Position as Projection: A Formal Theory of How Process Requirements Generate Organizational Structure

Organizational theory has long treated positions as design primitives – the building blocks from which structure is assembled. This paper argues that positions are derived quantities: projections of the organization's process space onto the personnel dimension. Drawing on and extending foundational work by Thompson (1967), Galbraith (1977), Puranam (2018), and Burton, Obel, and Hakonsson (2020), the paper develops a projection operator formalization that represents positions as linear mappings from process requirements to personnel coordinates. Three contributions emerge. First, the projection framework explains why reorganizations that change positions without changing processes systematically fail: they alter projections without altering the space being projected. Second, the specification-transmission mechanism explains why functional departments persist even when process-based structures are demonstrably superior: departments are containers for transmitting tacit specifications through proximity-based apprenticeship, and they compress as specifications become explicit. Third, as AI agents increasingly perform organizational functions without occupying traditional positions, the framework derives conditions under which positions will converge toward process nodes as specification-transmission functions are automated. Six propositions are derived. The framework provides a formal causal mechanism that has been implicit but unspecified in structural contingency theory – the transmission path from contingency factors through process space to structural configuration –and offers a formal account of how organizational structure will change as AI reshapes process execution.