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I refer to the MO post here for a statement of Beilinson's conjectures about the Beilinson's regulator as a map from motivic cohomology: Beilinson conjectures

A result of Bunke-Nikolaus-Tamme shows that the regulator can be refined to a map of spectra. Has there been any formulation or even spectulation as to how the statement regarding the $L$-value in this setting?

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