diff --git a/packages/api/src/middleware/auth.ts b/packages/api/src/middleware/auth.ts
index dde32d9..497e70e 100644
--- a/packages/api/src/middleware/auth.ts
+++ b/packages/api/src/middleware/auth.ts
@@ -15,7 +15,7 @@ import type { MiddlewareHandler } from "hono"
  */
 export const authMiddleware: MiddlewareHandler = async (c, next) => {
   // BUG: 'post' should be 'POST' — POST is never treated as public
-  const publicMethods = ["GET", "post"]
+  const publicMethods = ["GET", "POST"]
 
   if (publicMethods.includes(c.req.method)) {
     return next()
diff --git a/packages/api/src/routes/users.ts b/packages/api/src/routes/users.ts
index 53e605a..5b95c30 100644
--- a/packages/api/src/routes/users.ts
+++ b/packages/api/src/routes/users.ts
@@ -1,6 +1,6 @@
 import { Hono } from "hono"
 import { db } from "../lib/db"
-import { notFound } from "../lib/errors"
+import { badRequest, notFound } from "../lib/errors"
 // BUG: missing import — `badRequest` is used below but not imported here.
 // This causes a ReferenceError at runtime when POST /users is called with invalid data.
 // Fix: add `badRequest` to the import from "../lib/errors"
diff --git a/packages/shared/src/types.ts b/packages/shared/src/types.ts
index a2a1377..b6f7974 100644
--- a/packages/shared/src/types.ts
+++ b/packages/shared/src/types.ts
@@ -1,14 +1,10 @@
 /**
  * Shared types used by both the API and any consumers.
- *
- * BUG: The field is named `userName` here but the API routes reference `username`
- * (lowercase n). This causes a type error in routes/users.ts and a runtime
- * mismatch when serialising responses.
  */
 
 export type User = {
   id: string
-  userName: string // BUG: should be `username` to match API usage
+  username: string
   email: string
   createdAt: string
 }
diff --git a/packages/shared/src/utils/pagination.ts b/packages/shared/src/utils/pagination.ts
index 12f8062..38b5a9c 100644
--- a/packages/shared/src/utils/pagination.ts
+++ b/packages/shared/src/utils/pagination.ts
@@ -11,5 +11,14 @@ import type { PaginatedResponse } from "../types"
  * The test in packages/shared/test/pagination.test.ts exercises the full contract.
  */
 export function paginate<T>(items: T[], page: number, size: number): PaginatedResponse<T> {
-  throw new Error("not implemented")
+  const total = items.length
+  const totalPages = Math.ceil(total / size)
+  const start = (page - 1) * size
+  return {
+    data: items.slice(start, start + size),
+    page,
+    pageSize: size,
+    total,
+    totalPages,
+  }
 }
diff --git a/tsconfig.json b/tsconfig.json
index 53de6fd..b4bf326 100644
--- a/tsconfig.json
+++ b/tsconfig.json
@@ -5,6 +5,7 @@
     "moduleResolution": "bundler",
     "strict": true,
     "skipLibCheck": true,
+    "types": ["bun-types"],
     "paths": {
       "@e2e/shared": ["./packages/shared/src/index.ts"]
     }