Determine the exact bad-observer set below the thickness boundary

Determine the exact set of observers producing nowhere-dense radial images for initial-block Cantor sets with multiplicatively independent bases and c_a+c_b<1.

Background

For the thin regime c_a+c_b<1 with multiplicatively independent bases, the paper proves that an explicit open subset of observers has compact nowhere-dense radial images and that a dense arithmetic subset exists in each exterior corner region. These constructions do not determine whether additional bad observers occur elsewhere, particularly in side strips or near non-corner points of the product.

References

The exact bad-observer set below the thickness boundary is not determined. Theorem~\ref{thm:open-arms} supplies an explicit open subset, and Proposition~\ref{prop:dense-rational-observers} supplies a dense arithmetic subset of the four exterior corner regions. The side strips and the behaviour near non-corner points of the product remain unclassified.

— A thickness boundary and modular obstructions for two-set radial projections  (2609.03400 - Miwa, 3 Sep 2026) in Section Discussion, fourth bullet