The Peace Treaty with Japan signed on September 8, 1951 has to observe the Law of Nations to be lawful.
Japan renounced all rights of sovereignty over the said territories except Liancourt Rocks pursuant to Article 2 of the Treaty. However, the natural obligations of sovereignty thereover remaining with Japan were just suspended under foreign occupations and cannot be altered or abrogated abiding by the peremptory norm as a principle of the Law of Nations.
The USA is the principal occupying Power pursuant to Article 23(a) of the Treaty, such that restoring those disputed territories to normal status can only be made possible through the good offices of the US President under the Law of Nations based on the principle of territorial integrity as a moral, sacred duty toward Japan.