Geopotential Resolution of a Clock at One Part in 10 to the 18: Height Equivalent and Levelling Reach

Chronometric levelling turns a frequency comparison into a potential difference. In the weak field the relation is linear, yet its practical meaning depends on a single conversion: how much geopotential, and how much height, corresponds to the fractional uncertainty a clock can actually sustain after averaging, transport and link noise are included. This paper evaluates that conversion across seven uncertainty levels and separates the clock term from the link and systematic terms that usually dominate a field comparison. The computed results, taken from the deposited script, are as follows in summary: The computed rows entry 1 frac_unc is 1e-16. The computed rows entry 1 dW_m2_s2 is 8.99. The computed rows entry 1 height_m is 0.916. The computed rows entry 1 height_cm is 91.6. The computed rows entry 2 frac_unc is 3e-17. The computed rows entry 2 dW_m2_s2 is 2.7. The computed rows entry 2 height_m is 0.275. The computed rows entry 2 height_cm is 27.5. The computed rows entry 3 frac_unc is 1e-17. The computed rows entry 3 dW_m2_s2 is 0.899. The computed rows entry 3 height_m is 0.0916. The computed rows entry 3 height_cm is 9.16. The computed rows entry 4 frac_unc is 3e-18. The computed rows entry 4 dW_m2_s2 is 0.27. The study is a computation from stated assumptions, not a measurement, and its figures should be read at the precision those assumptions support.