You're making my head hurt. Also, perhaps part of the problem is that's not how Karma works.

Here are the actual rules for Karma exchange:

1. A person with good karma will increase their good karma by helping a person with good karma.

2. A person with good karma will increase their good karma by helping a person with bad karma.

3. A person with bad karma will increase their good karma by helping a person with good karma.

4. A person with bad karma will increase their good karma by helping a person with bad karma.

The steady-state of Karma is enlightenment - we all break free of the wheel and vanish into the universe in a cloud of patchouli-scented bliss. It may not be a good example for invariance. That might be what got you in trouble - you flippantly picked a religious concept you don't understand perfectly and then used it incorrectly to make your point.

Which - even accepting your terms, even accepting your math - I still don't understand and I have an engineering degree:

While trivial, it is indeed an invariant of the operation as it will work for any object.

WHAT is indeed an invariant of the operation? What are we defining here? An integer plus its negative integer will equal zero - so is that an invariant operation? But that's "invariant" as adjective, not "an invariant" as noun.

I get the condition of invariance - the Conway glider is a great example. But in the Conway glider example, what is the invariant? This is why I gave a counter-example of catalysts - you need them for the reaction, but their mass returns to solution in the course of the process.