Field Codes for Distributed Coupling Samplers and Certified Empirical Transport

תקציר מקורי באנגליתarXiv:2607.27078v2 Announce Type: replace-cross Abstract: In this paper, we formulate three communication tasks for empirical optimal transport: distributed coupling sampling, cost-evaluable coupling output, and scalar value-certified sampling. Our main result is a field-code compiler: any communicated transport field approximating an optimal empirical Monge map to error $\eta$ can be completed by sparse target-cell residuals into an exact-marginal value-certified sampler with scalar certificate $W_1(\mu,\nu)\leq U\leq W_1(\mu,\nu)+2\Delta$, where $\Delta$ is the public target-partition diameter. The certificate accuracy is controlled by $\Delta$ alone. The field error $\eta$ controls residual communication under a cell-margin condition; without a margin, $\eta$ alone does not bound residu