It is very common to speak of Russia (the Russian Federation) as some sort of continuation of the Soviet Union. While some aspects of that view do hold up, many do not.
It is commonly assumed that the Russian Federation continues to have nuclear capabilities because it inherited the warheads made by the Soviet Union. This seems plausible on its face, but
- the Russian Federation has not performed a single nuclear test in all 32 years of its existence. This is a stark contrast to the USSR's 735 nuclear tests in 42 years of the USSR's being a nuclear-capable country.
- Purportedly this is due to Russia continuing to honor the Comprehensive Nuclear-Test Treaty(CTBT) ratified by the USSR in 1990. However, the Wikipedia lists the treaty as being "not in force." So I am not certain Russia actually has any obligations until the treaty comes in force.
- Russia could withdraw from the treaty at will. It did withdraw from the Open Skies arms control treaty for example. It has also effectively withdrawn ("suspended participation") in the intermediate-range nuclear arms treaty. So it is certainly no stranger to ending nuclear arms treaties lately.
There is a credible reason to think that Russia may not be able to maintain its nuclear warheads in a working order.
Nuclear-Capable Missiles Do Not Equate to Nuclear Missiles
The US has effectively sponsored Russia's space program by using Russia's launchers and paying for them. This money provided funding for the training and maintaining of scientists and engineers involved in working on rocket engines. Surely some of it had to have trickled to the universities training students for those fields as well. So it is not surprising that Russia has developed some new short-range missile types in the recent years. The missile program was funded and stayed alive.
I don't see any reason to assume the same about the (very different) field of nuclear engineering and the fields supporting it (such as instrumentation, etc). And since some of these applied fields were actually studied in universities which were in Ukraine or other Soviet republics, it is unlikely that the education program for preparing professionals to maintain nuclear warheads stayed comprehensive.
The Russian Federation is not the USSR (not by a long shot)
- all the Soviet-era nuclear officers had to have retired after 32+ years.
- military officers were (de facto) the highest caste in the USSR. Military has not enjoyed almost any clout in the Russian Federation. And during the 90s it was questionable whether any funds were spend on maintaining any military equipment in a working order.
- electronics on nuclear warheads need to be replaced regularly because of the constant stream of radiation degrading them. It is unclear that the Russian Federation has the stockpiles of electronics fitted for its warheads or if it has the expertise to produce new ones.
- The education system in Russia suffered set backs during the 90s and most working scientists, and many science professors, had left the country for better-paying jobs abroad. This effected the space industry less because it continued functioning with the US sponsorship. But the same is not true of the nuclear industry.
- the Russian Federation has less than 1/2 the population of the USSR (144mil vs 289mil ). So not only have many of its best scientific minds left the country, but its pool of students who can be trained in advanced physics has also shrank.
- because of the large number of students being attracted to Computer Science fields, the number of students pursuing degrees in physics and engineering must have shrank as well.
In other words, the old guard is gone and there is a high chance that there is no one to train the new guard. Nor are there many highly-qualified candidates interested in getting stuck in what is now a dead-end job of maintaining nuclear warheads.
Despite all of these factors, it is still possible that Russia maintains enough experts capable of maintaining nuclear warheads and of being able to arm them ready for launch. I personally find that dubious at this stage, but it's not impossible.
Short of Russia performing a nuclear test, what can be done to verify that Russia in fact has warheads which can be armed and that it has people and system capable of arming them?
I am sure Russia has made some threats with respect to using its nuclear weapons in various scenarios which it finds undesirable. However, it is becoming increasingly clear that strategic bluffing is a very large part of Russia's defense doctrine. Which makes verification an even more important part of establishing that Russia is in fact a nuclear-capable country.