Claims

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1974_01_01_burgess_erdos: Erdős (Math. Balkanica 4, 1974) proves with Burgess that c(n) <= (2^n-2)((n+1)^n-2)-1 and says a theorem of Brauer gives c(n) < alpha n^(n+1); a congress volume; partial, claimed.

1998_02_01_hudelson: Hudelson (J. Combin. Theory Ser. A 81, 1998) bounds c(n) above by a constant times (2n)^(n-1) for every n, below the bound Burgess and Erdős proved; refereed; partial.

2018_03_24_connor_marmorino: Connor and Marmorino (J. Geom. 109, 2018) prove c(n) >= 2^(n+1)-1 for n >= 3, c(n) <= 1.8 n^(n+1) when n+1 is prime and c(n) <= e^2 n^n otherwise; refereed; partial.

2026_07_14_snyder: A Lean 4 theorem credited to Colin Snyder of Star Fleet Math states that c(n) is not of order at least n^n, through an explicit o(n^n) tiling threshold in odd dimensions; linked by the formal-conjectures catalog, not audited here.

2026_07_24_zeng: A proof-claim listing bounding the collective gcd threshold h(n) by a square-root scale whenever it exceeds P(n), with the consequence c(n) = o(n^n) for odd n, so the uniform lower bound c(n) >> n^n fails; a partial claim, unreviewed.

2026_08_05_korsky: A manuscript bounding c(n) above by (C max{P(n), n^(1/(4 sqrt e)+eps)})^n, with (log n)^2 in place of the power under GRH, and below for even n by about (1 - 1/log_2 3) n 2^n; partial, unreviewed.

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