Which of the following does not constitute a method of perfection in secured transactions?

In secured transactions, perfection refers to the legal process that secures the rights of a creditor against third parties concerning a debtor's collateral. Perfection can be achieved through various methods, including public filing, possession of the collateral, or automatic perfection under certain circumstances.

The option involving establishing a lien after a loan default does not constitute a method of perfection because it occurs after a default situation has arisen. In secured transactions, it is critical for a secured party to perfect their interest before default occurs to maintain priority against other creditors and protect their rights in the collateral. Merely establishing a lien after the loan has gone into default does not secure an interest that is recognized in the same way as methods of perfection do, such as filing or possession.

In contrast, public filing is a standard method where a security interest is recorded to notify others of the secured party's claim. Possession of the collateral also serves to perfect the interest by providing a tangible indication of the secured party's rights. Automatic perfection happens in certain situations by operation of law, such as when a purchase money security interest is created in consumer goods.

Thus, the action of establishing a lien post-default does not fit within the recognized methods of perfection at a point that conveys priority and public notice, making