Cuts and Options: A Theory of Strategic Autonomy in Production Networks¶

Stefane Fermigier (Abilian) · sf@abilian.com

Draft working paper v0.12, 2026-09-23. Complete draft; each theorem and proposition is verified numerically; Section 6.1 is stated as open and Section 6.2 holds one result, the rest open.

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Abstract¶

Modern production runs through deep vertical chains in which a producer needs all input classes and can, within each class, choose among substitutable suppliers. This paper develops the combinatorial theory of coercion and diversification on such structures. The scope is the channels through which a controller can deny or condition another actor's operation (physical supply, technology and licensing, legal reach, distribution). The slower channels acting on the same structure, influence over rule-setters, capital, and the capture of suppliers, reshape the structure itself over time and are treated as dynamics, in the research programme of Section 6 and in companion work. One result of that programme is stated: when mandated suppliers choose their own substrate, a clause buys what it names, and a count of independently owned suppliers or a named substrate induces a shared upstream controller; only a clause on the joint trace, with designated roles, buys an option.

Two dual quantities organize the statics: the coercion number $\kappa$, the size of the smallest coalition of controllers able to cut all feasible realizations of a buyer's production, and the option number $N$, the largest family of realizations sharing no controller. Coercion composes as a weakest link across independent input classes, and $N \leq \kappa$ always. The central result is a possibility theorem for certification failure: system-wide diversification can be strictly below every per-layer option count, with the gap opening just where the same controller appears at more than one layer. A per-layer independent-suppliers criterion, the form regulation actually takes, therefore certifies a quantity that can equal two at every layer while a single controller cuts everything. A forkable substrate acts as a standing, self-controlled option and caps exit costs. The graded Leontief operator of applied work coincides with the calculus in support and interpolates it monotonically in magnitude.

The primitives are classical; the mathematics is kin to minimal cut sets in reliability theory and to network interdiction. The certification theorem extends a known multitier-sourcing mechanism, diversification defeated by a shared upstream supplier, from random disruption to coalitions of identified controllers. The control overlay and the duality pair have, to our knowledge, no antecedent in the production-network economics literature. Applied to a measured 52-category graph of the European digital stack, the theory computes the following. Every European demand node has $\kappa = 1$, with five distinct blocs each able to cut unaided at full stack depth and the US bloc above the semiconductor floor for each buyer. On the legal channel both the US and China hold unilateral cut capability at full depth, and above the floor US law on its own cuts four of the six buyers. Each buyer already fails a per-layer test at the single-option classes. Inside the classes that pass, the certificate overstates: the public-sector buyer's cloud layer counts three independently controlled suppliers while the option number at full depth is one. These category-level figures are upper bounds at that resolution, since a class recorded with a single option, or a mixed category deniable by any one of its controllers, makes cutting easier than it is supplier by supplier. A supplier-resolution recomputation on pilot data splits both ways: a fully self-controlled productivity stack exists above the silicon floor, while the accelerator class offers seven suppliers under a single controller. The framework gives exact readings to the criteria in European cloud regulation and locates what they can and cannot certify.

Keywords: production networks, strategic autonomy, coercion, diversification, options, supply security, certification, digital sovereignty.

JEL: F52, L14, D85, L86, O25.

The paper's three-class example: every layer passes a two-independent-suppliers test, yet any two complete stacks share a controller, so the whole stack has one option. Per-layer certification can overstate diversification.

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Fermigier, S. (2026). Cuts and Options: A Theory of Strategic Autonomy in Production Networks.
Draft working paper v0.12, Abilian Econ Lab.
https://econ.lab.abilian.com/papers/theory/