-empty');
+      (this.parent as MQNode).domFrag().addClass('mq-hasCursor');
+      if (this.isEmpty())
+        (this.parent as MQNode).domFrag().removeClass('mq-empty');
 
       return this;
     };
     endsL.blur = function () {
-      this.parent.domFrag().removeClass('mq-hasCursor');
-      if (this.isEmpty()) this.parent.domFrag().addClass('mq-empty');
+      (this.parent as MQNode).domFrag().removeClass('mq-hasCursor');
+      if (this.isEmpty())
+        (this.parent as MQNode).domFrag().addClass('mq-empty');
 
       return this;
     };
diff --git a/src/commands/math/basicSymbols.ts b/src/commands/math/basicSymbols.ts
index 0128c4a8e..041d68166 100644
--- a/src/commands/math/basicSymbols.ts
+++ b/src/commands/math/basicSymbols.ts
@@ -193,7 +193,9 @@ class Digit extends DigitGroupingChar {
     ) {
       new SubscriptCommand().createLeftOf(cursor);
       super.createLeftOf(cursor);
-      cursor.insRightOf(cursor.parent.parent);
+      var gramp = cursor.parent.parent as MQNode;
+      pray('gramp exists', gramp);
+      cursor.insRightOf(gramp);
     } else super.createLeftOf(cursor);
   }
   mathspeak(opts: MathspeakOptions) {
diff --git a/src/commands/math/commands.ts b/src/commands/math/commands.ts
index e2fc7ecf9..893df10c3 100644
--- a/src/commands/math/commands.ts
+++ b/src/commands/math/commands.ts
@@ -540,13 +540,14 @@ class SupSub extends MathCommand {
   }
 }
 
-function insLeftOfMeUnlessAtEnd(this: MQNode, cursor: Cursor) {
+function insLeftOfMeUnlessAtEnd(this: MathCommand | MathBlock, cursor: Cursor) {
   // cursor.insLeftOf(cmd), unless cursor at the end of block, and every
   // ancestor cmd is at the end of every ancestor block
   var cmd = this.parent;
   var ancestorCmd: MQNode | Anticursor | Cursor = cursor;
   do {
     if (ancestorCmd[R]) return cursor.insLeftOf(cmd);
+    if (!ancestorCmd.parent || !ancestorCmd.parent.parent) break;
     ancestorCmd = ancestorCmd.parent.parent;
   } while (ancestorCmd !== cmd);
   cursor.insRightOf(cmd);
diff --git a/src/commands/text.ts b/src/commands/text.ts
index f0bed3d43..062dda60e 100644
--- a/src/commands/text.ts
+++ b/src/commands/text.ts
@@ -302,6 +302,7 @@ function TextBlockFuseChildren(self: TextBlock) {
  * Text contents must always be nonempty.
  */
 class TextPiece extends MQNode {
+  parent: MQNode;
   textStr: string;
 
   constructor(text: string) {
diff --git a/src/cursor.ts b/src/cursor.ts
index aafa2dfb3..a95e26cd3 100644
--- a/src/cursor.ts
+++ b/src/cursor.ts
@@ -112,6 +112,7 @@ class Cursor extends Point {
   /** Place the cursor before or after `el`, according the side specified by `dir`. */
   insDirOf(dir: Direction, el: MQNode) {
     prayDirection(dir);
+    if (!el.parent) return this.hide();
     this.domFrag().insDirOf(dir, el.domFrag());
     this.withDirInsertAt(dir, el.parent, el[dir], el);
     this.parent.domFrag().addClass('mq-hasCursor');
@@ -181,9 +182,9 @@ class Cursor extends Point {
       right,
     };
   }
-  unwrapGramp() {
-    var gramp = this.parent.parent;
-    var greatgramp = gramp.parent;
+  unwrapGramp(gramp: MQNode) {
+    var greatgramp = gramp.parent as MQNode;
+    pray('greatgramp exists', greatgramp);
     var rightward = gramp[R];
     var cursor = this;
 
@@ -365,7 +366,7 @@ class Cursor extends Point {
     return seln;
   }
   depth() {
-    var node: MQNode | Point = this;
+    var node: NodeRef | Point = this;
     var depth = 0;
     while ((node = node.parent)) {
       depth += node instanceof MathBlock ? 1 : 0;
diff --git a/src/services/keystroke.ts b/src/services/keystroke.ts
index ef64f678f..964ff8c68 100644
--- a/src/services/keystroke.ts
+++ b/src/services/keystroke.ts
@@ -351,11 +351,11 @@ class Controller_keystroke extends Controller_focusBlur {
   deleteDir(dir: Direction) {
     prayDirection(dir);
     var cursor = this.cursor;
-    var cursorEl = cursor[dir] as MQNode;
+    var cursorEl = cursor[dir];
     var cursorElParent = cursor.parent.parent;
     var ctrlr = cursor.controller;
 
-    if (cursorEl && cursorEl instanceof MQNode) {
+    if (cursorEl && cursorEl.parent && cursorEl instanceof MQNode) {
       if (cursorEl.sides) {
         ctrlr.aria.queue(
           cursorEl.parent
@@ -368,7 +368,11 @@ class Controller_keystroke extends Controller_focusBlur {
       } else if (!cursorEl.blocks && cursorEl.parent.ctrlSeq !== '\\text') {
         ctrlr.aria.queue(cursorEl);
       }
-    } else if (cursorElParent && cursorElParent instanceof MQNode) {
+    } else if (
+      cursorElParent &&
+      cursorElParent.parent &&
+      cursorElParent instanceof MQNode
+    ) {
       if (cursorElParent.sides) {
         ctrlr.aria.queue(
           cursorElParent.parent
diff --git a/src/tree.ts b/src/tree.ts
index 3ee3b13e8..2052b7c92 100644
--- a/src/tree.ts
+++ b/src/tree.ts
@@ -116,8 +116,7 @@ class NodeBase {
   [L]: NodeRef = 0;
   [R]: NodeRef = 0;
 
-  // TODO - can this ever actually stay 0? if so we need to add null checks
-  parent: MQNode = 0 as any as MQNode;
+  parent: NodeRef = 0;
 
   /**
    * The (doubly-linked) list of this node's children.
@@ -351,7 +350,11 @@ class NodeBase {
   write(_cursor: Cursor, _ch: string) {}
 }
 
-function prayWellFormed(parent: MQNode, leftward: NodeRef, rightward: NodeRef) {
+function prayWellFormed(
+  parent: NodeRef,
+  leftward: NodeRef,
+  rightward: NodeRef
+): asserts parent {
   pray('a parent is always present', parent);
   pray(
     'leftward is properly set up',