diff --git a/gdn-app/src/App.vue b/gdn-app/src/App.vue
index b5e072c..47ebf07 100644
--- a/gdn-app/src/App.vue
+++ b/gdn-app/src/App.vue
@@ -1,8 +1,8 @@
 <script setup lang="ts">
 import CNavbar from "./components/CNavbar.vue";
 import CNote from "./components/CNote.vue";
+import { Path, Segment } from "./lib/path";
 import { useUiStore } from "./stores/ui";
-import { pathAncestor } from "./util";
 
 const ui = useUiStore();
 
@@ -10,7 +10,8 @@ window.addEventListener("keypress", (ev) => {
   if (document.activeElement !== document.body) return;
 
   if (ev.key === "Escape") {
-    ui.focusPath = pathAncestor(ui.focusPath);
+    const parent = ui.focusPath.parent();
+    if (parent) ui.focusPath = parent;
     return;
   }
 });
@@ -20,7 +21,12 @@ window.addEventListener("keypress", (ev) => {
   <div class="flex h-screen touch-pan-x touch-pan-y flex-col">
     <CNavbar />
     <div class="h-full overflow-auto p-1 pr-5">
-      <CNote v-if="ui.anchorId" :noteId="ui.anchorId" :path="''" :forceOpen="true" />
+      <CNote
+        v-if="ui.anchorId"
+        :path="new Path()"
+        :segment="new Segment(ui.anchorId, 0)"
+        :forceOpen="true"
+      />
     </div>
   </div>
 </template>
diff --git a/gdn-app/src/components/CNote.vue b/gdn-app/src/components/CNote.vue
index 61c1bdb..12fdce7 100644
--- a/gdn-app/src/components/CNote.vue
+++ b/gdn-app/src/components/CNote.vue
@@ -1,7 +1,7 @@
 <script setup lang="ts">
+import { Path, Segment } from "@/lib/path";
 import { useNotesStore } from "@/stores/notes";
 import { useUiStore } from "@/stores/ui";
-import { pathAppend, pathSlice } from "@/util";
 import {
   RiAddLine,
   RiArrowDownSLine,
@@ -20,30 +20,30 @@ const notes = useNotesStore();
 const ui = useUiStore();
 
 const props = defineProps<{
-  noteId: string;
+  path: Path; // From root to here
+  segment: Segment;
   parentId?: string;
-  path: string; // From root to here
   forceOpen?: boolean;
 }>();
 
-const note = computed(() => notes.getNote(props.noteId));
+const id = computed(() => props.segment.id);
+const note = computed(() => notes.getNote(id.value));
 
 const parents = computed(() => {
-  let parents = notes.getParents(props.noteId);
+  let parents = notes.getParents(id.value);
   if (props.parentId) parents = parents.difference(new Set([props.parentId]));
   return [...parents].sort().map((id) => ({ id, text: notes.getNote(id)?.text }));
 });
 
-// Our children and their locally unique keys.
+// Our children and the
 const children = computed(() => {
   if (!note.value) return [];
   const seen = new Map<string, number>();
-  const children: { id: string; key: string }[] = [];
+  const children = [];
   for (const id of note.value.children) {
-    const n = seen.get(id) || 0;
-    seen.set(id, n + 1);
-    const key = `${id}-${n}`;
-    children.push({ id, key });
+    const iteration = seen.get(id) || 0;
+    seen.set(id, iteration + 1);
+    children.push(new Segment(id, iteration));
   }
   return children;
 });
@@ -54,8 +54,8 @@ const mode = ref<"editing" | "creating">();
 const mayOpen = computed(() => children.value.length > 0);
 const open = computed(() => mayOpen.value && ui.isOpen(props.path));
 
-const focused = computed(() => ui.focusPath === props.path);
-const pinned = computed(() => ui.isPinned(props.path));
+const focused = computed(() => ui.focusPath.eq(props.path));
+const pinned = computed(() => ui.isPinned(props.segment, props.parentId));
 const hover = computed(() => hovering.value && mode.value !== "editing");
 
 const creating = computed(() => mode.value === "creating");
@@ -91,7 +91,7 @@ function onClick() {
 
 function onPinButtonClick() {
   if (pinned.value) ui.unsetPinned();
-  else ui.setPinned(props.path);
+  else ui.setPinned(props.segment, props.parentId);
 }
 
 function onEditButtonClick() {
@@ -125,7 +125,7 @@ function onCreateEditorFinish(text: string) {
   note.value.children.push(newNote.id);
 
