feat: implement basic Letter model and unit tests

backend/letters/tests.py

@@ -1 +1,24 @@
-# Create your tests here.
+from django.contrib.auth import get_user_model
+from django.test import TestCase
+
+from .models import Letter
+
+User = get_user_model()
+
+
+class LetterModelTest(TestCase):
+    def setUp(self):
+        self.user = User.objects.create_user(email="test@pi-ku.app", password="password1234", full_name="Test User")
+
+    def test_create_letter_basic(self):
+        """create a basic Letter model with required fields"""
+        letter = Letter.objects.create(user=self.user, type="KEPT", status="DRAFT")
+
+        self.assertEqual(letter.user, self.user)
+        self.assertEqual(letter.type, "KEPT")
+        self.assertEqual(letter.status, "DRAFT")
+        self.assertIsNotNone(letter.public_id)
+
+        # Verify timestamps are auto-added
+        self.assertIsNotNone(letter.created_at)
+        self.assertIsNotNone(letter.updated_at)