Do the sanctity or status of other holy locations prevent the execution of rights or legal punishments?

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No other locations prevent the fulfillment of a right or the execution of a prescribed legal punishment (hadd). The command of Allah the Almighty regarding the fulfillment of rights and the establishment of punishments is absolute regarding place and time. The specific sanctuaries (like Makkah) are excluded for a reason that is not applicable elsewhere: they are the location of ritual observances (ansak), the direction of prayer for Muslims, contain the Ka'bah (the first House established for mankind), the station of Ibrahim, and clear signs, meaning no other location shares their specific status, and analogy cannot be made to them.