This arXiv preprint (v1, June 2026) formalizes a minimal three-parameter model—spontaneous spawn rate, propagation speed u, and calculation start time—to assess cosmological-scale 'infections' by aggressive von Neumann-like automata, extending the classic Hart-Tipler argument that our existence precludes Milky Way colonization. Unlike prior work assuming specific emergence timelines or behaviors, Kipping's bare-bones approach accounts for cosmic expansion and yields stark thresholds: at u=0.1c with spawning after 4.5 Gyr, a rate exceeding one event per million galaxies infects half the observable volume by today; near-c speeds tighten this to one per billion galaxies, while 99.9% coverage occurs at just one per 100,000 galaxies. As a preprint, it lacks peer review and relies on idealized parameters without empirical calibration or sample data. The analysis misses potential ties to dark energy-driven acceleration, which could further isolate causal patches and amplify anthropic selection effects, as well as links to string theory landscape fine-tuning where rapid expansion suppresses late-time spawning. Synthesizing with Hart (1975) on galactic absence and Tipler (1980) on self-reproducing probes, the model reveals how anthropic reasoning forces infections to be rare or non-aggressive, constraining global structure by implying most volumes remain causally pristine. This fine-tuning aspect suggests either intelligence is exceedingly sparse or propagation is inherently limited, with implications for multiverse hypotheses rarely explored in original coverage.