InForcedCriticalBand
plain-language theorem explainer
The definition specifies the forced critical recognition band for a given area and demand as the region where the load ratio exceeds its phase-transition minimum but remains below saturation. Runtime control theorems in recognition systems would cite this to enforce stable operating regimes. It is realized as a direct instantiation of the general critical band predicate using the fixed lower bound derived from phase-transition geometry.
Claim. The forced critical band for area $A$ and demand $D$ is the proposition that the load ratio satisfies $rho_{min} < D / R_{max}(A) < 1$, where $rho_{min}$ is the lower edge forced by phase-transition geometry.
background
In the critical recognition loading framework the load ratio is the ratio of demanded recognition rate to the maximum recognition bandwidth of the bounded region. Healthy operation requires this ratio to lie in a narrow band below saturation but above a minimum threshold set by phase-transition geometry. The module sketches control theorems on the native 8-tick cadence with stability judged over the 360-tick supervisory horizon forced by lcm(8,45).
proof idea
This is a one-line wrapper that applies the critical band predicate to the fixed lower bound rhoCriticalMin for the given area and demand.
why it matters
This definition supplies the fixed control band used by the runtime in the unification of recognition bandwidth and consciousness bandwidth. It fills the structural lemma slot for a fuller runtime or physics deployment theorem, anchoring the operating regime to the phase-transition geometry within the eight-tick octave framework. No downstream uses are yet recorded, leaving open the question of its integration into explicit stability proofs.
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