Cactus-shadow extension conjecture for the necklace formula

Let an embedded shadow have a block-adjacency graph that is a cactus, meaning that any two cyclic blocks share at most one vertex, and suppose that its cyclic blocks are annular in the sense of the source's necklace definition. The attached tree-like components may have arbitrary nesting, and Shapiro's local admissibility conditions are understood relative to the actual nesting of the building polygons.

Cactus-shadow extension conjecture. For any embedded shadow whose block-adjacency graph is a cactus and whose cyclic blocks are annular in the sense of the necklace definition, the formula of the source's necklace theorem remains valid even when the attached tree-like components have arbitrary nesting, provided that Shapiro's local admissibility conditions are interpreted with respect to the actual nesting of the building polygons.

This would extend the known tree--necklace formula beyond the previously treated nesting configurations. The supplied text identifies arbitrary nesting and global compatibility as remaining issues, and gives no evidence that the extension has been proved.