The definition of the SI unit "second" is stated as
with the explicitly added note that
This definition refers to a caesium atom at rest at a temperature of 0 K. This note was intended to make it clear that the definition of the SI second is based on a caesium atom unperturbed by black body radiation, that is, in an environment whose thermodynamic temperature is 0 K. The frequencies of all primary frequency standards should therefore be corrected for the shift due to ambient radiation [...]
In referring to a caesium atom in its "ground state", does this definition pertain to caesium atoms that are plainly and exactly unperturbed, whether by black body (ambient) radiation or due to any known or unknown perturbation?
If so, is there any requirement to determine (and possibly correct for) the perturbation, or "shift", of any and all primary frequency standards, besides the described "shift due to ambient radiation"?
In particular, is there any requirement to measure whether the durations of 9 192 631 770 periods of different primary frequency standards and/or of the same primary frequency standard in different trials, had been and remained equal to each other, by (presumably) unambiguous means (such as the "ideal clocks" described in MTW §16.4) ?