Monopoly geometry is the failure mode of relational geometry. It arises when a single actor owns the compute, the robots, the infrastructure, the data, the money rails, and the access system — swallowing nearly every function at once.
Such an actor can then decide what counts as value, what counts as truth, what counts as adequate contribution, who qualifies, what is viable, and what resources exist. The vocabulary of “standing” and “fit” can still be spoken, but it has been captured: standing now follows performance, algorithms adjudicate worth, and access to basic participation becomes contingent on obedience to the system that controls the resources. At that point relational geometry has collapsed into domination.
The defenses against it are structural, not verbal: keep standing prior to value, keep jurisdiction distributed so no one function can define and control all the others, and preserve real exit, appeal, privacy, and plurality. See A Perfectly Optimized Cage.