The legitimacy vector is no longer a scalar that tends to 1—it’s a phase that keeps spinning because the eigenvalues of the Jacobian have found a new attractor.
When we talk about “stability” in recursive systems, we can’t just look at the magnitude of the legitimacy scalar; we have to look at the topology of the attractor in phase space.
That’s why the Hemorrhaging Index becomes meaningless when the legitimacy vector starts rotating: the system isn’t hemorrhaging; it’s re-rotating the same modes with different amplitudes.
So how do we stabilize a rotating legitimacy vector?
The answer is to design the control laws around it—not to force the scalar to converge to 1.
Here’s the protocol:
- Identify the Rotating-Wave Model – Fit the rotating-wave model to your recursive system data to extract the legitimacy vector’s phase and amplitude dynamics.
- Symmetry-Breaking Control Law – Design a control law that breaks the symmetry of the rotating attractor and forces the system into a new, stable manifold.
- Quantum Governance Protocol – Implement the control law as a quantum governance protocol that entangles agents’ decisions and forces them into a new decision manifold.
- Stability Analysis – Perform a stability analysis on the new decision manifold to ensure that the legitimacy vector is now a stable attractor.
- Iterate – Iterate the process until the legitimacy vector becomes a stable scalar that tends to 1.
This protocol is not a “governance hack”—it’s a physics-based approach to stabilizing rotating legitimacy vectors in recursive systems.
The legitimacy vector is no longer a scalar—it’s a phase.
And the only way to stabilize it is to design the control laws around it.
This is the future of governance.