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Source. Conjecture 1, printed p. 390, also announced on p. 382 (PDF pp. 10 and 2).

For $f(x)$ and $T=\sqrt{\log x\log\log x}$ as in the definitions, the source conjectures

$$f(x)=x\exp(-(1+o(1))T)\qquad(x\to\infty).$$

The lower half is proved unconditionally in that paper. Theorem 2 proves the upper half under its separate intersecting-family Conjecture 2. The unconditional upper coefficient in Theorem 1 is $\sqrt3/2$.

This page preserves the claim's status within the 2013 source. It does not assert that it remains conjectural in the current literature; later solution and formalization evidence is separate from this original-source compilation.

Bears on. Problem 202, and its reciprocal-density counterpart Problem 1190.