rhoCriticalMin_eq
plain-language theorem explainer
The equality fixes the lower bound of the recognition load ratio at the square of the inverse golden ratio. Control theorists in the Recognition Science framework would reference it when setting the minimum threshold for stable operation below saturation. The proof reduces immediately to the corresponding equality for the band lower edge in the geometry module.
Claim. The critical minimum load ratio satisfies $$rho_{critical min} = phi^{-2}$$, where the load ratio is the ratio of demanded recognition rate to maximum bandwidth.
background
The Critical Recognition Loading module sketches a control theorem for the operating regime of recognition systems. The central variable is the load ratio rho = R_dem / R_max, with healthy operation required in the narrow band rho_min < rho < 1. The actuator uses the native 8-tick cadence while stability is judged on the 360-tick supervisory horizon given by lcm(8,45).
proof idea
The proof is a one-line wrapper that applies the theorem rhoBandLower_eq from RecognitionBandGeometry. Since rhoCriticalMin is defined as the abbreviation rhoBandLower, the equality follows by direct substitution.
why it matters
This result pins the numerical value of the lower edge of the sub-saturation control band. It supplies one of the structural lemmas needed for a fuller runtime or physics deployment theorem as described in the module documentation. The equality inherits the phi-based scaling forced by the self-similar fixed point in the Recognition Science framework.
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