Why urban heterogeneity limits the 15-minute city

The `15-minute city' has emerged as a central paradigm in urban planning, promoting universal access to work and essential services within short travel times. Its feasibility-particularly for commuting to work-has however rarely been examined quantitatively. Here, we show that proximity to employment is fundamentally constrained by the internal structure of urban economies. Combining urban geometry with empirically observed firm-size distributions, we derive a lower bound on commuting times that holds independently of planning choices or transport technologies. This bound reveals a sharp transition: when employment is sufficiently concentrated, no spatial rearrangement of workplaces can ensure uniformly short commutes, even under optimal placement. Applied to Paris and its near suburbs, we find that achieving universal 15-minute commutes would require substantial economic restructuring or differentiated mobility strategies. The relevant question is therefore not whether an $x$-minute city is achievable, but what the minimal feasible $x$ is given a city's economic structure and spatial scale.