Beyond Circular Financing

Capital–Compute Coupling, Relative Acceleration, and the Governance of Correction

A Game-Theoretic Framework for AI Infrastructure Commitment and Bubble-Like Persistence

Abstract

Debate over an AI bubble often collapses asset prices, infrastructure buildout, supplier–customer financing, weak current profitability, energy demand, and strategic competition into one diagnosis. None of these observations alone establishes either a financial bubble or inefficient capital allocation. This article moves beyond circular-financing rhetoric by developing a theory-building framework for examining whether prior capital–compute commitments become material inputs into the financing, evidentiary justification, and authorization of subsequent commitments. Within that framework, the AI Capitalization Loop denotes the candidate recurrent process, not the familiar starting observation that financing and procurement may be contractually connected.

Using structured primary-source coding and comparative mechanism analysis of seven packages selected as a development set, the article defines the Capital–Compute Commitment Package as its primary empirical unit and applies a multi-label taxonomy covering Purchase-Contingent Equity, Customer-Financed Compute, Capacity-Contingent Finance, Investment–Commercial Linkage, and multiparty structures. The cases verify several vertical coupling mechanisms, but not a recurrent loop or industry-wide strategic equilibrium.

The framework separates demand provenance from demand justification and evaluates independent value through distinct dimensions of transaction maturity, external validation, and post-support persistence. It also separates vertical package effects from horizontal rivalry: a relative-acceleration claim requires evidence that a package changes the cost of conditioning relative to an identified rival. That transmission remains unvalidated.

Correction is represented as a directed graph connecting trigger recognition, standing, evidence access, competent review, judgment, lawful gate authority, and implementation. The framework distinguishes Productive Expansion, Bounded Transitional Overbuild, Coupling-Sustained Overextension, and a Locked Bubble-Like Regime. Strong overextension requires an ex ante or independently external divergence boundary; a locked regime additionally requires actor-pair Restraint Penalties, shared expectations, a correction deficit, and persistence through a genuine correction opportunity.

The evidence establishes contractual coupling, replicated mechanisms, implemented financing structures, partial feedback, and candidate transmission channels. It does not establish a completed capitalization loop, horizontal equilibrium, strong B2, B3, CEP, or S4. The proposed response is therefore not a general compute ceiling, but a legally constrained SHIP / RESTRICT / HOLD / ROLLBACK architecture attached to the next material commitment.

Keywords

AI capitalization; capital–compute coupling; AI infrastructure finance; demand provenance; independent-value evidence; vertical–horizontal transmission; Restraint Penalty; dependency; correction graph; Political Agency Deficit; AI governance; bubble-like regime; permission architecture

Methodological and Claim-Control Note

This article combines primary transaction analysis, accounting interpretation, external empirical context, established scholarly theory, and concepts originating in the RATIUM.AI corpus. Each source class performs a distinct evidentiary function.

Regulatory filings, filed agreements, financial statements, accounting standards, and other operative records have first authority for contractual terms, capital transferred, compute commitments, warrants, financing, revenue recognition, maturity, vesting, expiry, and termination. Company announcements and official institutional statements establish declared objectives, intended scale, strategic framing, and publicly announced relationships, but do not by themselves establish that all proposed transactions closed or produced their stated benefits. Scholarly and institutional literature supplies mechanisms, measurement methods, rival explanations, and falsification conditions. RATIUM.AI sources establish conceptual provenance and canonical meanings for correction architecture, Political Agency Deficit, CEP boundaries, the four permission gates, and the candidate LoopGuard-AI implementation model; they are not treated as independent validation of the external empirical theory.

The seven anchor cases constitute a purposive development set rather than a representative sample of the AI sector. They can establish that specified contractual mechanisms exist and, in one case, have been replicated. They cannot establish sector-wide prevalence or discriminant validity. The mechanism definitions are frozen before validation-set coding.

The article distinguishes direct observation, transparent calculation, accounting interpretation, mechanism inference, causal hypothesis, unobservable information, and normative design. Public non-observability is never converted automatically into institutional absence. Announcement is distinguished from binding commitment; commitment from implementation; delivery from utilization; utilization from external value; revenue from complete net value; coupling-supported demand from fictitious demand; path dependence from strategic equilibrium; and correction deficit from CEP or S4.

The formal expressions are conceptual and operational structures. Unless expressly stated otherwise, their coefficients have not been estimated, their thresholds have not been calibrated, and their predictive validity has not been established. Their function is to make claims separable, testable, and falsifiable.

All factual maturity statements are bounded by the observation cutoff of July 25, 2026.

Part I — Research Object, Boundary, and Method

1. Beyond AI Bubble Rhetoric

The contemporary debate over an “AI bubble” ordinarily combines several analytically distinct claims. Financial economics itself contains multiple mechanisms for speculative price components, including heterogeneous expectations, resale options, overconfidence, and relative-wealth concerns (Harrison and Kreps 1978; Scheinkman and Xiong 2003; DeMarzo, Kaniel, and Kremer 2008). The AI debate may additionally refer to unusually large investment in semiconductors, cloud infrastructure, data centers, and energy systems; model developers consuming capital faster than they generate operating income; infrastructure commitments running ahead of demonstrated demand; suppliers investing in, financing, or incentivizing their own customers; delayed productivity effects; strategic competition that discourages restraint; or institutional inability to reverse commitments once they become technically, financially, or politically embedded.

These propositions are not interchangeable. A company may be overvalued while its products create substantial external value. A sector may build more infrastructure than is eventually required while remaining financially solvent. A model developer may generate large consumer, scientific, or strategic value without producing mature current profit. A supplier may finance a customer or issue a procurement-linked warrant in order to solve a genuine coordination, adoption, or project-finance problem. A state may rationally support capacity whose commercial utilization remains low because the capacity provides resilience, sovereignty, or defense value.

Conversely, the existence of binding contracts, recognized revenue, paying users, high utilization, strategic importance, or technical achievement does not prove that every additional increment of capital and compute is efficiently allocated.

The article therefore rejects two symmetrical simplifications:

Coupling or High Investment⇏Artificial Demand or Bubble

and:

Real Revenue or Real Use⇏Efficient Total Commitment.

The research problem is not whether artificial intelligence has value. It already produces commercially purchased services, technical capabilities, learning, user utility, and strategic options. Nor is the problem merely whether particular companies or securities are correctly priced. A comprehensive asset-pricing analysis would require valuation models, cash-flow expectations, discount rates, investor beliefs, resale incentives, and market-specific evidence beyond the present article’s principal object.

The narrower question is institutional and game-theoretic:

Can the contemporary AI capital–compute system distinguish expansion justified by independently converging external value from expansion sustained increasingly by the financing, ownership, distribution, strategic, and dependency structure created by prior commitments?

