Optically derived radio-frequency benchmark in methanol: a sub-kHz reference for astrophysical tests of fundamental physics

Methanol radio lines observed in space provide sensitive probes of whether the proton-to-electron mass ratio has changed over cosmic time, but such tests require laboratory rest frequencies with very high accuracy. Here, we determine the frequency of the astrophysically important 12.2 GHz 3₋₁E − 2₀E transition of CH₃OH by measuring near-infrared rovibrational transitions rather than the microwave line directly. Using wavelength-modulated NICE-OHMS locked to an ultra-stable optical frequency comb and referenced via a fiber link to a hydrogen-maser frequency standard, we measure Lamb-dip frequencies near 1.4 µm (216 THz) with 10 Hz statistical reproducibility and absolute uncertainties as low as 130 Hz. Pairs of optical transitions sharing common upper levels form a triangulation scheme that yields the ground-state rotational combination difference. We obtain 12,178,596.415(135) kHz, improving on earlier molecular-beam microwave spectroscopy by a factor of 20 and agreeing with a recent free-induction-decay measurement. This result establishes a sub-kHz laboratory benchmark for a key radio-astronomical methanol line and demonstrates that optical triangulation can be extended to non-chiral molecules with internal rotation.