diff --git a/scripts/patch-ap-collection-count-estimate.mjs b/scripts/patch-ap-collection-count-estimate.mjs
new file mode 100644
index 00000000..aeb567af
--- /dev/null
+++ b/scripts/patch-ap-collection-count-estimate.mjs
@@ -0,0 +1,77 @@
+/**
+ * Patch: replace countDocuments() with estimatedDocumentCount() in
+ * federation-setup.js followers/following collection dispatchers.
+ *
+ * All four calls are already wrapped in cachedQuery(), but on cache miss
+ * countDocuments() runs a full aggregate scan. estimatedDocumentCount()
+ * reads collection metadata — O(1).
+ *
+ * Covers: ap_followers (×2) and ap_following (×2) in collection pagination
+ * and counter dispatchers.
+ */
+
+import { access, readFile, writeFile } from "node:fs/promises";
+
+const candidates = [
+  "node_modules/@rmdes/indiekit-endpoint-activitypub/lib/federation-setup.js",
+  "node_modules/@indiekit/indiekit/node_modules/@rmdes/indiekit-endpoint-activitypub/lib/federation-setup.js",
+];
+
+const MARKER = "// [patch] collection-count-estimate";
+
+const replacements = [
+  {
+    old: `          const t = await collections.ap_followers.countDocuments();
+          return [d, t];`,
+    new: `          const t = await collections.ap_followers.estimatedDocumentCount(); ${MARKER}
+          return [d, t];`,
+  },
+  {
+    old: `        return await collections.ap_followers.countDocuments();`,
+    new: `        return await collections.ap_followers.estimatedDocumentCount(); ${MARKER}`,
+  },
+  {
+    old: `          const t = await collections.ap_following.countDocuments();
+          return [d, t];`,
+    new: `          const t = await collections.ap_following.estimatedDocumentCount(); ${MARKER}
+          return [d, t];`,
+  },
+  {
+    old: `        return await collections.ap_following.countDocuments();`,
+    new: `        return await collections.ap_following.estimatedDocumentCount(); ${MARKER}`,
+  },
+];
+
+async function exists(p) {
+  try { await access(p); return true; } catch { return false; }
+}
+
+let patched = false;
+for (const filePath of candidates) {
+  if (!(await exists(filePath))) continue;
+  let src = await readFile(filePath, "utf8");
+  if (src.includes(MARKER)) {
+    console.log(`[postinstall] patch-ap-collection-count-estimate: already applied in ${filePath}`);
+    patched = true;
+    break;
+  }
+  let changed = 0;
+  for (const { old, new: replacement } of replacements) {
+    if (src.includes(old)) {
+      src = src.replace(old, replacement);
+      changed++;
+    }
+  }
+  if (changed === 0) {
+    console.log(`[postinstall] patch-ap-collection-count-estimate: target snippets not found in ${filePath}`);
+    continue;
+  }
+  await writeFile(filePath, src, "utf8");
+  console.log(`[postinstall] patch-ap-collection-count-estimate: applied ${changed}/4 replacements in ${filePath}`);
+  patched = true;
+  break;
+}
+
+if (!patched) {
+  console.log("[postinstall] patch-ap-collection-count-estimate: no target file found");
+}