Claimant-Level Leximin Allocation of Irrigation Water in Lossy Multi-Source Networks Under Shortage Scenarios

Fair water allocation is difficult when claimants share lossy canals and reserve supplies. CTI-RLex (claimant–terminal-invariant robust lexicographic allocation) is a linear-programming workflow that raises the weakest guaranteed monthly service lexicographically across enumerated shortage and outage scenarios, subject to reach capacities, conveyance losses, source limits and a bounded recourse budget. Fairness follows claimants, not delivery records. The guarantee vector is unique in exact arithmetic and holds on every convex combination of the scenarios within the combined budget. On a three-claimant Utah benchmark, the minimum guarantee rises from 0.1077 under utilization maximization to 0.4195 at a 2.57% nominal-delivery cost, and bounded recourse adds 9.22% over a rigid plan. Under gauge-scaled supplies, the plan kept every guarantee in all 33 seasons of 1993–2025. On a fifteen-claimant county instance in nine components, the sorted vectors first differ at position two, 0.0689 against 0.0564 under a common floor. One claimant rather than four stays at the floor, at 0.9% lower nominal delivery. Within decree-priority tiers, it gives the same guarantees unless reservoir storage ranks after every decreed right. Recorded 2025 diversions match the seasonal timing of the modeled demand, but two canals diverted two to three times that demand. Both instances remain uncalibrated benchmarks.