What is the ruling on the prayer of one who prayed Dhuhr before its Adhan, considering the length of the shadow as evidence of the entry of Asr time? And is he permitted to use ignorance as an excuse if his prayer is invalid?

The time for Dhuhr prayer begins when the sun declines from the meridian towards the west and continues until the shadow of everything becomes equal to its length, after subtracting the shadow at zenith. The sign of the sun's decline is when the shadow starts to increase after reaching its shortest point, or by dividing the time between sunrise and sunset into two halves. If the Dhuhr prayer is performed after the sun's decline, it is valid, and one may rely on the call to prayer (adhan (definition)) of a mu'adhdhin who is knowledgeable of the time. It is not permissible to delay the prayer until after the time for Asr prayer begins, except in case of an excuse. It is obligatory to perform it in congregation at the mosque for those who hear the call. The default is that the prayer is valid and is only invalidated by certainty.