Beyond Static Bounds: Lovász Theta, Shannon Capacity, and the Dead End of Static Capacity Measures

This research preprint argues that Lovász theta is a powerful ceiling, not a road. Shannon graph capacity Θ(G) is an operational object: it is defined through strong graph powers, explicit construction witnesses, and a supremum over block lengths. Lovász theta ϑ(G) is a single static certificate that upper-bounds capacity for every graph. The theorem Θ(G) ≤ ϑ(G) is one of the great static results in combinatorics and information theory; the interpretive error begins when that certificate is promoted from ceiling to path—from static relaxation to operational capacity measure. The diagnostic landscape is the odd-cycle family. On C5, capacity and theta coincide at √5—an iconic equality that created an interpretive halo. On C7, theta is known in closed form while capacity remains open: C7 exposes the boundary of that halo. The paper names measurement-status drift and status inflation—the habit of treating a static upper bound as the operational measure of capacity—and proposes a realization-sensitive bookkeeping layer: path, cost, admissibility, endpoint semantics, and projection loss. The contribution is architectural: role separation, an eight-row requirements map, a design-level dynamic reading with explicit object slots, and a bridge supplement built on public KFE vocabulary and twenty cited references in graph capacity, Lovász theta, and related bounds. Related public background: KFE Technical Research Note v0.1, DOI 10.5281/zenodo.21198809. Version v0.2.4 — not peer-reviewed.