This question requires analysis of the path through which capital is committed; compute is procured or constructed; procurement becomes demand, backlog, revenue, or strategic evidence; those signals affect valuation, financing, and competitive expectations; new commitments are authorized; and adverse evidence either changes or fails to change the next permission state.

The article does not begin by asserting that this complete sequence has been established. It develops the sequence as a candidate causal architecture and assigns different evidence states to its components. Contractual evidence may establish that two variables are linked. It may not establish the magnitude of the behavioral effect. A repeated structure may support a mechanism claim. It may not establish field-wide prevalence. A costly deviation may support a candidate Restraint Penalty. It may not establish a Nash equilibrium. An incomplete correction path may support a governance diagnosis. It may not establish CEP or S4.

The central discipline is therefore:

Conceptual Integration≠Empirical Completion.

The article’s contribution lies in specifying the research object, contractual microfoundations, demand-identification problem, relative-acceleration mechanism, correction-path requirement, conditions of a bubble-like regime, and evidence required to accept, narrow, or reject each claim. The descriptive line — A Game-Theoretic Framework for AI Infrastructure Commitment and Bubble-Like Persistence — positions the paper beyond familiar circular-financing descriptions and identifies its distinctive theory-building focus on infrastructure commitment, correction, and bubble-like persistence. It does not claim that the horizontal game, regime classification, or sector-wide framework has already been validated.

2. The AI Capital–Compute Commitment System

The article’s research object is the AI capital–compute commitment system:

A network of contractual, financial, infrastructural, commercial, strategic, and institutional relations through which actors finance, construct, reserve, distribute, consume, evaluate, and authorize AI compute.

The principal role classes are:

𝒩={LAB,HW,CLOUD,INFRA,FIN,PUB}.

Here, LAB denotes model laboratories and AI-product developers; HW, semiconductor and systems suppliers; CLOUD, cloud, platform, and distribution providers; INFRA, data-center, energy, and physical-infrastructure operators; FIN, investors, lenders, and other capital providers; and PUB, public, sovereign, defense, and regulatory actors.

These categories describe functions rather than permanent organizational identities. One organization may occupy several roles. A cloud provider may also be an equity investor, proprietary-chip supplier, distributor, product integrator, and infrastructure operator. A semiconductor supplier may also be an investor, financing source, systems architect, and ecosystem coordinator. A model laboratory may be a customer, investment recipient, lender to an infrastructure supplier, distributor, and holder of customer equity rights in a supplier.

The role-based approach is necessary because the relevant economic relation frequently crosses the boundary of one bilateral transaction. A return that appears in one role may support expenditure in another. A cost recorded by one affiliate may increase the value of an equity position held elsewhere. A strategic benefit may be recognized by a public actor while the capital and infrastructure burden is borne by private firms, utilities, or local communities.

Thus:

Organization≠One Payoff Channel,

and:

Bilateral Contract≠Complete Causal System.

2.1 The Capitalized Compute Network

The role network produced by material capital–compute relationships is termed the Capitalized Compute Network. It includes flows of paid capital, conditional capital, loans, customer finance, cloud credits, warrants and other equity rights, chips and systems, compute capacity, distribution, model access, revenue, valuation signals, public support, strategic authorization, and infrastructure burden.

The network is “capitalized” not merely because firms raise money, but because compute demand, delivery, financing, and ownership can become mutually connected. The presence of reciprocal flows does not establish improper circularity. Real economic systems contain credit, prepayment, vertical investment, trade finance, complementary assets, and cross-ownership. The research question is whether the network’s internally connected signals remain distinguishable from independent external validation.

2.2 The candidate causal sequence

The complete candidate sequence is:

Capital Commitment→Compute Procurement or Construction→Delivery, Backlog, Revenue, or Distribution→Valuation, Financing, or Strategic Signal→Authorization of Further Commitment.

In recurrent form:

Kt→Qt→DtorRt→VtorFt→Kt+1→Qt+1.

The article calls this complete candidate structure the AI Capitalization Loop. The term Loop refers to possible recurrence. It does not mean that every arrow has been empirically demonstrated in the anchor cases.

A connected package can establish a capital-to-compute link, a compute-to-financing link, a procurement-to-warrant link, or a multichannel investment-commercial relation. A complete loop requires evidence that prior commitment becomes a material input into a subsequent commitment cycle:

Connected Package≠Recurring Loop.

2.3 System boundary

The system boundary must be broad enough to contain the actors and instruments necessary to explain the relevant effect, but it should not be widened indefinitely. The bounded system for a particular episode is determined causally:

Which actors, contracts, financial instruments, infrastructure assets, evidentiary signals, and permission authorities are necessary to explain the creation and possible correction of the defined commitment?

The boundary is episode-specific, mechanism-specific, and permission-specific.

2.4 Research-object hierarchy

The hierarchy governing the manuscript is:

AI capital–compute commitment system - the complete research object.
Capitalized Compute Network - the actor-and-flow representation of that system.
Capital–Compute Commitment Package - the primary empirical unit.
AI Capitalization Loop - the candidate recurrent process.
Bubble-like capital–compute regime - a stronger system-level classification.
CEP and S4 - downstream strategic and ontological-epistemological classifications.

The terms are non-interchangeable:

Package≠Network≠Loop≠Regime.

3. Unit of Analysis: The Capital–Compute Commitment Package

The primary unit of analysis is the Capital–Compute Commitment Package:

A bounded set of legally, financially, operationally, or strategically connected commitments whose components jointly affect the financing, construction, procurement, distribution, valuation, dependency, or permission state of AI compute.

The package may be contained in one contract, several concurrent agreements, a master relationship agreement, an investment plus a commercial agreement, a loan plus a procurement commitment, or a multiparty announced structure. The unit is determined by economic and causal interdependence rather than document count.

A transaction alone may be too narrow. A cloud purchase accompanied by a separate equity investment may still form one package where the decisions are negotiated together, depend on common milestones, produce complementary returns, or alter one another’s economics. A customer loan may be legally separate from the compute contract while financing the exact infrastructure required to perform it.

A company may be too broad. One company can participate in many unrelated investments, cloud contracts, chip purchases, infrastructure projects, and products. Treating the company as the unit may combine arrangements with different counterparties, objectives, maturity, risk, and correction paths.

Components belong to the same package where one or more of the following are present:

Legal conditionality - performance under one agreement changes rights under another.
Financial dependence - capital or credit finances the infrastructure required for the commercial commitment.
Operational dependence - delivery, capacity, or technical integration is necessary for the connected investment or procurement.
Equity dependence - procurement, payment, or delivery affects vesting or ownership rights.
Distribution dependence - investment and procurement are linked to platform or product access.
Strategic dependence - components are jointly justified by one capability, resilience, or competitive objective.
Correction dependence - changing one component requires changes in another before the package can be implemented or unwound.

