What is the correct time for Dhuhr to begin, and is "the length of a sandal strap" in the Hadith of Jibreel for precise determination or for estimation?

Scholars have unanimously agreed that the time for Dhuhr prayer begins when the sun declines from its meridian. No additional condition, such as the shadow reaching the length of a sandal strap, is required; the mere declination (zawal) is sufficient for the entry of Dhuhr's time. This consensus has been transmitted by several scholars, including Ibn al-Mundhir, Ibn Abd al-Barr, and Al-Nawawi. The hadith mentioning the Prophet's prayer (peace be upon him) when the shadow became like a sandal strap does not indicate a specific condition or requirement. Rather, it means that the declination does not become apparent with anything less than that, or that it refers to the completion of the prayer, not the beginning of its time, in order to reconcile the hadiths and align with the Quranic text: "Perform prayer at the decline of the sun." (17:78)