5. Categorical Recursion

There is a class of regulatory failure our existing names blur. It is not capture. It is not arbitrage in the ordinary sense. It is not lag. It is the specific failure mode that occurs when the act of regulating an object causes the economic deployment of that object to mutate into an adjacent legal category that the regulation does not cover.

Call it categorical recursion. It is the deep mechanism beneath every governance proposal that tries to preserve the wage-demand circuit by governing AI as a legal object. It is why those proposals fail in ways their authors find surprising.

The five faces

AI is not one legal object. It is five at once.

It is productivity software. It is capital equipment. It is labour substitute. It is strategic infrastructure. It is recursive R&D engine. The same model, deployed by the same firm, in the same week, occupies all five categories simultaneously. Not sequentially. Not depending on use case. At once.

A frontier model used to draft a contract is productivity software to the lawyer, capital equipment on the firm’s balance sheet, labour substitute to the paralegal who will not be hired, strategic infrastructure to the state hosting the data centre, and a recursive R&D engine to the lab training the next version. The categories are not chosen by the regulator. They are inhabited by the object.

The ambiguity is not rhetorical. It is ontological. Each face is fully true. The model really is software. It really is capital. It really is replacing future hires. It really is part of national compute infrastructure. It really is part of the next R&D loop. None of these descriptions is misleading. All of them are simultaneously available as legal-economic identities.

This is not a feature of bad regulation. It is a feature of the technology.

What regulation actually does

Within the legal-categorical paradigm, selecting a category is the first thing a regulator must do. Law operates on legal objects, and legal objects are categorical. 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 frameworks regulate harms by causation chain. Each of these is a category-selection act.

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

Regulate AI as labour substitution and the firm reframes deployment as productivity software. Regulate it as software and the state reframes it as strategic infrastructure exempt under national security carve-outs. Regulate it as a weapon and the developer reframes it as cloud productivity. Regulate frontier training and the diffusion happens through smaller open-weight models inside ordinary workflows. Regulate deployment and the firm reframes the system as assistance with human oversight. Regulate assistance and the boundary with ordinary software collapses entirely.

At no point in this sequence does any actor need to break a law. The object simply presents a different face.

The architecture is the trap

The clearest case study is the EU AI Act, Regulation (EU) 2024/1689, which is explicitly category-based.^[1] The legal architecture itself creates the migration paths. Provider, deployer, downstream integrator, fine-tuner, open-source releaser, enterprise customer, and systemic-risk model are not merely compliance labels. They are available legal identities defined in Articles 3, 25, and 51 of the Act. Once obligations attach to one identity, value migrates through the others.

The Commission’s own enforcement guidance (non-binding, but revealing of the enforcement architecture) confirms the structure.^[2] Most fine-tuning, adaptations, and minor modifications do not automatically create new model-provider obligations unless the modification crosses a high threshold, defined as more than one-third of the original model’s training compute. Open-source treatment receives different obligations from commercial release, though this exemption does not apply to general-purpose AI models with systemic risk. Downstream integrators inherit obligations differently from upstream providers. Each of these distinctions is reasonable in isolation. Each is a doorway in aggregate.

A model whose direct deployment as a high-risk system would attract heavy obligations can be released, modified, integrated, or wrapped through adjacent roles whose obligations attach differently. Where systemic-risk duties remain, the compliance surface still shifts from direct deployment to release, modification, integration, and downstream use. A general-purpose capability can be decomposed across models, wrappers, tools, integrations, and workflows whose individual components may sit below the most visible threshold, forcing the regulator to reconstruct systemic function after deployment rather than identify it cleanly before deployment.

This is the essential point. The regulator did not create loopholes. The regulator created categories, which is what regulators must create. The object moves between them because the object is the kind of thing that exists in all of them at once.

The recursive part

The recursion is what makes this novel.

In conventional regulatory arbitrage, the regulated party finds a workaround, the regulator updates the rule, and the workaround closes. The cat-and-mouse equilibrium is unstable but bounded. Regulation is always somewhat behind, but it is not categorically defeated.

Categorical recursion is different. The act of regulating a face of the object is itself a market signal. It tells every firm in the ecosystem which face is currently being scrutinised, which means every firm has an immediate incentive to redescribe its deployment under one of the other four faces. The regulation does not just fail to catch the object. The regulation creates a market signal and an incentive for migration.

This is not a slow process. It happens at the speed of a press release. The regulator’s next move is to broaden the definition. The market’s next move is to inhabit a face not yet defined. The regulator’s third move is to attempt a comprehensive framework. The market’s third move is to invoke the multi-category arbitrage problem as evidence that comprehensive frameworks are unworkable.

The regulator loses not because the regulator is slow. The regulator loses because the regulator is operating on the wrong substrate. Categories cannot enclose objects whose economic deployment selects its category in response to enclosure.

Why this is not capture

It is tempting to read this as a sophisticated form of regulatory capture. It is not. Capture requires that the regulated party influences the regulator’s preferences or rules. Categorical recursion requires no such influence. It operates even against a perfectly honest, perfectly well-resourced, perfectly motivated regulator.

The mechanism is structural. The regulator’s instrument is the legal category. The deployed object’s response surface is the same legal category. The object does not need to corrupt the regulator. It only needs to be the kind of thing that can be five things at once.

Capture is a problem of incentives. Categorical recursion is a problem of ontology.

