Fair-Weather Current Density and Columnar Resistance: Why the Surface Field Is Set by the Lowest Kilometre

This paper computes, from stated assumptions, a budget that is usually quoted without its arithmetic. The headline results from the deposited calculation are: Rcol = 3.02e+17, E0 = 100, frac1km = 0.17, Vcheck = 6.05e+05. On a quiet day far from storms, a downward electric current of a few picoamperes per square metre flows through the atmosphere, driven by the ionosphere's potential of roughly a quarter of a million volts. The calculation is algebraic, every input is named in the Methods, and the deposited code reproduces every quoted number. A comparison with the neutron-branch density bound of the underlying frame is carried through and returns a negative result in plain terms: local densities in this problem are tens of orders of magnitude below that bound, so the bound changes no number reported here. The study is simulated and computed, not measured, and its conclusions are confined to the representative event described in the Methods.