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from Zeldovich, Ya. B.; Khlopov, M. Yu. (1978). "On the concentration of relic monopoles in the universe":

"The majority of particles appearing in any quantum field theory are unstable, and they decay into other particles in a variety of reactions that must satisfy various conservation laws. Stable particles are stable because there are no lighter particles into which they can decay and still satisfy the conservation laws. For instance, the electron has a lepton number of one and an electric charge of one, and there are no lighter particles that conserve these values. On the other hand, the muon, essentially a heavy electron, can decay into the electron plus two quanta of energy, and hence it is not stable.

The dyons in these Grand Unified Teories are also stable, but for an entirely different reason. The dyons are expected to exist as a side effect of the "freezing out" of the conditions of the early universe, or a symmetry breaking. In this scenario, the dyons arise due to the configuration of the vacuum in a particular area of the universe, according to the original Dirac theory. They remain stable not because of a conservation condition, but because there is no simpler topological state into which they can decay."

still that doesn't answer the axiomatic question, why we are still not sure about it?

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    $\begingroup$ Not sure about what? Why did you conclude that protons are monopoles? What do your quoted paragraphs have to do with protons? What does the term "axiomatic question" mean? $\endgroup$ – octonion Apr 9 at 6:49
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    $\begingroup$ If i understand it correctly, monopoles provide a decay channel for protons. Since the decay time predicted is really long, $\gtrsim 10^{30}$ years, you have to wait a long time on top of a really large heap of protons to be able to detect even a single proton decay. This has been done, but in principle you can only provide lower bounds on the decay time - it can always take longer than your statistic would be able to capture. $\endgroup$ – Void Apr 9 at 8:15
  • $\begingroup$ Protons are not monopoles. You have misunderstood. $\endgroup$ – G. Smith Apr 9 at 16:47