Categorical Recursion: the object moves when you look at it

A failure mode our existing names blur

There is a kind of regulatory failure that the usual vocabulary hides. It is not capture. It is not arbitrage in the ordinary sense, and it is not lag. It is what happens when the act of regulating an object causes the economic deployment of that object to shift into an adjacent legal category the regulation does not cover.

Call it categorical recursion. It is the mechanism beneath every proposal that tries to preserve the wage-demand circuit by governing AI as a legal object, and it is why those proposals fail in ways their authors do not expect.

The previous essay, the Sorites Collapse Principle, showed that within any single use of AI there is no line between assistance and replacement. This essay adds the second axis. Even where a line could be drawn, the thing being regulated does not stay on one side of the legal map.

AI is five legal objects at once

AI is not one legal object. It is five simultaneously. It is productivity software. It is capital equipment. It is a substitute for labour. It is strategic infrastructure. It is an engine of recursive research and development. The same model, deployed by the same firm in the same week, occupies all five categories at once, not in sequence and not according to use case.

A frontier model drafting a contract is productivity software to the lawyer who uses it, capital equipment on the firm’s balance sheet, a labour substitute for the paralegal who will not be hired, strategic infrastructure to the state hosting the data centre, and part of a research loop for the lab training the next version. The regulator does not assign these categories. The object already lives in them.

The ambiguity is not rhetorical. Each face is literally true. The model really is software. It really is capital. It really is replacing future hires. It really is part of national compute capacity. It really feeds the next research cycle. None of these descriptions misleads, and all of them are available at once as legal and economic identities.

That is not a defect of bad regulation. It is a property of the technology.

Regulating begins by choosing a face

Inside the legal paradigm, the first thing a regulator must do is select a category. Law operates on legal objects, and legal objects are defined by category. The EU AI Act regulates AI systems by risk tier. Export controls regulate compute by capability threshold. Procurement rules regulate vendors by contract type. Liability regimes regulate harms by chains of causation. Each of these is an act of category selection.

Selection commits the regulator to a definition, and the definition becomes the surface against which the deployed object moves. The object does not need to evade the definition. It needs only to present a different one of its five faces.

Regulate AI as labour substitution, and the firm describes the deployment as productivity software. Regulate it as software, and the state recasts it as strategic infrastructure under a national-security exemption. Regulate it as a weapon, and the developer recasts it as cloud productivity. Regulate frontier training, and diffusion moves to smaller open-weight models inside ordinary workflows. Regulate deployment, and the firm describes the system as assistance under human oversight. Regulate assistance, and the boundary with ordinary software disappears.

At no point does anyone have to break a law. The object simply shows another face.

The legal architecture supplies the exits

The clearest case is the EU AI Act, Regulation (EU) 2024/1689, which is explicitly built on categories. Its architecture creates the routes of migration itself. Provider, deployer, downstream integrator, fine-tuner, open-source releaser, enterprise customer and general-purpose model with systemic risk are not just compliance labels. They are legal identities defined in Articles 3, 25 and 51. Once obligations attach to one identity, value moves through the others.

The Commission’s own guidance for general-purpose AI providers, non-binding but revealing, confirms the structure. Most fine-tuning, adaptation and minor modification does not create new provider obligations unless it crosses a high threshold, defined as more than a third of the original model’s training compute. Open-source release is treated differently from commercial release, although that exemption does not extend to general-purpose models with systemic risk. Downstream integrators inherit obligations differently from upstream providers. Each distinction is reasonable alone. Together they are a set of doors.

A model whose direct deployment as a high-risk system would carry heavy obligations can be released, modified, integrated or wrapped through neighbouring roles whose obligations attach differently. Where systemic-risk duties remain, the compliance surface shifts from direct deployment towards release, modification, integration and downstream use. A general-purpose capability can be split across models, wrappers, tools, integrations and workflows whose individual parts sit below the most visible threshold. The regulator is left reconstructing systemic function after deployment instead of identifying it before.

The market has already organised itself along these lines. Under the alliance Anthropic announced with DXC Technology in June 2026, DXC will train tens of thousands of engineers to embed Claude inside the systems it runs for banks, airlines and other regulated industries. In legal terms the capability arrives in those sectors as an IT services engagement, through the integrator and deployer identities, not as a labour policy decision. Nothing about that is evasion. It is the ordinary shape of enterprise technology, and it is exactly the shape a category-based rule cannot hold.

The regulator did not create loopholes. The regulator created categories, which is what regulators have to do. The object moves between them because it is the kind of thing that exists in all of them at once.

Every rule becomes a signal

What makes this new is the recursion.

In ordinary regulatory arbitrage, a regulated party finds a workaround, the regulator updates the rule, and the workaround closes. The contest is unstable but bounded. Regulation lags, but it is not structurally defeated.

Categorical recursion differs because the act of regulating one face is itself information. It tells every firm which face is under scrutiny, and gives every firm an immediate reason to describe its deployment under one of the other four. The rule does not merely fail to catch the object. It creates the signal and the incentive for the object to move.

This happens at the speed of a press release. The regulator broadens the definition, and the market occupies a face not yet defined. The regulator attempts a comprehensive framework, and the market points to the multi-category problem as proof that comprehensive frameworks cannot work.

