Formal treatment of implicit rerouting

Establish a formal characterization of when local tensor architectures and bond-dimension constraints rule out implicit rerouting of conditional dependencies between non-adjacent variables in fully connected tensor networks.

Background

The recovery proof assumes that a local tensor cannot internally reconstruct a conditional dependence between two non-adjacent variables from its incident bonds. The paper acknowledges that saturated bonds and sufficiently expressive local tensors may nevertheless encode such dependencies without activating the corresponding direct bond.

A formal result establishing sufficient architectural or bond-dimension conditions that exclude this phenomenon would make the rerouting-cost argument and the exact moral-graph recovery theorem rigorous without relying on the stated heuristic assumption.