Existence of collapse remains unproved in general

Prove that collapsing actually occurs for polygonal dynamics in projective space P^d that admit a scaling symmetry, beyond merely predicting potential collapse points via infinitesimal monodromy, at least for generic polygons over complete algebraically closed valued fields.

Background

While the paper identifies potential collapse points using infinitesimal monodromy and provides supporting numerical evidence, the authors note the lack of a general proof that collapsing occurs. This motivates the formulated conjectures and highlights a central unresolved aspect of the theory.

Establishing collapse would solidify the predictive framework and unify observed phenomena across diverse polygonal dynamics.