Can you mathematically guarantee a supply chain won’t break?
When a supplier fails, a port closes or a raw-material lane is disrupted, most organizations find out their network was fragile only after it breaks.
A digital twin that could say, in advance, “this network cannot fail here even under disruption X” would turn resilience from a retrospective exercise into a designed-in property — provided the guarantee is real, not decorative.
How it works
Two strictly separated tracks. One built first and prioritised; one exploratory and never allowed to inflate the other’s claims.
Track A — the digital twin. Event extraction → graph representation → GNN risk scoring → a causal layer with a structural causal model and counterfactual “what-if” reasoning.
Track B — the feasibility proof. Tests whether Hilbert irreducibility, a result from arithmetic geometry, can formally certify that a shipment plan is feasible.
Ground truth first. Every synthetic-data method is validated against a known ground truth before touching real data.
Event extraction → graph representation → GNN risk scoring → causal layer (SCM + counterfactual “what-if” reasoning).
Tests whether Hilbert irreducibility — a result from arithmetic geometry — can formally certify that a shipment plan is feasible.
What came out of it
Track A is working: a graph neural network trained on disruption scenarios cut shortfall-prediction error nearly in half against a non-neural baseline.
test MAE — GNN risk model vs. additive baseline, on held-out disruption scenarios
counterfactual estimates within tolerance of the known ground-truth causal model
| Additive baseline | 2.26 |
|---|---|
| GNN risk model | 1.29 |
Track B is where the honesty matters more than the elegance. The Hilbert-irreducibility framing turned out not to hold: a network’s feasible-shipment set is a bounded integer interval, and a bounded set cannot be the integral points of the unbounded structure the theorem requires. That is a negative result, documented rather than hidden.
“The Hilbert-irreducibility framing is a compelling narrative but currently lacks a formal reduction from supply-chain feasibility to integral points on a punctured linear algebraic group.”— independent review of the underlying mathematics, documented in the project record
The pivot is where the real result lives. Reframed as Hilbert bases of flow-conservation cones combined with numerical semigroups for minimum-order-quantity constraints, the project proved a Permanent Gap Characterization theorem for multi-echelon inventory networks: under a realistic per-period capacity cap, the classical “Chicken McNugget” problem — with pack sizes {6, 9, 20}, the quantity 43 can never be assembled — generalises to infinitely many order quantities that are not just hard to reach but permanently unreachable, verified computationally up to 50 periods.
Hilbert irreducibility (arithmetic geometry)
Hilbert bases of flow-conservation cones + numerical semigroups
Permanent Gap Characterization theorem
Under the hood
References
- Luger, C. (2024). Hilbert irreducibility for integral points on punctured linear algebraic groups. arXiv:2410.13403.
- Corvaja, P., Zannier, U. (2017). On the Hilbert property and the fundamental group of algebraic varieties. Math. Z. 286(1–2), 579–602.