The regulator does not lose because it is slow. It loses because it is working on the wrong material. Categories cannot enclose an object whose economic deployment chooses its category in response to being enclosed.

Capture is about incentives, and this is about what the object is

It is tempting to read this as a refined kind of regulatory capture. It is not. Capture requires the regulated party to influence the regulator’s preferences or rules. Categorical recursion requires no influence at all. It operates against a regulator that is perfectly honest, perfectly resourced and perfectly motivated.

The mechanism is structural. The regulator’s instrument is the legal category, and the deployed object’s room to manoeuvre is the same legal category. The object does not have to corrupt anyone. It has only to be the kind of thing that can be five things at once.

What moves is the wrapper, not the weights

The model does not literally evade anything. The network is stable, and the weights do not change to escape a rule. What moves is the legal and economic wrapper around them: provider, customer, tool, service, infrastructure, research artefact, fine-tune, agent, workflow, API, internal system, open-weight derivative.

The object does not evade as software. It evades as capital. Its technical core is stable enough to deploy, and its legal identity changes depending on where the rule attaches. Regulation attaches to manifestations. Capital moves through relations. That mismatch is the failure.

This identifies the real target. What would need governing is not AI as a technical object but AI as capital in motion, and motion is precisely what categories cannot hold.

Two axes together exhaust the regulatory surface

Categorical recursion sits on top of the Sorites problem. Within any one face, there is no clean line between assistance and replacement. Spell-check, autocomplete, draft generation and autonomous composition form one continuous gradient, and no rule can identify the moment a worker stopped being helped and started being substituted, because no such moment exists.

Recursion adds a second dimension. Suppose a regulator solved the Sorites problem within a face. The migration across faces would remain. Sorites makes each face ungovernable on its own terms. Recursion makes the choice of face arbitrary. Between them, they cover the whole regulatory surface.

That is why proposals that work on paper fail in deployment. The paper version assumes a stable object, showing a stable face, along a stable gradient. The deployed version is none of those.

Six gates any circuit defence must pass

Any regime meant to preserve the wage-demand circuit has to survive six failure modes at the same time. It must survive state defection, where a major power refuses the regime and gains advantage. It must survive firm-level reclassification, where companies redescribe deployments to escape coverage. It must survive open-weight diffusion, where capability spreads below the regulatory threshold. It must survive individual adoption, where billions of people make daily tool choices the regime cannot see. It must survive category arbitrage, where the deployed object moves to a face the regime does not cover. And it must survive the assistance-replacement gradient, where the Sorites problem dissolves the regulated distinction from within.

A regime that fails any one of these fails as a defence of the circuit. It may still reduce fraud, improve documentation, slow a particular deployment or create useful liability after harm. Those outcomes are real and worth pursuing for their own sake. They do not preserve mass labour absorption. The claim is narrow. It is that category-based instruments cannot defend the wage-demand circuit, not that regulation is pointless.

The record on circuit defence is consistent. The EU AI Act fails on category arbitrage and the Sorites gradient. Compute thresholds are, on the Frontier Model Forum’s own assessment, an imperfect proxy for risk that may miss small systems with harmful capabilities while catching large benign ones, and work at best as a first filter. Liability regimes fail on the gradient and on individual adoption. Procurement standards fail on firm-level reclassification. Frontier moratoria fail on state defection. Each is competent within its chosen face. None survives the object moving to the next one.

The regulator’s dilemma has no third option

The wage-demand circuit is preserved only by mass labour absorption. Mass absorption requires that AI deployed as a labour substitute be governable. But labour substitution is one face of an object with four others, and governing that face drives deployment to the rest. So no regime that works through legal categories defends the circuit.

A regulator who sees this has two options. The first is comprehensive coverage across all five faces, which demands a precision of definition and a coordination across domains that no institution can deliver, and which itself becomes the signal for the next migration. The second is to abandon categories for outcome-based rules. That requires defining the outcome to be prevented, which returns the problem to definition, which returns it to category. Inside the legal-categorical paradigm there is no third option. The paradigm is the constraint.

What lies outside the paradigm is not regulation. Direct ownership of the compute layer, mandatory redistribution of the gains from automation, and public deployment with non-market allocation rules do not depend on choosing a category, because they act on the flow of value rather than on the deployed object. Whether any of them preserves the circuit, rather than replacing it, is the subject of the next essay.

The regulatory question, as usually posed, has an answer. The deployment moves when it is looked at, and the looking causes the moving. The regulatory state will not defend the circuit, not for lack of will, but because it is applying object-categories to a flow of value.

What would refute this

This essay is refuted by a category-based instrument that holds AI deployed as labour substitution in place without the deployment migrating to another of its legal identities, and that measurably preserves entry-level hiring and junior-to-senior ratios in the sectors it covers. Instruments that succeed at other purposes, such as fraud prevention, safety, documentation or liability, do not count, because the claim is scoped to defending the circuit.

The weaker form of refutation would show that one of the five faces dominates in practice, so that regulating it captures most deployment without migration. The test is empirical. If a rule aimed at labour substitution were followed by stable headcount in the covered work, rather than by reclassification of the same deployments as software, services or infrastructure, the essay would be wrong.