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I'm looking to understand the appropriate formalism to represent a protocol step where Alice sends Bob a proof of knowledge of an exponent. Is it accurate to depict this step using an arrow annotated with $\mathrm{PoK}(a:g^{a})$?

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You probably want a zero-knowledge proof of knowledge, so could write ZKPoK. Otherwise the notation is fine and most readers would probably understand what you meant. (But since such notation is not entirely standardized, it wouldn't hurt to add some explanation of your notation in the text.)

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