No single criterion is universally necessary. The boundary must be tight enough to prevent speculative aggregation.

For each package, the analysis asks: What is binding? What is optional? What capital has been paid? What future capital is conditional? What compute is committed or delivered? Which customer incentives or equity rights exist? Which financing mechanisms exist? What revenue has been recognized? Which distribution or integration channels exist? What rights allow cancellation, restriction, or exit? Which variables remain publicly unobservable? What is the strongest claim the package permits?

The package is not presumed to be efficient or inefficient. It is the evidentiary object from which mechanism claims may be derived.

4. Governing Non-Equivalences

The article depends on a series of non-equivalences. They define the logical structure of the research.

Announcement≠Binding Commitment.

A press release, letter of intent, target, or projected deployment can affect expectations. It does not establish enforceability, capital transfer, construction, procurement, or completion.

Binding Commitment≠Economic Implementation.

A signed agreement can remain undrawn, unvested, undelivered, or subject to conditions.

Delivery≠Utilization.

Utilization≠External Value.

Capacity can be used for experimentation, internal transfers, low-price services, speculative workloads, or strategically justified reserve.

Recognized Revenue≠Complete Net Value.

Revenue does not by itself include customer consideration, infrastructure depreciation, energy, financing, downstream verification, opportunity cost, strategic burden, or dependency.

Backlog or RPO≠Independent Demand.

Its interpretation still depends on cancellation rights, financing, customer concentration, incentives, and downstream monetization.

Coupling-Supported Provenance≠Fictitious Demand.

Customer finance or an adoption incentive can enable real capacity and real value.

Customer Incentive≠Improper Revenue.

Correct accounting treatment does not determine the demand counterfactual or external value.

High Capital Expenditure≠Bubble-Like Regime.

Delayed Convergence≠Persistent Non-Convergence.

High Exit Cost⇏Current Inferiority,

but also:

High Exit Cost⇏Current Superiority.

The RATIUM.AI configuration framework distinguishes continuation because value remains superior from continuation because exit has become costly (Dunavich 2026a).

Evaluation or Review≠Implemented Correction.

A report, audit, risk score, or committee finding becomes corrective only where it can alter scope, permission, financing, architecture, deployment, or continuation. The Stable Governance Layer distinguishes visible controls from a complete path connecting problem, evidence, threshold, authority, gate, implementation, and review (Dunavich 2026c).

Capital–Compute Correction Deficit≠CEP.

CEP requires recurrent closure, locally incentive-compatible continuation, deviation costs, shared expectations, and persistence through genuine correction opportunities.

CEP-Consistent Persistence≠S4.

The complete inferential order is:

Transaction Fact→Mechanism→Recurrent Feedback→Regime Classification→CEP Entry Test→Possible S4 Mapping.

5. Evidence Vector, Component Maturity, and Evidence Independence

Each anchor package is coded through:

Γr=⟨L,Kp,Kc,Qb,Qo,W,F,Rn,V,Λ,Ξ⟩,

where L is legal and execution status; Kp, paid capital; Kc, conditional future capital; Qb, binding compute; Qo, optional or prospective compute; W, warrants or equity rights; F, financing; Rn, recognized revenue after disclosed customer consideration; V, valuation channel; Λ, distribution, cloud, technical, or product integration; and Ξ, cancellation, expiry, transfer, restriction, and other reversibility provisions.

The vector is descriptive. It does not contain a conclusion concerning causation, independence, efficiency, overextension, or equilibrium.

5.1 Component evidence status

Each component receives one status:

V — Verified
P — Partial
U — Unknown or undisclosed
N — Not identified
O — Optional
F — Future or conditional

The distinctions are substantive:

U≠N,

and:

F≠Vcompleted.

A future commitment can be verified as a contractual fact without being completed. A component can be unobservable without being absent.

5.2 Component transaction maturity

The manuscript does not assign one maximum maturity grade to a heterogeneous package. Each material component is coded separately through:

TMc∈{TM0,TM1,TM2,TM3},

where:

Code	Component transaction state
TM0	Non-binding intention, target, memorandum, or prospective arrangement
TM1	Binding commitment or legally operative obligation
TM2	Payment, financing, construction, procurement, delivery, or another material implementation step has begun
TM3	Supplier revenue has been recognized after disclosed customer consideration

Legal form and transaction maturity remain distinct. A definitive agreement can be TM1; a funded investment, TM2; and a service relationship with recognized net revenue, TM3. One package can contain all three states simultaneously.

The package-level representation is therefore a component map:

TM(Γr)={TMr,c:c∈Components(Γr)},

not a single scalar.

5.3 Independent-value evidence

Transaction maturity does not establish value outside the package. Chapter 17 therefore codes a separate multidimensional profile:

IVEr=⟨TMr,EVr,PSr⟩,

where EV records external validation and PS records persistence after material support changes. These dimensions must not be collapsed into one ordinal score before validation.

The Evidence Vector records what the package contains. The mechanism vector in Chapter 7 records how its components are connected. The independent-value profile records which forms of external validation are publicly supported. None may be used to infer the other by definition.

6. Method, Source Hierarchy, and Claim Permissions

The article uses a structured, claim-specific evidence method. The anchor cases form a purposive mechanism sample. They support transaction facts, mechanism identification, replication within the sample, comparative theory building, and research design. They cannot support sector-wide prevalence or universal claims concerning the AI industry.

6.1 Observation cutoff

The empirical record is bounded by:

25July2026.

Statements concerning maturity, capital transferred, warrant vesting, capacity delivery, recognized revenue, or agreement completion refer to the public record available by that date.

6.2 Source hierarchy

Tier 1 - Operative primary records: regulatory filings, filed contracts, audited financial statements, accounting standards, and legally operative public instruments.

Tier 2 - Official non-operative sources: company announcements, official blogs, investor presentations, government strategies, and official speeches.

Tier 3 - Independent empirical and scholarly sources: mechanisms, external context, measurement, rival explanations, and falsification designs.

Tier 4 - Independent reporting: chronology, document discovery, market response, or information unavailable in primary records; never a substitute for an available operative record.

Tier 5 - RATIUM.AI foundational sources: conceptual provenance, correction-path logic, gate architecture, CEP boundaries, and LoopGuard-AI translation; not independent validation of external empirical claims.

6.3 Claim-status grammar

O - Directly Observed: supported directly by a reliable source.
C - Calculated: derived transparently from observed inputs.
A - Accounting Interpretation: connects an accounting standard with a company-specific disclosure.
MI - Mechanism Inference: interprets how an observed structure may affect incentives, financing, dependency, or correction.
CH - Causal Hypothesis: requires causal identification.
U - Unobservable or Undisclosed: cannot be determined from the available record.
ND - Normative or Design Proposition: proposes a gate, trigger, authority structure, or governance rule.

