IsUnderloaded
plain-language theorem explainer
A recognition system is underloaded when its load ratio, the ratio of demanded recognition rate to maximum bandwidth, stays at or below the threshold rhoMin. Control theorists building stability margins for semantic condensation models would cite this predicate to flag regimes below the target band. The definition is a direct comparison that applies the loadRatio function to area and demand.
Claim. A system with minimum load ratio $rho_min$, area $A$, and demand $D$ is underloaded when $D / R_max(A) leq rho_min$, where $R_max(A)$ is the recognition bandwidth of the region.
background
The module sketches a control theorem for recognition systems whose central variable is the load ratio rho = R_dem / R_max. Healthy operation is claimed to lie in the narrow band rho_min < rho < 1, with the actuator on the native 8-tick cadence and stability judged over the 360-tick supervisory horizon. Recognition bandwidth is the maximum event rate permitted by the holographic bound: R_max(A) = A / (4 ell_P^2 k_R 8 tau_0) with k_R = ln(phi).
proof idea
One-line definition that applies loadRatio to the supplied area and demand, then compares the result against rhoMin.
why it matters
This predicate supplies one of the structural lemmas for the critical loading control theorem. It sits inside the module that enforces the sub-saturation regime rho_min < rho < 1 and connects directly to the recognition bandwidth definition that encodes the 8-tick cadence and Planck-area bound. No downstream uses are recorded, so it remains a building block awaiting integration into full stability or runtime theorems.
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