Peer-to-peer collaborative systems operating offline face a problem that centralized architectures dissolve by fiat: when no single node holds all the data, and peers connect only sporadically through mesh networks, what does consistency even mean? The framework of IntersectionAtomicity and IntersectionCC answers by shifting the unit of reasoning from the global state to the overlap — the specific data subsets that two peers share. Atomicity and consistency guarantees apply only where interests intersect, not across the entire system.
This reframing is more than a relaxation of classical distributed computing constraints. It acknowledges that in a sparsely connected, partially replicated world, demanding global consistency is not just expensive but meaningless — peers that never share data have no consistency relationship to violate. The formal model lets developers reason about what guarantees actually matter for their users, defined by the geometry of data overlap rather than by architectural ideals.
The structural insight: guarantees in distributed systems are not properties of the system as a whole but of the intersections between participants. Consistency is local to shared context. When you stop demanding that the whole world agree and instead ask only that overlapping views cohere, the problem becomes solvable — and the solution maps to how collaboration actually works.
(arXiv:2603.03899)