We derive a discrete gauge–coupling dictionary from a rectangular two–torus compacti-fication T 2 selected by the Principle of Least Information (PLI). The dictionary ties eachStandard-Model (SM) coupling αi to a compact geodesic length Li and a small integer mul-tiplicity mi through a single compactification scale K, αi = K mi/L2i . Using only integers≤ 7, we find an isotropic baseline solution with R2/R1 = 1, axis integer k = 7, asymmetricpair (p, q) = (5, 2), multiplicities (mx, my , mpq ) = (2, 1, 4), and K = 0.854580, which yieldsα1(MZ ) = 0.017092, α2(MZ ) = 0.034183, α3(MZ ) = 0.117873,i.e. an overall RMS error of 0.80% vs. the canonical targets. The electroweak ratio α2/α1 = 2follows exactly from the multiplicity pattern on an isotropic T 2. For comparison, ananisotropic accuracy leader with R2/R1 = p4/3 , k = 7, (3, 2), (3, 2, 3), and K = 0.564011achieves RMS 0.40%. Both solutions use only integers and one common scale; percent-levelthreshold corrections (KK/brane matching) can absorb the residuals without introducingfloats. We present the MDL (description-length) rationale, numerics at MZ . High Energyfine structure constant calculated accurately, 1/127. In the second Metrology Paper we apply discrete PLI based parameters in to the calculation of couplings to ascertain if the "No Float" belief that integers are the most PLI appropriate values to minimise Information required to describe the universe.