Certified Elimination of Source Candidates Under Capacity, Transit-Time, and Deadline Constraints.

Source identification is constrained not only by network connectivity but also by whether a finite message can reach observed nodes before a deadline. We study deterministic source-candidate elimination in directed networks with arc capacities and transit times. A time-expanded construction gives an exact causal network-coding characterization in which a candidate is retained if and only if its temporal min-cut to every required recipient is at least the message size. Rejection is therefore conservative for any weaker compliant routing or replication protocol. We derive an equivalent minimum-cost circulation computation, monotone certificates under parameter uncertainty, and closed-form formulas for bidirected trees, including linear-time evaluation for uniform capacities and an O(|V|log2|V|) centroid decomposition algorithm for heterogeneous capacities. Protocol-generated experiments show zero true-source eliminations and substantial refinement in routing regimes. Held-out calibration supports transfer to unseen networks. On benchmark representations of 40 real backbone topology families with 50 to 197 nodes, mean candidate retention falls from 99.3% under static screening to 25.3% under exact temporal screening, without true-source elimination. A focused RLNC diagnostic attributes weak refinement in coding-rich regimes to the static screen retaining all candidates and to broad temporal feasibility, while decode-before-forward restrictions create a substantially larger protocol gap.