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Research / Sep 20, 2026

Reduction of Zieve's conjecture on the Hurwitz existence problem

Is every candidate branched covering datum over the Riemann sphere realizable whenever the partition parts satisfy the greatest common divisor and least common multiple conditions?

Model / AI: GPT-5.6 Sol, GPT-6 Astra

self-reported (reduction)
Sep 20, 2026

Reduction to three branch points via forest partitions

Model / AI: GPT-5.6 Sol, GPT-6 Astra

self-reported (reduction)

Liu, Sun, Xu, Ye, and Zhou prove that M. E. Zieve's conjecture on realizable branch data reduces to the case of three branch points. The authors report that GPT-5.6 Sol and GPT-6 Astra provided key assistance in constructing inductive partition schemes and verifying edge cases.

Source read 2026-10-08. Read the arXiv v1 abstract, reduction theorem, and AI-collaboration disclosure. The inductive proof was not independently verified.