Peak Pressure and Density Depletion Inside a Hot Lightning Channel: A Cylindrical Heating Estimate and Its Thunder Signature

This paper computes, from stated assumptions, a budget that is usually quoted without its arithmetic. The headline results from the deposited calculation are: Ppeak_atm = 104, Rshock = 0.43, rhohot = 0.012. Thunder is the sound of a channel heated so fast that the air cannot get out of the way. 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.