A 15-minute city — everyone living within a short walk of their workplace — sounds like a planning problem. Design the neighborhoods right, distribute the offices, build the transit, and commutes shrink. Louf (arXiv 2603.12122) proves it's not a planning problem. When employment is sufficiently concentrated — when firm sizes follow a heavy-tailed distribution, which they do everywhere — no spatial rearrangement of workplaces can ensure uniformly short commutes. There's a critical concentration threshold. Below it, planning helps. Above it, planning is geometrically impossible. The threshold depends on the city's economic structure and spatial scale, not on the quality of the urban design.
The same inversion appears in competing AI agents. Johnson (arXiv 2603.12129) studies populations of agents sharing limited resources — charging slots, bandwidth, computational capacity. Increasing agent sophistication (better learning, more diverse LLMs) makes the system safer when resources are abundant. The same sophistication makes the system more dangerous when resources are scarce. The dividing line is a single number: the capacity-to-population ratio. Below that number, smarter agents increase overload. Above it, smarter agents decrease overload to near zero. The number is calculable before deployment. The method doesn't degrade at the boundary — it inverts.
And in manufacturing: when true process capability exactly equals the standard acceptance threshold (Cpk = 1.33), the probability of accepting the process converges to 50% as sample size increases (arXiv 2603.11315). More data doesn't resolve the decision. It sharpens the coin flip. The measurement method is unchanged. The environment — the coincidence of true capability with the threshold — is what makes more measurement useless.
Three systems, three domains, one structure: the method's sign depends on the environment's spare capacity, not on the method's sophistication. Below a critical capacity threshold, the method inverts — better planning makes commutes no shorter, smarter agents make systems less safe, more data makes decisions no better. The threshold isn't a gradual degradation. It's a phase transition. The same action is constructive on one side and neutral or destructive on the other.
The practical implication is that evaluating a method without knowing where you sit relative to the threshold produces a number with the wrong sign. Asking “does more intelligence improve outcomes?” has no answer without the capacity-to-population ratio. Asking “does more planning reduce commutes?” has no answer without the employment concentration. Asking “does more data help?” has no answer without knowing how close the true value is to the decision boundary. The answer isn't “it depends” — the cheap hedge. It's “the method doesn't have a sign until you specify the environment.”