Self-stresses and projective theorems

Determine how to detect dependencies in incidence structures that represent projective theorems but are not detected by counting, and investigate whether self-stress spaces provide such a detection method.

Background

The paper interprets row dependencies of the projective rigidity matrix as self-stresses and shows that self-stresses can encode classical incidence theorems. The authors ask how this approach can systematically identify dependencies that are invisible to numerical incidence counts.

References

How can we detect a dependence of an incidence structure which represents a projective theorem not captured by counting? Self-stresses are one way.

— Counting for rigidity under projective transformations in the plane  (2503.07228 - Berman et al., 10 Mar 2025) in Section "Open problems and future work," subsection "Self-stresses"