An interesting question, one that relies on certain mathematical ordering principles in the current form of the inquiry. It is noticeable that you implicitly applied a sort of set/subset/superset reasoning to the question, particularly from the areas of number theory and set theory, though I think your question can be removed from that sort of or organization but still retain its essential merit.
You do provide a thoughtful basis for attempting to classify and delineate where exactly singular identity can give way to multiplicity, and somewhat inevitably, division and conflict. Now, you conjecture that this boundary exists as a readily identifiable, or as you more strongly state, in an "intrinsically" defined manner based upon the current state of a system. This already begins to suggest social theories of organization, as well as cognitive and psychological theories of the individual. For this, I am not qualified to answer, but I think you would perhaps enjoy as a starting point Sigmund Freud's Civilization and Its Discontents, which more or less discusses how people came to organize themselves, and how conflict can be intrinsically present through the suppression of human instincts.
To provide a personal judgement on your conjecture, I think that it is false, and by way of counterexample. You seem to implicitly rely upon the assumption that there can only be one level of unity, lets say level
n, and therefore disunity results at level
n + 1. This becomes problematic, because in your example, you show that any level of unity must necessarily rely on preceding levels of unity, i.e.,
n - 1, which is a contradiction, as
n - 1 necessarily implies, by the hypothesis, that level
n is disunity. We have reached a contradiction, but how? This is motivated by a physical interpretation of what is going on. For example and in a more concrete sense, can you have national coherency without the cohesion and harmony of a family? Without the cohesion and harmony of social or political organization? Perhaps yes, perhaps not. Essentially, the way in which you attempt to order 'unity' is highly intriguing, but not entirely iron clad. Interesting attempt of applying mathematical ordering to think about, though.