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The well-known baryon and lepton numbers of the standard model of quarks andleptons are extended to include new fermions and bosons in a simple structurewith several essential features. The usual heavy right-handed neutrino singlets(for neutrino mass and leptogenesis) are related to the axion which solves thestrong CP problem. At the same time, baryon number is broken softly, allowingthe proton to decay. Associated with this breaking, a long-lived dark-mattercandidate (called the pseudo-sakharon) emerges. This new insight connectsproton decay to a new component of dark matter.

Syndetic Extension of Baryon and Lepton Numbers: Proton Decay and Long-Lived Dark Matter