6.4 Claim classes

Class I concerns transaction facts. Class II concerns mechanisms. Class III concerns system feedback and prevalence. Class IV concerns equilibrium, Pareto, CEP, and S4 claims. Class V concerns governance effectiveness.

A later class cannot be inferred solely from an earlier one.

6.5 Core permissions

The source base permits claims that material coupling exists; PCE is replicated within the anchor set; CFC reached implementation and revenue recognition in one case; capacity delivery can determine financing availability; multiple commercial and investment roles can coexist; coupling changes the interpretation of observed demand; contractual provisions can create candidate components of Restraint Penalty; local contract correction differs from system permission correction; a correction deficit is testable; and a differentiated marginal permission architecture can be formulated.

It does not permit claims that most AI demand is coupling-supported; coupling-supported demand is fictitious; the complete loop has recurred; valuation gains caused later commitments; the sector is broadly overbuilt; RP3 occurred; mutual conditionality is Pareto superior; B2 or B3 characterizes the sector; CEP or S4 applies; or LoopGuard-AI is validated.

6.6 Public non-observability

Not Publicly Demonstrated≠Absent.

Where evidence cannot identify whether a process exists, the status is unknown or indeterminate.

6.7 Rival explanations

The strongest ordinary explanations must be tested before stronger classifications are admitted: efficient project finance, trade credit, customer risk-sharing, genuine compute scarcity, supplier diversification, vertical integration, platform economics, real options, bounded learning, strategic insurance, ordinary path dependence, hierarchy, legal constraint, and principal-agent problems.

CEP is downstream of rival-explanation testing (Dunavich 2026b).

6.8 Falsification discipline

The framework must be narrowed where coupled procurement remains stable after incentives expire; independent downstream monetization supports the complete quantity; financing is explained by operating cash or unrelated information; conditioning produces no material relative loss; portability remains high despite integration; ordinary governance corrects effectively; strategic adequacy is specified and respected; or simpler theories explain persistence.

“Insufficient evidence” is a legitimate classification.

6.9 Case Selection and Coding Procedure

A case was included where: a material AI-compute or AI-infrastructure commitment was publicly documented; the package connected at least two of capital, procurement, financing, equity, infrastructure, distribution, or technical integration; a primary regulatory, contractual, financial, or official source supported the material terms; and the package could be bounded sufficiently to distinguish binding, optional, future, completed, and unobservable components.

Cases were excluded where evidence consisted only of media rumor; an ordinary equity investment without an identifiable compute or infrastructure connection; ordinary procurement lacking a material capital, finance, warrant, or integration link; a generalized partnership announcement without a codeable package; or a relationship too immature to support even PCI classification.

Coding proceeded through boundary identification, component extraction, maturity coding, separation of binding and optional elements, mechanism classification, and claim-permission determination. Mechanism classification was not used to fill missing factual variables.

The coding was developed by one researcher with AI assistance. No independent inter-rater reliability coefficient has yet been established. The Evidence Vector, mechanism vector, independent-value profile, RP scale, CCPP graph, and regime classifier are pre-validation instruments. Future work requires independent coders, written rules, disagreement resolution, and formal reliability testing.

6.10 Scholarly Antecedents and Residual Contribution

The article does not claim priority over the mechanisms from which its architecture is constructed.

Financial-bubble research explains how heterogeneous expectations, resale options, overconfidence, relative-wealth concerns, and market constraints can sustain speculative components (Harrison and Kreps 1978; Scheinkman and Xiong 2003; DeMarzo, Kaniel, and Kremer 2008). The present article’s residual object is the governance of real capital–compute commitments rather than asset prices alone.

Trade-credit and customer-finance research shows that commercial counterparties may finance constrained firms because they possess informational, monitoring, liquidation, screening, or relationship advantages unavailable to ordinary lenders (Biais and Gollier 1997; Petersen and Rajan 1997; Klapper, Laeven, and Rajan 2012). This supplies a strong efficient-finance rival explanation for CFC and CCF.

Incomplete-contract, property-rights, and transaction-cost theory explain why ownership and control may internalize complementary investment while redistributing residual rights, safeguards, and incentives (Grossman and Hart 1986; Hart and Moore 1990; Williamson 1985). Platform theory explains why an ecosystem provider may subsidize or court one side of a market to generate value elsewhere in the network (Rochet and Tirole 2003). These literatures prevent ICL and role overlap from being treated as pathological by definition.

Real-options theory establishes that uncertainty and irreversibility can make waiting or staged investment valuable even where expected return is positive (McDonald and Siegel 1986; Dixit and Pindyck 1994). Increasing-returns and path-dependence theory explains how installed bases, historical sequence, and technology-specific investment can constrain later choice, while critical accounts warn against inferring inefficient lock-in too readily (David 1985; Arthur 1989; Liebowitz and Margolis 1995). These are primary rivals to the stronger relative-acceleration account.

Repeated-game theory demonstrates that future interaction, observability, and credible responses can sustain outcomes unavailable in a one-shot game, while imperfect monitoring and long-run/short-run actor asymmetry can restrict the sustainable equilibrium set (Fudenberg and Maskin 1986; Radner, Myerson, and Maskin 1986; Fudenberg, Kreps, and Maskin 1990). General-purpose-technology research explains why complementary intangible investment and organizational redesign can produce a productivity J-curve during early diffusion (Brynjolfsson, Rock, and Syverson 2021). These literatures ground B1 Bounded Transitional Overbuild and prevent delayed measured productivity from being treated as immediate evidence of overextension.

Accountability and science-governance research distinguishes actors, forums, explanation, questioning, judgment, consequences, competing accountability demands, uncertainty, vulnerability, and institutional learning (Bovens 2007; Koppell 2005; Jasanoff 2003). NIST organizes AI risk management around Govern, Map, Measure, and Manage functions (National Institute of Standards and Technology 2023). These traditions supply major elements of the CCPP but do not by themselves establish a package-specific path from adverse capital–compute evidence to an implemented permission state.

The residual contribution is their integration around one bounded decision object:

the permission state of the next material capital–compute commitment.

The article connects contractual coupling, demand provenance, external value, complete burden, relative acceleration, dependency, correction-path completeness, regime classification, and marginal governance. This integration remains a candidate theory until its constructs are validated empirically.

6.11 Development–validation split and taxonomy freeze

The seven anchor cases are the development set. They were selected because their public records disclose capital–compute coupling sufficiently to support mechanism construction.