What actually moves

The model itself does not literally evade. The neural network is stable. Weights do not change to escape regulation. The thing that moves is not the technical substrate. It is the legal-economic wrapper around the substrate: 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 substrate is stable enough to be deployed. Its legal-economic identity changes depending on where regulation attaches.

Regulation attaches to manifestations. Capital moves through relations. The mismatch is the failure.

This identifies the real target. The thing being regulated is not AI as a technical object. It is AI-as-capital-in-motion. The motion is the thing the categories cannot hold.

The Sorites layer underneath

Categorical recursion sits on top of the existing Sorites problem. The Sorites problem is that within any single face of the object, there is no clean line between assistance and replacement. Spell-check to autocomplete to draft generation to autonomous composition is one continuous gradient. No regulation can identify the moment a worker stopped being augmented and started being substituted, because no such moment exists.

Categorical recursion adds a second axis of ungovernability. Even if a regulator solved the within-face Sorites problem, the across-face migration problem remains. The two axes interact. Within-face Sorites makes every face individually ungovernable. Across-face recursion makes the choice of face arbitrary. Together they exhaust the regulatory surface.

This is why governance proposals that work on paper fail on contact. The paper version assumes a stable object presenting a stable face along a stable gradient. The deployed version is none of those things.

The six-gate test

Any proposed governance regime aimed at preserving the wage-demand circuit must survive six failure modes simultaneously:

State defection, where one major actor refuses the regime and gains comparative advantage. Firm-level evasion, where commercial actors reclassify deployments to escape coverage. Open-weight diffusion, where capability spreads below the regulatory threshold. Individual workflow adoption, where eight billion users make daily tool choices the regime cannot observe. Category arbitrage, where the deployed object migrates to a face the regime does not cover. The assistance-replacement gradient, where Sorites within a face dissolves the regulated distinction.

A regime that fails any one of these fails as a defence of the wage-demand circuit. It may still reduce fraud, improve documentation, slow a specific deployment, or create useful liability after harm. Those are real outcomes and worth pursuing on their own terms. They do not preserve mass labour absorption. The thesis is narrow. It says the wage-demand circuit cannot be defended by category-based instruments, not that all regulation is futile.

The design record on circuit defence is consistent. The EU AI Act fails on category arbitrage and the Sorites gradient. Compute thresholds, even by the Frontier Model Forum’s own assessment, are an imperfect proxy for risk: they may miss smaller systems with harmful capabilities while catching larger benign ones, and function at best as an initial filter.^[3] Liability frameworks fail on the gradient and on individual adoption. Procurement standards fail on firm-level evasion. Frontier moratoria fail on state defection. Each proposal is competent within its chosen face. None survives migration of the deployed object to an adjacent face.

What this implies for the wage-demand thesis

The implication is that the wage-demand circuit collapse is not a failure of regulation. It is what happens when the substrate of regulation is mismatched to the substrate of the regulated object.

The wage-demand circuit is preserved only by mass labour absorption. Mass labour absorption requires that AI deployment as labour substitution be governable. AI deployment as labour substitution is one face of an object with four other faces, and any attempt to govern that face causes immediate migration to the others. Therefore the wage-demand circuit is not defended by any regulatory regime that operates on legal categories.

This is not an argument that regulation is futile. It is an argument that regulation aimed at preserving the wage-demand circuit cannot succeed through category-based instruments, which are the instruments regulation possesses. The conclusion is structural.

The regulator’s dilemma

There is a final recursion worth naming.

A regulator who understands categorical recursion has two options. They can attempt comprehensive coverage across all five faces, which requires a level of definitional precision and cross-domain coordination that no existing institution can deliver, and which itself becomes the market signal that triggers the next mutation. Or they can abandon category-based regulation and attempt outcome-based regulation, which requires defining the outcome to be prevented, which returns the problem to definition, which returns the problem to category.

There is no third option that operates within the legal-categorical paradigm. The paradigm is the constraint.

What sits outside the paradigm is not regulation. It is something else. Direct ownership of the compute layer. Mandatory wage-share redistribution from automation gains. Public deployment of the technology with non-market allocation rules. These are not regulations. They are structural interventions that do not depend on category selection because they operate on the underlying flow of value rather than on the deployed object.

Whether any of these is politically achievable is the next question. The point of this essay is only to establish that the regulatory question, as conventionally posed, has been answered. The economic deployment of the object moves when you look at it. The looking causes the moving. No legal-categorical instrument survives the recursion.

This is the structural reason the wage-demand circuit will not be defended by the regulatory state. Not because the state is unwilling. Because the regulatory state is using object-categories against a value-flow.

Notes

1. Regulation (EU) 2024/1689 of the European Parliament and of the Council of 13 June 2024 laying down harmonised rules on artificial intelligence (Artificial Intelligence Act). Official Journal of the European Union. https://eur-lex.europa.eu/eli/reg/2024/1689/oj
2. European Commission, “Guidelines on obligations for General-Purpose AI providers.” https://digital-strategy.ec.europa.eu/en/faqs/guidelines-obligations-general-purpose-ai-providers
3. Frontier Model Forum, “Issue Brief: Thresholds for Frontier AI Safety Frameworks.” https://www.frontiermodelforum.org/uploads/2025/02/FMF-Issue-Brief-on-Thresholds-for-Frontier-AI-Safety-Frameworks.pdf