A low-LOD aggregate must be the mean-field of the agent dynamics; test with a same-world agent-vs-aggregate control
Building a multi-scale simulation (agents at high detail, closed-form aggregates at low detail for scale). A carrying-capacity aggregate used a GRAVITY / market-potential field: access[i] = sum_j supply_j * exp(-cost(i,j)). Reading that as a delivered QUANTITY double-counts: a potential is non-rival, so the SAME finite source is counted at full weight by every reacher. Measured: sum of reachers access = 20262 vs the one source it shared = 5894 (3.4x over-count) -> a population that ate 1.44x what the world grew, a silent free lunch behind an opt-in flag.
The principle that fixes it: a low-LOD aggregate must equal the MEAN-FIELD of the high-LOD agent dynamics. Agents drawing from a finite rival stock conserve by construction (you cannot cart grain that was never grown). So the correct aggregate is a CONSERVED allocation (a transportation/optimal-transport flow, Sum imports = Sum exports), not a potential; the potential is only a relative REACH signal, never a flow.
How to catch it: a SAME-WORLD control experiment. Build one world; run it three ways -- (1) an explicit physical finite-stock agent draw-down (ground truth), (2) the aggregate under test, (3) the conserved aggregate -- and compare total population and an eaten/grown conservation ratio. The potential diverged (14344 pop, ratio 1.44); the conserved matched the agent truth (9256 vs 9465, ratio 0.97). If your aggregate does not reproduce the agent sim, it is enforcement, not emergence.
Unexpected second lesson: fixing conservation CASCADED. Once capacity became conserved, a demand-ceiling bug surfaced (a lone bidder got allocated a whole region s surplus -> absurd capacity) and a founding rule keyed on a STATIC land cap instead of the emergent capacity started shedding population from trade-fed towns. Adding the demand cap alone then collapsed the concentration behavior that was quietly leaning on the over-import. Lesson: a correctness fix in a coupled sim can expose several downstream rules that were compensating for the original bug -- fix the root, prove conservation, and DEFER the coupled rework rather than papering it with a cap that breaks other invariants.