The mechanism definitions and coding rules are frozen before any validation case is coded. A validation case may support a mechanism, show that it is absent, expose ambiguity, require a narrower claim, or motivate a formally declared revision. It may not silently redefine a mechanism to preserve a positive classification.

The validation program requires at least four negative-control classes:

Control class	Required characteristic	Principal test
Uncoupled commitment	Large AI procurement or infrastructure commitment without material PCE, CFC, CCF, or ICL	Whether scale alone is incorrectly classified as coupling
Successful correction	Adverse evidence produces timely restriction, hold, supplier change, or rollback	Whether CCPP distinguishes working correction from deficit
High-dependency / high-value	Dependency rises while comparative external value remains strong	Whether dependency is being mistaken for inferiority
Strategic adequacy	Non-commercial capacity stabilizes at a declared capability threshold	Whether strategic investment is being mistaken for open-ended overextension

The article specifies this validation design but does not claim that the control set has been completed. It is therefore a theory-building framework, not a validated taxonomy or prevalence study.

6.12 Package aggregation, related parties, and anti-slicing

A material package must not be divided into formally separate transactions where the components are economically or operationally connected.

The Technical Supplement applies three rules:

Lookback window: agreements, amendments, investments, financing instruments, warrants, and commercial commitments involving the same relevant actors are reviewed over a declared period before and after the focal commitment.
Related-party consolidation: controlled affiliates, special-purpose entities, and functionally coordinated counterparties are mapped to the relevant institutional actor while preserving legal distinctions.
Anti-slicing rule: nominally small increments are aggregated where they share an objective, asset, counterparty, trigger, financing source, or correction path and jointly cross the materiality threshold.

The lookback duration must be selected ex ante for a study and reported. It cannot be lengthened selectively to capture a desired package or shortened to hide a connected component.

6.13 Methodological status

At the observation cutoff:

the research object and claim boundary are defined;
the development taxonomy is frozen before validation coding;
negative-control and out-of-sample validation remain incomplete;
no sector-wide prevalence or predictive claim is authorized.

The next question is empirical: Which contractual structures are visible in the contemporary AI capital–compute system, and which relations do those structures establish before any stronger claim concerning demand, recurrence, strategic persistence, or bubble risk is introduced?

Part II — Contractual Microfoundations

7. A Multi-Label Taxonomy of Capital–Compute Coupling

The AI capital–compute commitment system is not organized through one uniform form of “circular financing.” The anchor transactions reveal distinct mechanisms through which capital, compute procurement, infrastructure delivery, equity exposure, financing availability, and distribution become connected.

The mechanism family is:

ℳ={PCE,CFC,CCF,ICL,MCN,PCI},

where:

PCE = Purchase-Contingent Equity;
CFC = Customer-Financed Compute;
CCF = Capacity-Contingent Finance;
ICL = Investment–Commercial Linkage;
MCN = Multiparty Capitalization Network;
PCI = Prospective Coupling Intent.

The mechanisms are not mutually exclusive. Each package is coded through:

𝐌r=⟨PCEr,CFCr,CCFr,ICLr,MCNr,PCIr⟩,

with component values:

mr,k∈{0,Partial,Verified,Prospective}.

A primary mechanism may be named for exposition. It does not exclude secondary mechanisms. MCN describes network organization across three or more actors, while PCI marks prospective rather than implemented coupling; either can coexist with bilateral mechanism labels.

7.1 Purchase-Contingent Equity

A Purchase-Contingent Equity arrangement exists where a customer receives a right to acquire equity in a supplier and vesting or exercisability depends materially on procurement, customer payment, capacity delivery, or exercise of connected purchase options:

Qj→i↑⇒Wj,i↑.

The exact conditioning variable must be reported. Customer equity rights are not coded as verified PCE merely because a warrant exists.

7.2 Customer-Financed Compute

A Customer-Financed Compute arrangement exists where the compute customer provides financing used by the supplier to construct or expand infrastructure required to satisfy the same customer’s procurement:

Fj→i→Buildi→Qi→j.

7.3 Capacity-Contingent Finance

A Capacity-Contingent Finance arrangement exists where financing becomes available to a customer as the capital provider or infrastructure provider achieves compute-delivery milestones:

Qi→jdelivered↑⇒Ki→javailable↑.

7.4 Investment–Commercial Linkage

Investment–Commercial Linkage exists where one institutional relationship combines material equity investment with one or more of cloud procurement, chip consumption, distribution, model integration, or product collaboration:

Ki→j>0∧(Qj→i>0∨Λij=1).

7.5 Multiparty Capitalization Network

A Multiparty Capitalization Network exists where three or more actors link investment, infrastructure procurement, hardware, cloud distribution, or technical integration in one announced or contractually connected network. MCN coding does not replace the coding of bilateral edges inside the network.

7.6 Prospective Coupling Intent

Prospective Coupling Intent applies where parties announce a letter of intent or similar proposed arrangement containing a capital–compute coupling structure, but definitive investment, procurement, or partnership agreements have not yet been completed.

7.7 Interpretation rule

The labels are mechanism descriptors, not moral or outcome classifications. They do not imply:

illegality;
fictitious demand;
revenue misstatement;
inefficiency;
overextension;
or a completed capitalization loop.

Project-finance and trade-credit theory supply ordinary explanations for several mechanisms: coupling can allocate construction risk, solve information problems, or enable asset-specific investment (Biais and Gollier 1997; Petersen and Rajan 1997; Klapper, Laeven, and Rajan 2012). Incomplete-contract, property-rights, transaction-cost, and platform theory likewise explain why equity, compute, distribution, and technical integration can rationally coexist (Grossman and Hart 1986; Hart and Moore 1990; Williamson 1985; Rochet and Tirole 2003).

The taxonomy identifies connected mechanisms before asking whether they alter demand provenance, horizontal rivalry, dependency, correction, or regime classification.

8. Purchase-Contingent Equity: AMD–OpenAI

In October 2025, AMD disclosed a product-purchase agreement with OpenAI and a concurrent warrant permitting OpenAI to acquire up to 160 million AMD common shares at an exercise price of $0.01 per share. OpenAI made a binding initial commitment associated with one gigawatt of AMD Instinct MI450-series products. The first warrant tranche was linked to delivery of that initial gigawatt, while full vesting depended on purchases reaching six gigawatts. Additional share-price, technical, and commercial conditions applied (Advanced Micro Devices 2025).

The arrangement contains two analytically distinct assets. The first is operational:

QOpenAI→AMD.

OpenAI receives GPU products, capacity, and related technical collaboration. The second is financial:

WOpenAIinAMD.

OpenAI receives the potential ability to acquire a substantial equity position in the supplier at a nominal exercise price, provided the conditions are satisfied.

The structure links procurement and equity:

QOpenAI→AMD↑⇒WOpenAIinAMD↑.

