Claims

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2026_01_29_barreto_kang_kim_kovac_zhang: Barreto, Kang, Kim, Kovač and Zhang prove that growth at the golden-ratio rate, limsup a_n^{1/phi^n} = infinity, already forces the sum of 1/(a_n a_{n+1}) to be irrational, and that no slower rate does.

2026_01_29_feng_et_al: Theorem 2 of the Gemini case study by Feng, Trinh, Bingham and twenty-one coauthors answers the question yes, by an argument the agent Aletheia found and the human authors wrote up.

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