Infinite loop in `BTreeIndex.takeInternal` when using orderBy and limit with `undefined` indexed values

[1bod]

• I've validated the bug against the latest version of DB packages

Describe the bug
When a collection contains items where an indexed field (used in orderBy) evaluates to undefined, and the query uses both .orderBy() and .limit(), the BTreeIndex.takeInternal method enters an infinite loop. This happens because nextPair(undefined) returns [undefined, undefined] (an array) instead of undefined, so the while loop condition pair !== undefined is always true.
To Reproduce
https://stackblitz.com/edit/vitejs-vite-xcu9tcef?file=src%2FApp.vue

<script setup lang="ts">
import {
  createCollection,
  eq,
  useLiveQuery,
  localStorageCollectionOptions,
} from '@tanstack/vue-db';

const collection = createCollection<{
  id: number;
  assignedTo?: { id: number };
}>(
  localStorageCollectionOptions({
    id: 'tasks',
    storageKey: 'app-tasks',
    getKey: (item) => item.id,
  })
);

// Add an item with undefined assignedTo
collection.insert({ id: 1, assignedTo: undefined });

// Query with a filter on assignedTo.id
const { data } = useLiveQuery((q) =>
  q
    .from({ item: collection })
    .where(({ item }) => eq(item.assignedTo.id, 35))
    .orderBy(({ item }) => item.taskDate, 'desc')
    .limit(1)
);

// Insert another item - this triggers the infinite loop
collection.insert({ id: 2, assignedTo: { id: 35 } });

</script>

<template>
  <div>
    {{ data }}
  </div>
</template>

Debug information:

When pausing in the debugger, execution is stuck in btree-index.ts at takeInternal:

Variables at freeze:

pair = [undefined, undefined]
key = undefined
keys = Set with one empty string
result = []
n = 1

Expected behavior
The takeInternal method should handle undefined keys gracefully.

[kevin-dp]

/reproduce

[claude]

Investigation and Fix Summary

I've analyzed and fixed this issue. Here's what I found:

Root Cause

The infinite loop occurs in BTreeIndex.takeInternal because of how the BTree's nextHigherPair() method handles undefined:

1. nextHigherPair(undefined) is designed to return the minimum pair (to start iteration from the beginning)
2. When an item's indexed field evaluates to undefined, the minimum key in the tree can be undefined
3. After processing the undefined key, takeInternal sets key = undefined and calls nextHigherPair(undefined) again
4. This returns the same minimum pair, creating an infinite loop

Fix

The fix introduces a START_ITERATION sentinel symbol to distinguish between:

• "Start from the beginning" (when from parameter is undefined)
• "Continue from the actual undefined key" (when the indexed value is undefined)

The loop also detects when nextPair returns the same key that was passed in, breaking out to prevent infinite iteration.

PRs

• Reproduction test: [repro] BTreeIndex infinite loop with undefined indexed values (issue #1186) #1187 - Adds tests that demonstrate the bug and verify the fix
• Fix: [fix] BTreeIndex infinite loop with undefined indexed values (issue #1186) #1188 - Implements the fix with minimal changes to btree-index.ts

Both new tests pass, and all 1934 existing tests continue to pass.