On the Returns to Scale of Organisational Coordination
A mathematical proof for hub-mediated intelligence architectures
d²P/dn² < 0 → d²P/dn² > 0
The sign of the second derivative flips. Not a refinement of the theory — an inversion.
Abstract Bilateral coordination architectures — the organisational model used by virtually every firm in history — exhibit strictly negative returns to scale on coordination, with marginal cost growing linearly in team size while the coordination burden grows quadratically. Hub-mediated intelligence architectures, in which a shared knowledge layer absorbs coordination as a side effect of productive work, exhibit strictly positive returns to scale under defined conditions. A fourth necessary condition is identified — emotionally intelligent knowledge governance — without which the knowledge utility function degrades and the positive-returns property is lost. Three theorems, a corollary, and specific points of contradiction with Coase (1937), Brooks (1975), Dunbar (1992), Chandler (1962), Mintzberg (1979) and Porter (1985).
Cite this paper
Davis, A. L. T. (2026). On the Returns to Scale of Organisational Coordination: A Mathematical Proof for Hub-Mediated Intelligence Architectures. Altimist Ltd, working paper v1.1 (Public Edition), 4 July 2026.