Reputation, Residual Power, and Verification Investment in Digital Settlement

Static residual-trust analysis treats the residual surface of an issuer or operator as institutional given. This paper embeds thatpartition in a repeated interaction with endogenous reputation and user exit. An operator chooses verification investment av,residual intensity ar, and (optionally) disclosure; users update reputation from residual incidents and allocate adoption against anoutside option. Under stated regularity conditions there exists a discount-factor threshold beta* such that for all beta > beta* theMarkov-perfect verification level strictly exceeds the myopic benchmark. Assumption A3 (strictly increasing continuation valuein reputation) is derived from supermodular primitives. A calibrated numerical example with incident probability p =ar/(1+kappa av) yields beta* approximately 0.4 under the reported parameters. Incomplete-contract mapping to retail CBDC clarifies why residual power remains large under short horizons. Open zero-knowledge settlement artefacts illustrate high avwith named residual operator power. Keywords: residual trust; reputation; repeated games; verification; CBDC; incomplete contracts; zero-knowledge settlement. JEL: C73, D82, D86, E42, G28. Working paper; not peer-reviewed. Numerical results are illustrative, not empirical estimates of any live system.