Perfect overlap policies have no support-tensor amplification

Exact statement

If the support-overlap graph $J_\psi$ is perfect, then $\Omega_\infty(\psi)=\Omega(\psi)=\alpha(J_\psi)$ . Thus the Cartesian support-tensor packing rate is already attained in one layer. Pure shuffle and full synchronization are the empty- and complete-graph boundary cases.

StatusSelf-contained sandwich proof from classical perfect-graph and Lovász-theta facts

External reviewNo documented external or specialist review of these FPRD results is recorded.

Context

The criterion distinguishes policies whose one-layer support-packing analysis is asymptotically complete from policies that may exhibit tensor synergy.

Proof or evidence

For perfect J, its complement is perfect, so alpha(J)=chi(complement J). The standard sandwich alpha <= Theta <= Lovasz theta <= chi(complement J) collapses to equality.

Perfect-policy criterion →

Verification notes

Empty, complete, and cyclic policy controls agree with the graph construction; the unrestricted theorem is symbolic.

Limitations

Perfection is sufficient, not necessary, for Theta(J)=alpha(J).
The criterion concerns local split rate, not total reachable automaton size without an expression-level realization theorem.

Open work

Use perfect-graph recognition as a policy compiler gate before finite-power XCC search.