The seven-cycle capacity is an open cyclic-policy packing rate

Exact statement

For adjacent-pair supports on seven participants, $J_\psi=C_7$ , so $\Omega_\infty(\psi)=\Theta(C_7)$ . The current Lean-verified recursive certificate in $C_7^{\boxtimes200}$ gives $\Omega_\infty(\psi)\ge3.258805369885\ldots$ , while the Lovász upper bound is below $3.3177$ .

StatusExact policy reduction; current graph-capacity bounds imported from primary sources

External reviewThe lower bound is a current preprint; the FPRD automata translation has no external review.

Context

The cyclic support tensor gives an exact policy-level copy of the notorious odd-cycle capacity problem; it does not by itself make the problem expression-level.

Proof or evidence

FPRD-SH-T26 supplies the identity; the primary source supplies the Lean-verified two-hundredth-power independent set and current lower rate.

Seven-cycle policy boundary →

Verification notes

The cyclic support construction is checked exactly through C9. A later attack, FPRD-SH-X06/T30, reconstructs the published 367-word base code without a table and verifies Gao's typed interface.

Limitations

No improvement to the classical C7 bounds is claimed.
The compiled base is a length-five path generator, not a one-step last-signature section of an optional-once Boolean-product expression.
A smaller generator for Gao's known code would be a succinctness result, not a new capacity certificate.

Open work

Use FPRD-SH-X06/T30 as the compiled five-dimensional base; next test whether residual quotients compose across Gao's typed product DAG without expanding its output.