A new paper, with arguments generated largely by LLMs and checked by Radchenko and Wheeler, claims to resolve Zauner's conjecture on SIC-POVM existence in every dimension, ranked #227# overall in my LLM-based ranking of the most important open problems in mathematics ( Stark units for real quadratic fields and reciprocity laws — October 4: The disclosure says almost all the document and its arguments "were generated by large language models (LLMs) and edited by humans." The claimed breakthrough completes a chain of earlier work: - Appleby–Flammia–Kopp gave a construction of SICs in every dimension, conditional on two conjectural ingredients: Stark properties and a special-value identity ([January 2025] - Radchenko–Wheeler proved algebraicity of the relevant special values and the identity needed for the construction ([September 18, 2026] - The October 4 follow-up claims the missing reciprocity laws and unitary conjugates, completing the argument for SIC existence in every dimension. This also represents a major claimed advance on Hilbert's twelfth problem (#36#) for real quadratic fields. The general problem over arbitrary number fields remains open. The paper explicitly leaves a stronger square-root refinement of Stark’s conjecture untreated; that refinement is not needed for the SIC conclusion. I haven't found a public formalization of this proof.