Small maximal Sidon sets

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foundations/: The blocking criterion, the cubic counting bound, and the Ruzsa benchmark.

source_notes/: Paper summaries and source comparisons used in the research on Problem 156.

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The target and the scale

For every sufficiently large $N$, construct a strong Sidon set $A\subset[1,N]$, maximal in this interval, with $|A|\le C N^{1/3}$ for an absolute constant $C$, or prove that no such bound exists. Strong Sidonicity counts unordered pair sums, including doubles. For $x\notin A$, the blocking criterion is

$$x\in A+A-A\quad\text{or}\quad 2x\in A+A.$$

The counting bound gives the cubic-root lower scale. Ruzsa's lifting argument gives $O((N\log N)^{1/3})$. The logarithm-free question remains open.