Is a free, non-Muslim citizen (Dhimmi) who breaks a treaty subject to execution by retaliation for killing a Muslim slave?

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A free non-Muslim who breaks the covenant (Dhimmi) is not executed by retaliation for killing a Muslim slave because a free person is not subject to retaliation for killing a slave due to the lack of parity between them. Furthermore, he is not subjected to the prescribed punishment (Hadd) for slandering a Muslim, so he should not be killed for killing one, similar to the case of a father regarding his son. However, the Dhimmi is liable for the monetary value (Qimah) of the slave. If the Dhimmi kills a Muslim, the covenant is broken, as demonstrated by the incident reported concerning a Dhimmi who mistreated a Muslim woman, which led to Umar (may Allah be pleased with him) executing and crucifying him. The conditions stipulated to Abd al-Rahman ibn Ghanam explicitly state that intentionally striking a Muslim voids the covenant, as this act is contrary to the security granted and causes harm to Muslims, constituting a breach equivalent to joining in fighting Muslims or refusing to pay Jizyah.