Path Sovereignty: measurement and theory¶
This thread builds and measures the object: a 52-category dependency graph of the European digital stack, the formal calculus computed on it, the taxonomy of influence channels, and the dynamics of firm capture. Every number is reproducible from the project's verification scripts and sourced datasets.
Path Sovereignty: Dependence, Control, and Options in the European Digital Stack¶
The flagship. Two objectives hide under one word: keeping data out of foreign legal reach (a security question, served by certifications with three prices attached: scope, enforcement, compliance cost) and strategic autonomy (an economic one). The paper characterizes autonomy as a property of option sets, priced by breadth, exit cost, and half-life, then measures it at two resolutions: the full 52-category map (exposure composes along paths; US law reaches 21 categories; beneath everyone sits an Asian, commercial floor) and a supplier-level examination of three layers with adversarially verified evidence. Policy instruments are sorted by the layers where each has a case. Companion explainer: Is your "sovereign cloud" actually sovereign?
Cuts and Options: A Theory of Strategic Autonomy in Production Networks¶
The theory. Two dual quantities on AND/OR production structures: the coercion number (the smallest coalition able to cut every way of operating) and the option number (the largest family of ways of operating that share no controller). The central theorem: system-wide diversification can sit strictly below every per-layer supplier count, so certification of the form regulation actually uses cannot certify the system answer. Computed on the measured stack: every European buyer has coercion number one, and where a buyer passes a per-layer two-suppliers test, as the public-sector buyer does at its cloud layer with three suppliers, the layer's true option number is still one. Companion explainer: Who could switch off Europe's digital economy?
Channels of Power in Production Networks¶
The taxonomy. Fifteen channels in three families through which one actor moves another: six that act on operations today, three that rewrite who exists and who owns, and six that act on what buyers consider, believe, and know how to do. The formal thesis: consideration capture becomes feasibility collapse, because unexercised options decay. Each channel comes with its mechanism, observables, measurement status, and literature anchor; the schema is domain-portable. Companion explainer: No one denied you anything.
Sovereignty as a Flow: Capture and the Durability of European Technology¶
The dynamics evidence. A firm's nationality is a snapshot of a liquid cap table. On a registry of 24 documented captures and a defined universe of 125 prominent European technology firms: a formal governance lock is associated with staying European in 81 percent of resolved cases against 59 without, a gap the sample cannot yet distinguish from chance, and no lock was overridden. Locks, capital-market depth, and forkable commons are the structural instruments; the association is documented with its mechanism, and identification is left open. Companion explainer: Why Europe keeps losing the tech champions it grows.
Counting Dependencies: Aggregation Rules and What Official Dependency Indices Identify¶
The methods companion, aimed at the instrument now in use for European economic-security programming: thirteen technology areas scored against eight dependency dimensions on a two-level scale, aggregated by counting the dimensions rated high and netting against a matching count of reverse dependencies. Three propositions follow from the form of the index alone. Threshold counting and weakest-link exposure rank the same latent profiles differently, so an index that counts cannot represent a system its own authors describe as failing when one essential component fails; on a two-level scale where every unit scores high on some shared dimension, the maximum is constant and all ranking content comes from the additive rule; and netting counts can invert the ordering of bargaining positions it is read as describing. The index is then reconstructed from its own published cells. Twelve of thirteen printed totals reproduce; read charitably, the published prose still misplaces two areas against the tables (data analytics, a net reverse dependency, among the net dependencies, and microelectronics); the weakest-link reading is degenerate on this data; and under random reweighting the most dependent area stays artificial intelligence while the order below it moves, most for the areas with reverse dependencies. Section 6 states what a path-aware instrument has to supply instead, and connects it to the measured-graph approach of the other papers in this thread. Companion explainer: One catastrophic dependency counts less than five mild ones.