diff --git a/src/host/reconcile.ts b/src/host/reconcile.ts
index 2266441..57f781d 100644
--- a/src/host/reconcile.ts
+++ b/src/host/reconcile.ts
@@ -156,6 +156,46 @@ export function resetUpdateQueue(): void {
   flushScheduled = false;
 }
 
+export function longestIncreasingSubsequence(arr: number[]): number[] {
+  if (arr.length === 0) return [];
+
+  const tails: number[] = [];
+  const tailsIdx: number[] = [];
+  const prev: number[] = new Array(arr.length).fill(-1);
+
+  for (let i = 0; i < arr.length; i++) {
+    const val = arr[i]!;
+    let lo = 0;
+    let hi = tails.length;
+    while (lo < hi) {
+      const mid = (lo + hi) >>> 1;
+      if (tails[mid]! < val) {
+        lo = mid + 1;
+      } else {
+        hi = mid;
+      }
+    }
+    if (lo > 0) {
+      prev[i] = tailsIdx[lo - 1]!;
+    }
+    if (lo === tails.length) {
+      tails.push(val);
+      tailsIdx.push(i);
+    } else {
+      tails[lo] = val;
+      tailsIdx[lo] = i;
+    }
+  }
+
+  const result: number[] = new Array(tails.length);
+  let k = tailsIdx[tails.length - 1]!;
+  for (let j = tails.length - 1; j >= 0; j--) {
+    result[j] = k;
+    k = prev[k]!;
+  }
+  return result;
+}
+
 export interface MatchedChild<I> {
   oldFiber: Fiber<I>;
   newChild: UElement;
@@ -166,6 +206,7 @@ export interface ChildClassification<I> {
   matched: MatchedChild<I>[];
   added: { newChild: UElement; index: number }[];
   removed: Fiber<I>[];
+  moves: Map<number, Fiber<I>>;
 }
 
 export function reconcileChildren<I>(
@@ -267,5 +308,16 @@ export function reconcileChildren<I>(
     }
   }
 
-  return { matched, added, removed };
+  const oldIndices = matched.map((m) => oldFibers.indexOf(m.oldFiber));
+  const lisPositions = longestIncreasingSubsequence(oldIndices);
+  const lisSet = new Set(lisPositions);
+
+  const moves = new Map<number, Fiber<I>>();
+  for (let i = 0; i < matched.length; i++) {
+    if (!lisSet.has(i)) {
+      moves.set(i, matched[i]!.oldFiber);
+    }
+  }
+
+  return { matched, added, removed, moves };
 }
\ No newline at end of file
diff --git a/src/mod.ts b/src/mod.ts
index 24334cc..e2c3f30 100644
--- a/src/mod.ts
+++ b/src/mod.ts
@@ -21,7 +21,7 @@ export type { HostConfig, Root } from "./host/config.js";
 
 export type { Fiber, Effect } from "./host/fiber.js";
 
-export { scheduleUpdate, flushUpdates, reconcileProps, commitEffects, wireSignalToFiber, resetUpdateQueue, reconcileChildren } from "./host/reconcile.js";
+export { scheduleUpdate, flushUpdates, reconcileProps, commitEffects, wireSignalToFiber, resetUpdateQueue, reconcileChildren, longestIncreasingSubsequence } from "./host/reconcile.js";
 export type { MatchedChild, ChildClassification } from "./host/reconcile.js";
 
