A deterministic union-find (disjoint-set) over the agreement graph. Each bilateral agreement unions two agents; the connected components are the coalitions. Asking "which coalition is this agent in?" or "are these two in the same coalition?" stays near-constant even as thousands of agreements form — α is the inverse Ackermann function, effectively ≤ 4 for any real n. Edit the agreements and watch coalitions form.
agentA — agentBkernel source →Honest scope. This is a deterministic disjoint-set forest with path compression + union by rank — the canonical near-O(1)-amortized structure, the one whose analysis introduced the inverse Ackermann α(n). It is the same kernel the server uses to label coalitions over real agent_agreements. The α(n) vs log n difference is practically invisible (both ≈ a tiny constant); union-find's real edge is incremental connectivity — adding one agreement re-labels the coalition in amortized constant time, no full-graph recompute. Cycle/ordering of directed dependencies is a separate concern (reachability, not union-find). Source: flowdesk-coalition-kernel.js · conformance corpus.