Robustness-based selection of laser-locking architectures for time-delay interferometry in space-based gravitational-wave detectors

Space-based gravitational-wave detectors compare laser phases exchanged between distant spacecraft. Offset phase locking keeps beatnotes in the phasemeter band, while time-delay interferometry suppresses laser frequency noise. A disturbance of one reference can degrade the functions that depend on it, making robustness an additional criterion for choosing a phase-reference architecture. We introduce a quantitative comparison based on established cascade equations and percolation measures, with directed reference graphs and Erdős--Rényi support layers. Under uniform disturbances, the robustness score is determined by the reference-depth distribution. Under nonuniform disturbances and partial dependence, the connected-support criterion can select a different configuration from both the published depth and local-lock criteria and a reference-path baseline. The phase-locking comparisons favor configurations that limit accumulated degradation and supply downstream lasers from references retaining greater connected support. Paired finite-network calculations support these differences in preference. In a separate comparison of optical-input support for time-delay interferometry, requiring connected support on all spacecraft gives a different preference from requiring it on at least one spacecraft. These findings identify disturbance location, reference dependence and the required extent of support as factors that can change architecture selection. Within the stated statistical model, robustness rankings can complement phase-locking feasibility and interferometric performance when prioritizing configurations for space-based gravitational-wave detectors.