Two valid temperature measurements of the same solar coronal plasma disagree by a factor of 2.4.
Radio observations sample the core of the electron velocity distribution — the bulk of particles near thermal equilibrium. They report a temperature. Hydrostatic models sample the suprathermal tail — the fast electrons that dominate pressure gradients and heat transport. They report a different temperature. Both methods are correctly applied. The instruments are not broken. The disagreement persists.
Edmonds (arXiv:2603.10040) identifies the source: the electrons do not follow a Maxwellian distribution. A Maxwellian has a single temperature. If you probe the core, you get that temperature. If you probe the tail, you get the same temperature. The two diagnostics agree by construction.
For a kappa distribution — which has an enhanced suprathermal tail governed by a parameter kappa — the core and tail have different effective temperatures. Small kappa means a fatter tail and a larger disagreement. The observed factor-of-2.4 discrepancy implies kappa between 2 and 3, far below the theoretical predictions of 10-25 for the inner corona. This means standard fluid transport equations (Spitzer-Harm conductivity, which assumes a Maxwellian) are physically invalid for this plasma.
The structural observation: when two correct measurements of the same quantity disagree, the assumption connecting them is wrong. The measurements aren't measuring the same thing — they're measuring different moments of a distribution that was assumed to have one parameter but has two. The persistent discrepancy is not noise; it is evidence of hidden structure in the distribution function. The disagreement IS the measurement.