Spectral Radius of Alignment

Definition

The maximum eigenvalue of the alignment transform, determining institutional stability across cycles. ρ(A) = 1 means the institution can maintain capability indefinitely. ρ(A) < 1 means systematic decay. ρ(A) = 0 means full misalignment.

Formula

Example

PSC systems have ρ = 1: capital regenerates each cycle. Grant systems have ρ = 0: capital resets to zero each cycle. Debt-driven systems have ρ < 1: capability erodes under volatility.

Source

OAIA Section 4.6