What is the foundational basis for establishing Al-Qasamah in a murder claim?

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The basis for Al-Qasamah is established through the narration concerning the killing of Abdullah ibn Sahl in Khaybar. His kinsmen approached the Prophet (peace be upon him) after suspecting the Jews. The Prophet commanded that fifty men from the accusers should swear an oath against one individual from the accused party, who would then be handed over to them. When the claimants objected to swearing regarding an event they did not witness, the Prophet asked if the Jews would clear themselves by the oaths of fifty of their own. Upon the claimants' assertion that the Jews were disbelievers and misguided, the Messenger of Allah (peace be upon him) paid the blood-money (Diyah) from his own treasury. This narration is agreed upon (Muttafaq 'alayh).