The Minimal Basis of Coordination

This paper proves a minimality result for coordination dynamics: any persistent system of finite agents must solve exactly three irreducible problems—signal extraction, boundary stabilization, and overload management. These problems are independent, jointly sufficient, and minimal. No fourth independent coordination problem exists. The derivation requires only four assumptions weaker than those in economics or game theory: finiteness (bounded capacity, energy, time), information excess (environment supplies more input than agents can process), time-extended coordination (repeated interaction, not single-shot), and nonstationarity (environment changes over time). These apply equally to neurons, organisms, firms, markets, and civilizations. Signal extraction compresses raw input into decision-relevant state representations—mandatory given finite processing capacity and Shannon channel limits. Boundary stabilization hardens repeated interactions into persistent interfaces (roles, protocols, rules)—mandatory to amortize coordination cost over time. Overload management handles regimes where environmental change exceeds design capacity—mandatory to prevent catastrophic rather than graceful failure. Apparent alternatives (incentives, culture, power, learning, strategy) are shown to be reducible to one or more of the three. Strategy in particular exists only when overload is sufficiently suppressed; it collapses under entropy swarming rather than constituting a separate problem. The technical appendix connects the triad to the constraint–information field formalism: signal extraction corresponds to existence of informative gradients in the information field, boundary stabilization to temporal stability of the constraint field, and entropy swarming to curl dominance when state-dependent feasibility projections induce non-integrable effective dynamics. A lemma proves that feasibility projection generically induces curl with an irreducible geometric floor. The result is a basis decomposition of coordination dynamics forced by finiteness, time extension, and nonstationarity—not a behavioral taxonomy but a structural necessity.