Derive boundary and equivalence cases for cart quantity

POST /api/cart/items accepts:

The contract states quantity is an integer between 1 and 10 inclusive. A request that violates the schema returns 422 with {"code":"VALIDATION_ERROR"}. An unknown productId returns 404 PRODUCT_NOT_FOUND. An unauthenticated request returns 401 UNAUTHENTICATED.

Your task: produce the minimum set of test cases you would actually run, using equivalence partitioning and boundary value analysis. For each, give the input, the expected status, and — this is the part candidates skip — say why that case is in the set. Then name what you would not test, and why.