Claims

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1997_01_01_gethner_stark: Gethner and Stark prove, from any starting point, that no walk to infinity on the Gaussian primes has steps of length at most 2, a negative answer for every step bound up to 2.

2019_08_27_das: An arXiv note of August 2019 claimed that no infinite sequence of distinct Gaussian primes off the axes has bounded steps; its author withdrew it in September 2024, saying that the paths of its Theorem 3 miss primes.

2024_01_16_stumpenhusen: A three-page arXiv preprint of January 2024 claimed that no bounded-step walk on the Gaussian primes reaches infinity; its author withdrew it the next day, saying that the width of the moat was not correctly computed.

2026_09_26_openai: The release manuscript proves that for every step bound D the components of the distance-D graph on Gaussian primes have bounded size, so no infinite bounded-step sequence of distinct Gaussian primes exists; Lean proof built here.

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