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The “rock” on which the Dome of the Rock sits is probably the “Eben ha-Shetiyah” or “foundation stone,” which is what the Holy of Holies was built around, and upon which the Ark of the Covenant* rested. There is no good candidate for that spot within the “City of David” temple hypothesis.
*Don’t worry, it’s being examined by top men right now. What men? *Top* men.