Dependence-Aware Risk Certification for Adaptive Spatial Coordination in Spatiotemporal Random Bipartite Matching

Methodological preprint for a dependence-aware, domain-level conditional deficit-risk certificate for adaptive spatial coordination in spatiotemporal random bipartite matching. For a candidate spatial coordination domain, the certificate combines the domain's aggregate conditional expected surplus with an aggregate conditional variance computed from the full cross-zone covariance matrix, so that cross-zone dependence enters the risk assessment directly. These moments define the certificate ratio b_t(C) = V_t(C) / (V_t(C) + delta_t(C)^2), and the conditional one-sided Chebyshev (Cantelli) inequality yields the threshold implication that a bounded certificate ratio bounds the domain-level deficit probability. The statement is finite-sample, non-asymptotic, conditional on valid decision-time moments, and holds at the coordination-domain level rather than as a system-wide probability guarantee.