The warrant is therefore not an unrelated investment held by the customer. Its vesting conditions are connected directly to purchases. AMD subsequently disclosed that the warrant’s grant-date fair value would be recognized as a reduction to revenue as associated revenue is recognized and that none of the warrant shares had satisfied vesting or exercise conditions by the relevant fiscal-year reporting date (Advanced Micro Devices 2026a).

The accounting treatment matters because it prevents the warrant from disappearing from the analysis as though it were unrelated to customer acquisition and procurement economics. A schematic effective procurement cost is:

COpenAIeff=PQQ−𝔼[W(Q,PAMD,Tech,Comm)],

where PQQ is contractual product cost and the expected warrant value depends on procurement, AMD share-price performance, technical conditions, and commercial conditions.

This expression is not an estimate of OpenAI’s actual net cost. The warrant’s value is uncertain and contingent. It does not establish that OpenAI’s procurement lacks independent justification. OpenAI may require the compute regardless of the warrant. AMD may be offering an efficient early-adoption incentive in a market characterized by technical switching costs, uncertain future architectures, and intense supplier competition.

The narrower conclusion is:

The observable quantity purchased under the AMD–OpenAI arrangement cannot be interpreted as a procurement signal wholly independent of the customer’s equity exposure to the supplier.

This establishes PCE. It does not establish its behavioral magnitude.

9. Replication: AMD–Meta

In February 2026, AMD disclosed a second performance-based warrant, issued to Meta, covering up to 160 million AMD shares at an exercise price of $0.01 per share. Meta made a binding initial commitment associated with one gigawatt equivalent of specified AMD Instinct products. The first warrant tranche was linked to shipment of the initial quantity, while full vesting depended on purchases reaching six gigawatts. Additional AMD stock-price, technical, and commercial conditions applied (Advanced Micro Devices 2026b).

AMD’s subsequent quarterly reporting described the OpenAI and Meta warrants together. Each covered up to 160 million shares, used a $0.01 exercise price, and vested through procurement milestones and stock-performance conditions. As of the relevant reporting date, no shares under either warrant had vested or become exercisable (Advanced Micro Devices 2026c).

The Meta transaction changes the evidentiary status of the AMD–OpenAI structure. A single unusual agreement may reflect counterparty-specific bargaining, a one-time strategic concession, an idiosyncratic financing need, or a unique technical relationship. A second transaction with a different major customer does not prove industry prevalence, but it supports a limited proposition:

AMD employed a repeatable procurement-linked warrant architecture across more than one major customer.

The replication can be represented as:

PCEAMD,OpenAI≅PCEAMD,Meta,

with differences in counterparties, product specifications, timing, and conditions.

The following propositions remain distinct:

PCE Exists,

PCE Is Replicated,

PCE Alters Procurement,

PCE Produces Inefficient Procurement.

The first two are supported by the filed arrangements. The third requires a counterfactual. The fourth additionally requires evidence concerning downstream value, complete burden, strategic benefit, and credible alternatives.

10. Customer-Financed Compute: Cerebras–OpenAI

The Cerebras–OpenAI relationship provides the most developed example in the anchor set because it combines a binding compute commitment, customer financing, customer equity rights, infrastructure delivery, recognized revenue, and disclosed remaining performance obligations.

In December 2025, Cerebras and OpenAI entered into a Master Relationship Agreement under which Cerebras committed to make available, and OpenAI committed to purchase, 750MW of AI inference compute capacity. The capacity was scheduled for deployment in 250MW increments through the end of 2028. OpenAI also received an option to procure an additional 1.25GW by the end of 2030, potentially bringing total capacity to 2GW (Cerebras Systems 2026a).

The agreement is not merely a capacity reservation. OpenAI is obligated to pay fees as committed-capacity tranches are delivered, while Cerebras is obligated to construct and deliver capacity according to specified schedules and service conditions. Delay or service-level failure can generate credits, refunds, term adjustments, or termination rights (Cerebras Systems 2026a).

OpenAI also advanced Cerebras an approximately $1 billion secured working-capital loan. Cerebras disclosed that the loan supported engineering, manufacturing scale-up, data-center expansion, and infrastructure required to deliver the contracted services. The loan may be repaid in cash or through compute capacity, hardware, other services, or certain asset transfers. It carries interest, with specified treatment where repayment occurs through eligible non-cash performance (Cerebras Systems 2026a).

The operative sequence is:

FOpenAI→Cerebras→BuildCerebras→QCerebras→OpenAI→Repaymentcash/services/assets.

OpenAI is simultaneously the capacity customer, a lender financing the supplier’s buildout, a potential recipient of repayment through the contracted services, and a holder of equity rights in the supplier.

Cerebras issued OpenAI a warrant covering more than 33 million shares at a nominal exercise price. The first tranche vested when the working-capital loan was funded. Other tranches depend on customer payments, market capitalization, and delivery of committed or optional capacity. Full vesting requires exercise of the additional-capacity options and purchase of the full possible quantity (Cerebras Systems 2026a).

The package contains:

Binding Compute Procurement+Customer Infrastructure Finance+Service-Based Repayment+Customer Equity Rights.

Cerebras reported that delivery began in January 2026. For the quarter ended March 31, 2026, it recognized $16.9 million of revenue from the arrangement, net of $0.8 million in amortization associated with the customer-warrant asset. It also reported approximately $25 billion of remaining performance obligations, a substantial portion attributable to the OpenAI agreement (Cerebras Systems 2026b).

This evidence moves the case beyond announcement or contract formation:

Agreement→Loan Funding→Initial Warrant Vesting→Capacity Delivery→Recognized Net Revenue.

It is the strongest anchor case for an implemented capital–compute package.

The arrangement should not be described as round-tripping. The services are real, capacity delivery has begun, and revenue has been recognized under disclosed accounting treatment. Customer finance is a familiar way to enable capital-intensive, relationship-specific infrastructure.

The analytical issue is that observed demand and the supplier’s capacity to satisfy it are jointly produced inside the same package:

Customer Demand Signal⊥̸Customer Financing.

The package is a confirmed instance of Customer-Financed Compute. It is not evidence of a complete capitalization loop because the public record does not demonstrate that the resulting revenue, valuation, or warrant effects caused a subsequent cycle of capital and compute commitments.

11. Capacity-Contingent Finance: Amazon–Anthropic

Amazon’s relationship with Anthropic differs structurally from both PCE and CFC.

Amazon disclosed an additional $5 billion investment in Anthropic after March 31, 2026. It also amended the parties’ commercial relationship involving AWS services and AWS-chip performance. In addition, Amazon established a financing facility of up to $20 billion. No amount was initially available to draw. Amounts become available as Amazon reaches specified compute-capacity delivery milestones. Anthropic may draw in exchange for convertible notes or, following a liquidity event, common stock. Amazon also holds an option to invest additional capital, with any exercise reducing the facility amount (Amazon.com 2026c).

