I would recommend not calling such things invariants and not thinking about them in the same way you think about invariants. If you would allow a comparison to physics then you would call such things assumptions: frictionless pulleys, small angle deflections, much slower than light speed, less than nuclear density. The physical theory developed is then correct while the assumptions hold. If you are making such an assumption and your language supports it, add a debug assertion if possible.

For me, invariants are constructs of the design of an algorithm. A list doesn't change while iterating over it-by construction, not because someone else owns the reference and promises not to change it concurrently. This structure can only be instantiated via this function which ensures that that string field can always contains only numeric digits. Those are invariants, thing you enforce by design so you can rely on that later. Assumptions instead are things you do not enforce but rely on anyways.

Back to physics, an invariant would generally be something like conservation of energy or the speed of light being universal. Both of these things are only invariant in certain physical theories which enforce them by construction.