Geometric Obstructions as Dynamical Phase Transitions in Representation Growth

We interpret the dynamical growth model introduced in “Phase Transitions in STFO-Weighted Representation Growth” as a toy model for geometric obstructions in the senseof Geometric Complexity Theory. We show that dominance transitions in the STFO-shadow naturally correspond to changes in admissible growth trajectories, and argue thatrepresentation-theoretic obstructions can be viewed as forbidden histories in a growth process.This reframes complexity separation as a dynamical phase problem rather than a staticmultiplicity problem.