What is the validity of the interpretation that states there is a decreed lifespan (ajal maqdi) and a specified lifespan (ajal musamma), and that the decreed lifespan can be delayed, unlike the specified lifespan?

This interpretation is incorrect and none of the imams of tafsir (Qur'anic exegesis) have stated it. It is refuted by the verse: "Allah takes the souls at the time of their death, and those that do not die [He takes] during their sleep. Then He keeps those for which He has decreed death and releases the others for a specified term."

Therefore, both death and the specified term are by Allah's decree. Scholars have differed in interpreting the two terms mentioned in the verse: "It is He who created you from clay and then decreed a term and a specified term is with Him." Their interpretations do not include the distinction mentioned in the question.

The Ahl al-Sunnah wal-Jama'ah (Sunnis) affirm that the one who is killed dies at the term appointed by Allah, contrary to the view of the Mu'tazilah who claim that killing cuts off life. The appointed term is one, it does not change, nor does it come early or late. Everything that happens in a person's life is written and predestined with Allah.

As for citing the verse: "And no aged person is granted [additional] life nor is anything reduced from his life except that it is in a register," it is not valid, because the verse does not imply the existence of two terms, but rather refers to Allah's comprehensive and prior knowledge of all lifespans.