 export { TransformRegistry, childCtx, matchesSchema, ctx as transformCtx } from "./transform/registry.js";
diff --git a/test/lis-move-detection.test.ts b/test/lis-move-detection.test.ts
new file mode 100644
index 0000000..b343201
--- /dev/null
+++ b/test/lis-move-detection.test.ts
@@ -0,0 +1,178 @@
+import { describe, it, expect } from "vitest";
+import type { Fiber } from "../src/host/fiber.js";
+import type { UNode } from "../src/core/schema.js";
+import { longestIncreasingSubsequence, reconcileChildren } from "../src/host/reconcile.js";
+
+function makeFiber(key: string | undefined, tag: string): Fiber<string> {
+  return {
+    instance: `inst-${tag}-${key ?? "nokey"}`,
+    tag,
+    props: {},
+    key,
+    children: [],
+    parent: null,
+    effect: null,
+    signalDisposers: [],
+    prevProps: null,
+  };
+}
+
+function makeElement(type: string, key?: string): UNode {
+  return { type, props: {}, children: [], ...(key !== undefined ? { key } : {}) };
+}
+
+describe("longestIncreasingSubsequence", () => {
+  it("empty array → empty result", () => {
+    expect(longestIncreasingSubsequence([])).toEqual([]);
+  });
+
+  it("single element → [0]", () => {
+    expect(longestIncreasingSubsequence([5])).toEqual([0]);
+  });
+
+  it("already ordered [0, 1, 2] → all stay", () => {
+    const result = longestIncreasingSubsequence([0, 1, 2]);
+    expect(result).toEqual([0, 1, 2]);
+  });
+
+  it("[2, 0, 1] → LIS positions: [1, 2] (values 0, 1 stay)", () => {
+    const result = longestIncreasingSubsequence([2, 0, 1]);
+    expect(result).toEqual([1, 2]);
+    const moved = [0, 1, 2].filter((i) => !result.includes(i));
+    expect(moved).toEqual([0]);
+  });
+
+  it("reversed [3, 2, 1, 0] → LIS length 1, three moves", () => {
+    const result = longestIncreasingSubsequence([3, 2, 1, 0]);
+    expect(result).toHaveLength(1);
+    const moved = [0, 1, 2, 3].filter((i) => !result.includes(i));
+    expect(moved).toHaveLength(3);
+  });
+
+  it("[0, 4, 2, 3, 1] → LIS covers 0, 2, 3", () => {
+    const result = longestIncreasingSubsequence([0, 4, 2, 3, 1]);
+    expect(result.length).toBeGreaterThanOrEqual(3);
+    const vals = result.map((i) => [0, 4, 2, 3, 1][i]!);
+    for (let i = 1; i < vals.length; i++) {
+      expect(vals[i]).toBeGreaterThan(vals[i - 1]!);
+    }
+  });
+});
+
+describe("reconcileChildren LIS move detection", () => {
+  it("already ordered children → no moves", () => {
+    const oldFibers = [
+      makeFiber("a", "div"),
+      makeFiber("b", "span"),
+      makeFiber("c", "p"),
+    ];
+    const newChildren = [
+      makeElement("div", "a"),
+      makeElement("span", "b"),
+      makeElement("p", "c"),
+    ];
+    const result = reconcileChildren(oldFibers, newChildren);
+    expect(result.moves.size).toBe(0);
+  });
+
+  it("reordered children → moves for out-of-order", () => {
+    const oldFibers = [
+      makeFiber("a", "div"),
+      makeFiber("b", "span"),
+      makeFiber("c", "p"),
+    ];
+    const newChildren = [
+      makeElement("p", "c"),
+      makeElement("div", "a"),
+      makeElement("span", "b"),
+    ];
+    const result = reconcileChildren(oldFibers, newChildren);
+    expect(result.moves.size).toBeGreaterThan(0);
+    expect(result.matched).toHaveLength(3);
+  });
+
+  it("adding child at start doesn't move existing ones (LIS covers all old)", () => {
+    const oldFibers = [
+      makeFiber("b", "span"),
+      makeFiber("c", "p"),
+    ];
+    const newChildren = [
+      makeElement("div", "a"),
+      makeElement("span", "b"),
+      makeElement("p", "c"),
+    ];
+    const result = reconcileChildren(oldFibers, newChildren);
+
+    expect(result.matched).toHaveLength(2);
+    expect(result.added).toHaveLength(1);
+    expect(result.moves.size).toBe(0);
+  });
+
+  it("reversed list → LIS of length 1, three moves", () => {
+    const oldFibers = [
+      makeFiber("a", "div"),
+      makeFiber("b", "span"),
+      makeFiber("c", "p"),
+      makeFiber("d", "section"),
+    ];
+    const newChildren = [
+      makeElement("section", "d"),
+      makeElement("p", "c"),
+      makeElement("span", "b"),
+      makeElement("div", "a"),
+    ];
+    const result = reconcileChildren(oldFibers, newChildren);
+    expect(result.matched).toHaveLength(4);
+    expect(result.moves.size).toBe(3);
+  });
+
+  it("[2, 0, 1] pattern → index 0 stays, indices 2 and 1 move", () => {
+    const oldFibers = [
+      makeFiber("a", "div"),
+      makeFiber("b", "span"),
+      makeFiber("c", "p"),
+    ];
+    const newChildren = [
+      makeElement("p", "c"),
+      makeElement("div", "a"),
+      makeElement("span", "b"),
+    ];
+    const result = reconcileChildren(oldFibers, newChildren);
+
+    const oldIndices = result.matched.map((m) => oldFibers.indexOf(m.oldFiber));
+    const lisPositions = longestIncreasingSubsequence(oldIndices);
+    const lisSet = new Set(lisPositions);
+
+    const movedIndices = result.matched
+      .map((_, i) => i)
+      .filter((i) => !lisSet.has(i));
+    expect(movedIndices.length).toBeGreaterThan(0);
+
+    const stayedIndices = result.matched
+      .map((_, i) => i)
+      .filter((i) => lisSet.has(i));
+    expect(stayedIndices.length).toBeGreaterThan(0);
+  });
+
+  it("moves map contains old fibers that need moving", () => {
+    const oldFibers = [
+      makeFiber("a", "div"),
+      makeFiber("b", "span"),
+    ];
+    const newChildren = [
+      makeElement("span", "b"),
+      makeElement("div", "a"),
+    ];
+    const result = reconcileChildren(oldFibers, newChildren);
+
+    expect(result.moves.size).toBe(1);
+    for (const fiber of result.moves.values()) {
+      expect(oldFibers).toContain(fiber);
+    }
+  });
+
+  it("no matched children → empty moves", () => {
+    const result = reconcileChildren([], [makeElement("div", "a")]);
+    expect(result.moves.size).toBe(0);
+  });
+});
\ No newline at end of file