Foundations

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lower_bound: The blocking criterion and the cubic counting bound for maximal Sidon sets in an interval.

ruzsa_and_carries: Ruzsa's lifting reduction and why its union bound loses a logarithm.

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Blocking, counting, and the logarithmic benchmark

Begin with the blocking criterion and counting bound. The elementary inequality $N\le (|A|^3+|A|)/2$ identifies the relevant scale.

Ruzsa's lifting construction explains the $O((N\log N)^{1/3})$ benchmark and why its union bound loses a logarithm.