The geometric case of the Erdős similarity conjecture
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
Scope
The formalization proves the dyadic case of the Erdős similarity conjecture. For every $0<\eta<1$, it constructs a compact set $E\subset[0,1]$ of measure greater than $1-\eta$ that contains no affine copy of ${2^{-n}:n\ge1}$. Explicitly, for every translation $x$ and every nonzero real dilation $s$, some point $x+s2^{-n}$ lies outside $E$. Both signs of $s$ are included.
Comparator links
| Result | Comparator statement |
|---|---|
| Positive-measure avoidance of every affine dyadic sequence | DyadicAvoidance.lean |