What are the conditions for contracting marriage when parties approach a ruler (Hakim) at the inception of the contract?

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When parties approach the ruler at the beginning of the contract, the ruler shall not marry them except under the conditions required for the marriage of Muslims. This is based on the statements of Allah, the Exalted: "And if you judge, judge between them with justice" (Quran 5:42) and "And judge between them by what Allah has revealed" (Quran 5:49). Furthermore, there is no necessity to validate their existing contract structure.