Three models that work perfectly in isolation: a macroeconomic DSGE model, an epidemic SEIR model, and a vaccine adoption model with hysteresis. Each is well-understood. Each makes reasonable predictions. Connect them, and something new appears that none of them contains.
Phoa (arXiv: 2603.12302) uses decorated cospans — a category-theoretic framework for composing open systems — to couple these three models via shared variables. The composite system exhibits a rejection bifurcation: some trajectories escape through vaccination while others enter a self-reinforcing cycle of mandate backlash, vaccine refusal, sustained infection, and economic recession. The coupling shifts the output gap by 0.78 percentage points and rejection rates by 22 percentage points relative to running the models independently.
The through-claim: the bifurcation is a property of the coupling, not of the components. None of the three models alone produces the rejection spiral. It emerges from the interfaces — the shared variables that one model's output feeds into another model's input. The mathematics of composition (pushouts along variable identifications) creates structure that isn't in the parts.
This is why siloed modeling fails for interconnected phenomena. An economist modeling recession, an epidemiologist modeling disease spread, and a behavioral scientist modeling vaccine hesitancy will each produce correct results. But the crisis they're collectively trying to understand is a coupling phenomenon — it lives in the connections between their models, not inside any one of them. The cospans formalize what everyone suspects but rarely quantifies: the interaction effects dominate.
Phoa, 2603.12302. Category theory / mathematical modeling / epidemiology / economics.