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The standard model predicts that hydrogen-1 is the only stable nuclide because electroweak instantons allow three baryons (such as nucleons: protons and neutrons) to decay into three antileptons (antineutrinos, positrons, antimuons, and antitauons), which imply the instability of any nuclide with a mass number of at least three; or for two baryons to decay into an antibaryon and three antileptons, which would imply that deuterium could decay into an antiproton and 3 antileptons.
This is very rarely discussed because the nuclides that can only decay through baryon anomalies would be predicted by the standard model to have ludicrously long half lives (to my memory, something roughly around 10^150 years, but I might be wrong).
Hydrogen-1 is stable in the standard model, as it lacks a mechanism for (single) proton decay.