Claims

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2025_12_26_van_doorn_tang: Van Doorn and Tang's Theorem 1.1 (Math. Proc. Cambridge Philos. Soc. 2026), that v(k) >= exp(c k^2) for an absolute c and every k >= 1, with the upper bound v(k) <= c_0^((2/5 + o(1)) 2^k) from the Elsholtz-Planitzer count.

2026_09_16_van_doorn: Every integer between 2 and exp exp sqrt(k/(2 c_0)), c_0 = 14/log 2, occurs as a denominator in some k-term decomposition of one for large k, so v(k) exceeds that bound; a claimed, AI-generated note with an author-side Lean file.

2026_09_25_openai: The OpenAI mathematics release's Corollary 1.3 of 25 September 2026, that exp(exp(k/600)) <= v(k) <= 1 + k^(2^(k-1)) for large k with the slope of log log v(k)/k between log 2/257 and log 2, accepted as a partial answer.

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