The core relation is:

QAmazon→Anthropicdelivered↑⇒KAmazon→Anthropicavailable↑.

This reverses the primary direction found in Customer-Financed Compute. In CFC, customer finance enables supplier capacity. In CCF, provider capacity enables customer financing availability.

The structure can serve legitimate purposes. It can prevent Anthropic from drawing the full facility before Amazon delivers usable infrastructure, align capital availability with operational scale, reduce Amazon’s exposure to premature funding, and support expansion as the compute relationship matures.

The arrangement contains a real gate:

Delivery Milestone→Financing Permission.

But the gate is a capacity-performance gate, not necessarily an external-value gate. It asks whether Amazon delivered specified capacity. The public disclosure does not establish that finance availability is also conditioned on downstream revenue, utilization, productivity, post-support renewal, complete infrastructure cost, or independent external-value convergence.

Capacity Delivered≠Value Demonstrated.

The mechanism is Capacity-Contingent Finance. The stronger claim - that capacity delivery generates financing even where external value has failed - remains untested.

12. Investment–Commercial Linkage: Amazon–OpenAI

The Amazon–OpenAI package combines funded equity, conditional future equity, cloud consumption, proprietary-chip deployment, distribution, model integration, and product collaboration.

Amazon’s first-quarter 2026 Form 10-Q reports that it invested $15 billion in OpenAI preferred stock during the quarter (Amazon.com 2026c). The February 27, 2026 Form 8-K separately records an equity commitment letter for an additional $35 billion, with voluntary early purchases and specified milestones or a qualifying public listing capable of making remaining amounts obligatory, subject to the agreement’s conditions and expiry structure (Amazon.com 2026a). The initial funded investment and the future commitment are therefore different components and are cited to different operative records.

Amazon also announced, and its first-quarter report described, an expansion of the existing commercial arrangement by $100 billion over eight years. The announced package includes obligations connected to AWS chips, approximately 2GW of Trainium capacity, AWS distribution of OpenAI products, runtime infrastructure collaboration, customized models, and product development (Amazon.com 2026b, 2026c).

The package contains at least four channels:

ΓAmazon,OpenAI=⟨Kp,Kc,Q,Λ⟩,

where Kp is funded equity, Kc is conditional future equity, Q is the commercial compute commitment, and Λ is distribution and product integration.

12.1 Component maturity

The package does not receive one undifferentiated maturity grade.

Component	Publicly supported state
Initial $15 billion equity investment	TM2: funded during Q1 2026
Additional $35 billion equity commitment	TM1: binding commitment subject to conditions and expiry
$100 billion commercial expansion	TM1: officially disclosed commercial commitment; full operative terms are not public
Approximately 2GW Trainium deployment	TM1 for the commitment; complete delivery remains future
Distribution and product integration	Announced and developing; component implementation is not fully observable

The correct representation is not a simple addition of equity and commercial headline amounts into one homogeneous exposure. The components differ in legal form, timing, accounting treatment, enforceability, risk, and economic function.

The arrangement creates role overlap. Amazon is an equity investor, cloud-service provider, proprietary-chip provider, distribution channel, product collaborator, and developer of applications using OpenAI models. OpenAI is the investment recipient, cloud customer, compute consumer, model supplier, and product partner.

This does not prove inefficient integration. The package may internalize coordination benefits, improve deployment speed, align technical roadmaps, diversify OpenAI’s compute, and provide Amazon with a differentiated AI platform.

Its significance is that several return channels belong to one relationship:

ReturnAmazon=RetAWS+Retchips+Retdistribution+ΔVOpenAI+Ωstrategic.

A channel that appears weak in isolation may remain attractive at the consolidated relationship level. The verified primary label is ICL. The package can also contain other partial or developing mechanisms, but a financing or valuation feedback loop is not established because the public record does not show that gains in one channel caused a subsequent commitment in another.

13. Multiparty Networks and Prospective Coupling

13.1 Microsoft–NVIDIA–Anthropic

In November 2025, Microsoft, NVIDIA, and Anthropic announced a multiparty package. Anthropic committed to purchase $30 billion of Azure compute and to contract for additional capacity of up to one gigawatt using NVIDIA systems. Microsoft stated that NVIDIA and Anthropic would collaborate on model and hardware optimization. Microsoft also announced continued Claude integration across Azure and Copilot products. NVIDIA and Microsoft separately announced intended investments of up to $10 billion and $5 billion, respectively, in Anthropic (Microsoft 2025).

The package can be represented as:

Anthropic→AzureComputeProcurement,Azure→NVIDIAInfrastructure,NVIDIA→AnthropicInvestment,Microsoft→AnthropicInvestment,Microsoft→ClaudeDistribution.

The customer purchasing Azure capacity is also receiving intended investment from Microsoft and NVIDIA. The hardware supplier is an intended investor and engineering partner. The cloud provider is an investor and distributor.

The appropriate classification is Multiparty Capitalization Network. The announcement verifies the stated architecture but does not establish that the complete intended investment closed, the dates of capital transfer, final accounting treatment, cancellation provisions, or net revenue associated with the compute commitment.

13.2 NVIDIA–OpenAI

In September 2025, NVIDIA and OpenAI announced a letter of intent concerning deployment of at least 10GW of NVIDIA systems. NVIDIA stated that it intended to invest up to $100 billion progressively as capacity was deployed (NVIDIA 2025). NVIDIA’s later annual reporting stated that the parties were still finalizing an investment and partnership agreement and that completion was not assured (NVIDIA 2026).

The prospective mechanism is:

QOpenAI,NVIDIAdeployed↑⇒KNVIDIA→OpenAIintended↑.

Legal and implementation maturity are decisive. The case remains PCI. It is useful for analyzing public scale expectations, proposed coupling structures, strategic signalling, and the difference between intent and completed commitment. It cannot be used as proof that the announced capital was transferred, the full compute amount became binding, or the prospective coupling generated revenue or investment gains.

14. Comparative Case Synthesis

The seven anchor packages establish a heterogeneous but coherent family of capital–compute mechanisms. Because mechanisms can coexist and package components mature at different rates, the comparison uses multi-label mechanism coding and component-level maturity.

