Asymptotic support packing is Shannon capacity

Exact statement

With $\Omega(\psi)=\alpha(J_\psi)$ and $\Omega_\infty(\psi)=\sup_{k\ge1}\Omega(\psi^{\otimes k})^{1/k}$ , the support-tensor theorem gives $\Omega_\infty(\psi)=\Theta(J_\psi)$ . Every finite simple graph occurs as $J_\psi$ for a uniform support policy.

StatusSelf-contained corollary and constructive graph-representation proof; exact audit passes

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

Context

Cartesian support tensors have an exact asymptotic packing rate. This is a policy/graph dictionary; it does not by itself construct an expression-level prefix automaton realizing a code.

Proof or evidence

Apply FPRD-SH-T25 at every power and take roots. For universality, represent each graph edge by a shared token and pad every vertex support with private tokens to the common positive width max(1, Delta(G)).

Shannon-capacity identity →

Verification notes

Uniform support representations reproduce all 1,099 simple graphs through five vertices; tensor products were checked on every graph through four vertices.

Limitations

Unrestricted policies inherit the full difficulty of general Shannon capacity.
The identity alone does not improve a classical capacity bound.
A tensor signature is already a vertex of the strong power; expression reachability is a separate semantic layer.

Open work

Compile structured graph codes into reachable expression automata without treating tensor vertices as already-reachable letters.