   const lastChild = children.value.at(-1);
-  if (lastChild) ui.focusPath = pathAppend(props.path, lastChild.key);
+  if (lastChild) ui.focusPath = props.path.concat(lastChild);
 
   onCreateEditorClose();
 }
@@ -152,9 +152,9 @@ function onCreateEditorFinish(text: string) {
         <div
           class="rounded"
           :class="focused ? 'hover:bg-neutral-300' : 'hover:bg-neutral-200'"
-          @click.stop="ui.toggleOpen(props.path)"
+          @click.stop="ui.toggleOpen(path)"
         >
-          <RiArrowDownSLine v-if="open && props.forceOpen" size="16px" class="text-neutral-400" />
+          <RiArrowDownSLine v-if="open && forceOpen" size="16px" class="text-neutral-400" />
           <RiArrowDownSLine v-else-if="open" size="16px" />
           <RiArrowRightSLine v-else-if="mayOpen" size="16px" />
           <RiArrowRightSLine v-else size="16px" class="text-neutral-400" />
@@ -194,10 +194,10 @@ function onCreateEditorFinish(text: string) {
     <div v-if="open && children.length > 0" class="flex flex-col pl-2">
       <CNote
         v-for="child of children"
-        :key="child.key"
-        :noteId="child.id"
-        :parentId="props.noteId"
-        :path="pathAppend(path, child.key)"
+        :key="child.fmt()"
+        :path="path.concat(child)"
+        :segment="child"
+        :parentId="id"
       />
     </div>
 
diff --git a/gdn-app/src/lib/assert.ts b/gdn-app/src/lib/assert.ts
new file mode 100644
index 0000000..6f61092
--- /dev/null
+++ b/gdn-app/src/lib/assert.ts
@@ -0,0 +1,16 @@
+export class AssertionError extends Error {}
+
+export function assert(condition: boolean, description?: string): asserts condition {
+  if (condition) return;
+  if (description === undefined) {
+    description = "assertion failed";
+    console.error("assertion failed");
+  } else {
+    console.error("assertion failed:", description);
+  }
+  throw new AssertionError(description);
+}
+
+export function assertUnreachable(): never {
+  assert(false, "unreachable code reached");
+}
diff --git a/gdn-app/src/lib/path.ts b/gdn-app/src/lib/path.ts
new file mode 100644
index 0000000..97b903c
--- /dev/null
+++ b/gdn-app/src/lib/path.ts
@@ -0,0 +1,81 @@
+import { assert } from "./assert";
+
+export class Segment {
+  constructor(
+    readonly id: string,
+    readonly iteration: number,
+  ) {
+    assert(Number.isInteger(iteration), "n must be an integer");
+    assert(iteration >= 0), "n must not be negative";
+  }
+
+  static parse(text: string): Segment {
+    const match = text.match(/^([^/]+):([0-9]{1,10})$/);
+    assert(match !== null, "invalid segment string");
+    return new Segment(match[1]!, Number.parseInt(match[2]!));
+  }
+
+  fmt(): string {
+    return `${this.id}:${this.iteration}`;
+  }
+
+  eq(other: Segment): boolean {
+    return this.fmt() === other.fmt();
+  }
+}
+
+export class Path {
+  readonly segments: readonly Segment[];
+
+  constructor(segments: Segment[] = []) {
+    this.segments = segments.slice();
+  }
+
+  static parse(text: string): Path {
+    if (text === "") return new Path();
+    return new Path(text.split("/").map((it) => Segment.parse(it)));
+  }
+
+  fmt(): string {
+    return this.segments.map((it) => it.fmt()).join("/");
+  }
+
+  eq(other: Path): boolean {
+    return this.fmt() === other.fmt();
+  }
+
+  slice(start?: number, end?: number): Path {
+    return new Path(this.segments.slice(start, end));
+  }
+
+  concat(...other: (Path | Segment)[]): Path {
+    const result = this.segments.slice();
+    for (const part of other) {
+      if (part instanceof Segment) result.push(part);
+      else result.push(...part.segments);
+    }
+    return new Path(result);
+  }
+
+  parent(): Path | undefined {
+    if (this.segments.length === 0) return undefined;
+    return this.slice(0, -1);
+  }
+
+  /**
+   * All ancestors of this path (including the path itself), ordered by
+   * decreasing length.
+   */
+  ancestors(): Path[] {
+    const result = [];
+    for (let i = this.segments.length; i >= 0; i--) {
+      result.push(this.slice(0, i));
+    }
+    return result;
+  }
+
+  isPrefixOf(path: Path): boolean {
+    if (path.segments.length < this.segments.length) return false;
+    return path.slice(0, this.segments.length).eq(this);
+  }
+}
diff --git a/gdn-app/src/stores/ui.ts b/gdn-app/src/stores/ui.ts
index 91cdad7..12c15e2 100644
--- a/gdn-app/src/stores/ui.ts
+++ b/gdn-app/src/stores/ui.ts
@@ -1,47 +1,49 @@
-import { pathAncestors, pathLiesOn, pathSlice } from "@/util";
+import { Segment, Path as UiPath } from "@/lib/path";
 import { defineStore } from "pinia";
 import { ref, watchEffect } from "vue";
 
