Exploring the stability of the proton-to-electron mass ratio with quasar spectra

We present a new constraint on the variation of the proton-to-electron mass ratio, [Formula: see text], based on high-resolution spectra of molecular hydrogen absorption lines in the quasar J0405–443. Utilizing updated laboratory wavelengths and a comprehensive treatment of systematic uncertainties, we find [Formula: see text] at redshift [Formula: see text]. This result is derived under the assumptions of a spatially uniform [Formula: see text] across the absorbing cloud and a shared velocity structure for all molecular hydrogen transitions, where the same velocity components apply to each transition. Within this modeling framework, our result represents the most stringent constraint on [Formula: see text]-variation to date and provides a sensitive test of physics beyond the Standard Model over cosmological timescales.