What is the authenticity and meaning of the two hadiths: "Four rak'ahs before Dhuhr are equivalent to the prayer of the pre-dawn hours (sahar)," and "Four [rak'ahs] before Dhuhr with no salutation between them, for which the gates of heaven are opened"?

The first Hadith reported from Abdullah ibn Umar (may Allah be pleased with them both) from the Prophet (peace be upon him): "Four rak'ahs before Dhuhr after Zawwal (midday) are counted as their equivalent in the prayer of Sahar..." This is a gharib (unusual) hadith with a weak chain of transmission. Its meaning is that these four rak'ahs are equivalent to four rak'ahs of the Sahar prayer, and Sahar refers to the last sixth of the night.

The second Hadith reported from Abu Ayyub from the Prophet (peace be upon him): "Four rak'ahs before Dhuhr, without a salam in between, for which the gates of heaven are opened." This hadith was weakened by Abu Dawud and declared hasan (good) by Al-Albani. Its meaning is that for these four continuous rak'ahs, the gates of heaven are opened. These are called the Sunnah of Zawwal and are different from the pre-Dhuhr Sunnah.