 export const useUiStore = defineStore("ui", () => {
   const anchorId = ref<string>();
-  const focusPath = ref<string>("");
+  const focusPath = ref<UiPath>(new UiPath());
   const openPaths = ref<Set<string>>(new Set());
-  const pinned = ref<string>(); // The last two segments of the path
+  const pinned = ref<{ segment: Segment; parentId?: string }>();
 
   // Ensure all nodes on the focusPath are unfolded.
   watchEffect(() => {
     // The node pointed to by the path itself doesn't need to be unfolded.
-    for (const ancestor of pathAncestors(focusPath.value).slice(1)) {
-      openPaths.value.add(ancestor);
+    for (const ancestor of focusPath.value.ancestors().slice(1)) {
+      setOpen(ancestor, true);
     }
   });
 
-  function isOpen(path: string): boolean {
-    return openPaths.value.has(path);
+  function isOpen(path: UiPath): boolean {
+    return openPaths.value.has(path.fmt());
   }
 
-  function setOpen(path: string, value: boolean) {
-    // Move the focusPath if necessary
-    if (!value && isOpen(path) && pathLiesOn(path, focusPath.value)) {
-      focusPath.value = path;
-    }
-
+  function setOpen(path: UiPath, value: boolean) {
     // Don't update openPaths unnecessarily.
     // Just in case vue itself doesn't debounce Set operations.
-    if (value && !isOpen(path)) openPaths.value.add(path);
-    else if (!value && isOpen(path)) openPaths.value.delete(path);
+    if (value && !isOpen(path)) {
+      openPaths.value.add(path.fmt());
+    } else if (!value && isOpen(path)) {
+      // Move the focusPath if necessary
+      if (path.isPrefixOf(focusPath.value)) focusPath.value = path;
+
+      openPaths.value.delete(path.fmt());
+    }
   }
 
-  function toggleOpen(path: string) {
+  function toggleOpen(path: UiPath) {
     setOpen(path, !isOpen(path));
   }
 
-  function isPinned(path: string): boolean {
-    return pathSlice(path, -2) === pinned.value;
+  function isPinned(segment: Segment, parentId?: string): boolean {
+    if (!pinned.value) return false;
+    return pinned.value.segment.eq(segment) && pinned.value.parentId === parentId;
   }
 
-  function setPinned(path: string) {
-    pinned.value = pathSlice(path, -2);
+  function setPinned(segment: Segment, parentId?: string) {
+    pinned.value = { segment, parentId };
   }
 
   function unsetPinned() {
diff --git a/gdn-app/src/util.ts b/gdn-app/src/util.ts
deleted file mode 100644
index 225f7b6..0000000
--- a/gdn-app/src/util.ts
+++ /dev/null
@@ -1,33 +0,0 @@
-function pathString(keys: string[]): string {
-  return keys.join("/");
-}
-
-function pathParse(path: string): string[] {
-  if (path === "") return [];
-  return path.split("/");
-}
-
-export function pathSlice(path: string, start: number, end?: number): string {
-  return pathString(pathParse(path).slice(start, end));
-}
-
-export function pathAppend(path: string, key: string): string {
-  return pathString(pathParse(path).concat(key));
-}
-
-export function pathAncestor(path: string): string {
-  return pathSlice(path, 0, -1);
-}
-
-export function pathAncestors(path: string): string[] {
-  const parsedPath = pathParse(path);
-  const result = [];
-  for (let i = parsedPath.length; i >= 0; i--) {
-    result.push(pathString(parsedPath.slice(0, i)));
-  }
-  return result;
-}
-
-export function pathLiesOn(p1: string, p2: string): boolean {
-  return pathAncestors(p2).indexOf(p1) >= 0;
-}