Loop Analysis — feedback-cycle decomposition

Two systems can share the same spectral radius rho and still be different animals: in one, feedback lives in a single strong loop (there is a keystone to break); in the other it is spread across many weak cycles (no single point of intervention). This operator opens the loop structure behind rho on exactly the same weighted graph.

How it reads

loops[] lists cycles with strength; concentration near 1 = keystone regime (targeted backstop plausible), near 0 = distributed regime (interventions must act on the web, not a link). Read together with spectral_fragility_v1 (same matrix, dominant root) and dissipation_v1 (where the flow goes).