Assessment Degradation in Coupled Processing Networks

We prove that in any processing network where (i) assessment channels are coupled to the system they monitor, (ii) coupling introduces systematic bias proportional to the coupling level, and (iii) bias compounds multiplicatively through sequential processing layers, the perception gap between the system’s actual state and its self-assessed state is a strictly increasing, convex function of the system-level coupling. We then derive the power-law exponent of this relationship from the organisational structure of hierarchical networks. The derivation depends on a single empirically constrained parameter: the maximum span of control at minimal coupling (m₀). Using the span-of-control relationship m = m₀/C, with m₀ constrained by the published organisational-psychology range rather than by the programme’s own data, the derived exponent is 1.60. The empirical exponent, measured independently from regression on scored coupling data, is 1.50 under v3 scoring (1.61 under prior v2 scoring). The difference is 0.10 under v3 (0.01 under v2): the empirical value sits just below the lower edge of the derivation’s [1.53, 1.85] bracket — consistent with span-of-control values at or slightly above the top of the published range — rather than being a near-exact match. (The narrower [1.54, 1.66] band quoted in the programme’s earlier deposits corresponds to the m₀ ≈ 21–29 sub-range, not the full 15–30 range.) The exponent is proved to be size-independent: city-states and empires have the same exponent, differing only in the perception gap’s magnitude. Falsification conditions are stated.