Evaluating the Periodic Sustainability of Cislunar Logistics Architectures: A Reproducible Methodology with an Artemis III–Derived Case Study

Campaign-level assessments of human lunar exploration architectures are commonly performed over finite horizons, which can conceal systematic buffer drawdown and asset drift beyond the simulated window. This paper presents a reproducible methodology in which sustainability is formalized as a periodic (steady-state) property of the coupled inventory–asset system, defined with respect to the modeled state variables and enforced as a binary feasibility gate on all performance evaluation. The architecture is represented as an event-driven multi-commodity flow over a reduced, SpaceNet-compatible network, equivalent to a time-expanded formulation, with propellant demand coupled to transported mass through the rocket equation. Standard measures of effectiveness are augmented with three dimensionless indicators and a composite index whose alignment with the dominant principal component of the trade space is tested a posteriori. On an Artemis III-derived case study the reference cycle closes (z=1, 32.3-day margin), yet 18 of 81 nominally feasible design points lose periodic sustainability under launch-delay perturbations, all 18 classifications being statistically significant at the 95% level. Periodic-state closure thus provides a formal criterion for cycle-to-cycle depletion that requires no arbitrary horizon choice. Applied unchanged to three architectures spanning nearly seven-fold in launch mass, the analysis shows an expendable direct-descent concept leading every mass-normalized indicator at a fixed two-crew objective, an ordering that is stable under ±30% dry-mass and ±10% specific-impulse perturbations, while a Gateway hub becomes preferable once orbital infrastructure and extensibility are valued. This study regenerates deterministically from a single input dataset.