MnF₂, the textbook two-sublattice antiferromagnet, has reemerged as a prototypical altermagnet, yet the sublattice-odd exchange that defines this identity remains under active debate: it enters the magnon splitting only in quadrature with the dipole–dipole interaction, its magnitude suppressed and its sign erased. An overdetermined first-principles total-energy mapping resolves this scale as a seventh-neighbor imbalance δJ₇≃+8 μeV. The resulting Hamiltonian, with the dipole–dipole interaction included explicitly, reproduces the low-energy gap and the visible finite-momentum splitting. A longitudinal field B∥ c then acts as a linear amplifier of the hidden scale, opening two signed, field-linear readouts. The first is the compensation field B^∗(Q), the position of minimum splitting, which is equal and opposite at the rotation-related partner momenta: a shift from zero field is itself evidence of a finite imbalance, its side gives the sign, and its magnitude, |B^∗|≃0.34~T here, gives the scale. The second is the fixed-field contrast of the partner splittings, ≃0.14~meV at 1~T, six times the zero-field excess: a sign check from just two spectra. Both readouts survive a 0.12~meV energy resolution, and the construction carries over to any easy-axis collinear altermagnet, bringing μeV altermagnetic exchange within present instrumental reach.