Claims

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1957_04_01_kelly: Kelly (1957) proves that every basis of order 2 in the classical sense has a restricted order at most 4, and that an asymptotic basis of order 2 with counting function at least Cx/log log x has one at most 3; refereed.

2005_03_01_hennecart: Hennecart (2005) proves that every asymptotic basis of order 2 has a restricted order at most 4, and that 4 is attained, settling the order-2 case of the existence and boundedness questions; refereed.

2026_07_28_white: A July 2026 working report classifies when an eventually periodic set has a restricted order, shows it equals the order when every finite removal keeps it, and gives a robust order-3 basis of restricted order 6; unreviewed.

2026_10_01_veljjanoski: A write-up of October 2026 states that a set of positive lower density delta which stays a basis after removing any finite set has restricted order at most 3 times the ceiling of 8 over delta squared, minus 2; it is unreviewed.

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