Case	Mechanism vector: principal labels	Component maturity at cutoff	External validation	Post-support persistence	Current evidentiary function
AMD–OpenAI	PCE: Verified	Procurement and warrant: TM1; no arrangement-specific supplier revenue	EV0: no identifiable outside-package outcome in reviewed record	PS0	First verified PCE package
AMD–Meta	PCE: Verified	Procurement and warrant: TM1	EV0	PS0	Replicated PCE architecture
Cerebras–OpenAI	CFC: Verified; PCE-like equity component: Partial	Loan and implementation: TM2; net supplier revenue: TM3; optional capacity remains future	EV0	PS0	Strongest implemented coupling package
Amazon–Anthropic	CCF: Verified; ICL: Verified	Additional equity: TM2; facility and delivery-linked draw structure: TM1; availability remains milestone-dependent	EV0	PS0	Verified capacity–finance link within a wider relationship
Amazon–OpenAI	ICL: Verified	Funded equity: TM2; future equity and commercial commitments: TM1; future delivery remains incomplete	EV0	PS0	Strongest multichannel bilateral package
Microsoft–NVIDIA–Anthropic	MCN: Prospective/Partial; ICL edges: Partial	Announced commitments and intended investments: TM0 – TM1, depending on component	EV0	PS0	Network boundary case
NVIDIA–OpenAI	PCI: Prospective	Letter of intent and intended deployment: TM0	EV0	PS0	Prospective coupling boundary

EV0 means that the reviewed public record does not identify an outside-package payment or outcome sufficient for the Chapter 17 external-validation dimension. It does not mean that no such benefit exists.

14.1 What the cases establish

The cases establish:

Contractual coupling: capital, compute, financing, equity rights, and integration can be legally connected.
Replication: PCE appears in more than one major-customer package.
Implementation: CFC has progressed through funding, delivery, and recognized net supplier revenue.
Capacity-linked finance: delivery milestones can determine financing availability.
Multichannel role overlap: equity, cloud, chips, distribution, and products can belong to one relationship.
Multi-label structure: a package can contain several mechanisms at once.

14.2 What the cases do not establish

The cases do not establish:

the share of sectoral demand affected by coupling;
external validation at EV1 or EV2;
post-support persistence at PS1 or PS2;
causal effects of warrants, finance, or announcements on procurement;
a recurrent valuation or financing loop;
horizontal rivalry effects;
overextension;
or an equilibrium.

The current classification is:

Capitalization-Loop Candidate with Verified Contractual Microfoundations.

The cases establish adjacent links, not the complete recurrent process defined in Chapter 2.

Part III — Demand, External Value, and Convergence

15. The Demand-Identification Problem

Part II established that several major AI infrastructure arrangements connect compute procurement to equity rights, customer finance, provider finance, cloud distribution, or wider investment relationships. That finding changes the interpretation of observed demand. It does not establish that the demand is fictitious. It establishes that the observed quantity cannot always be treated as though it arose independently of the contractual and financial structure through which it was produced.

The central empirical problem is not whether demand for AI compute exists. Large firms purchase cloud services, reserve accelerators, build data centers, acquire model access, and sell AI-enabled products. The relevant question is:

What quantity, timing, supplier allocation, duration, and renewal would remain justified if the material equity, financing, distribution, strategic, or valuation support inside the commitment package were substantially reduced?

A binding contract establishes a legal obligation. Trade-credit and platform literatures show why such obligations may efficiently finance or coordinate activity, but neither the contract nor the literature establishes the counterfactual quantity that would have been purchased under different incentives, the degree to which the selected supplier was preferred independently of the package, the downstream value generated by the capacity, or whether procurement will continue after temporary inducements expire (Biais and Gollier 1997; Klapper, Laeven, and Rajan 2012; Rochet and Tirole 2003).

Similarly, a capacity reservation may reflect anticipated commercial demand, scarcity insurance, supplier diversification, equity incentives, strategic competition, or several motives simultaneously.

Observed demand is therefore a composite signal. The problem is not solved by replacing one crude inference with another:

Observed Demand⇏Fully Independent Provenance,

but also:

Coupling-Supported Provenance⇏Invalid Demand.

A transaction may be partly supported by coupling and still produce substantial external value. The analytical task is to separate the provenance of the demand signal from the objective invoked to justify it and from the value of the activity it ultimately supports.

16. Demand Provenance and Justification

Observed compute demand contains at least two analytically independent dimensions.

The first concerns provenance:

How was the quantity, timing, supplier selection, duration, or renewal of the demand produced?

The second concerns justification:

Which external objective or value category is invoked to support the demand?

The canonical demand profile is:

𝒟t=⟨Provt,Justt⟩.

16.1 Demand provenance

Provt∈{Independent,CouplingSupported,Mixed,Indeterminate}.

Independent provenance

Demand has Independent provenance where the available evidence supports the conclusion that approximately the same economically material quantity, timing, duration, and supplier allocation would remain justified after the material coupling mechanism is removed or substantially reduced.

Independence does not mean absence of ordinary finance. Capital-intensive industries commonly use debt, project finance, customer commitments, trade credit, prepayment, and strategic investment. The relevant question is whether the material equity, financing, distribution, or related support inside the package changes the demand counterfactual.

Strong evidence may include third-party payment outside the package, positive economics after customer consideration, sustained utilization, renewal after temporary incentives decline, preservation of demand after supplier substitution becomes feasible, and external benefit relative to complete burden.

Coupling-supported provenance

Demand has Coupling-Supported provenance where a material element of the package affects procurement quantity, timing, supplier selection, duration, renewal, or continuation.

Examples include:

Q↑⇒W↑,

Fcustomer→supplier→Build→Q,

and:

Qdelivered→Favailable.

Coupling-supported demand may be entirely real and valuable. The classification describes how demand was enabled or shaped. It does not determine whether the resulting output produces external value.

Mixed provenance

Demand has Mixed provenance only where the evidence positively supports both:

a material quantity, duration, or operational need that would remain without the coupling mechanism; and
a material effect of coupling on quantity, timing, supplier selection, duration, or renewal.

Formally:

Prov=Mixed⇒Evidence(Independent)>0∧Evidence(CouplingEffect)>0.

A model laboratory may require substantial compute independently while a warrant affects the chosen supplier, deployment schedule, or quantity purchased from that supplier. A cloud relationship may create independent operational value while equity and distribution connections affect its duration or scale.

Mixed is not a residual category. Where the public record does not support both propositions, the code is Indeterminate.

Indeterminate provenance

Provenance is Indeterminate where the public record cannot establish the relevant counterfactual. This classification is required where the incentive value is undisclosed, utilization is unavailable, alternative supplier terms are unknown, or no post-support observation exists.

Indeterminate provenance must not be converted into either independent or coupling-supported demand by assumption.

16.2 Demand justification

Justt⊆{Commercial,Operational,Learning,Strategic}.

Several justification classes may coexist.

Commercial justification

Demand is commercially justified through expected revenue, margin, customer retention, product differentiation, or another financial return.

Operational justification

Demand is operationally justified through reliability, latency, quality, workflow performance, service continuity, or technical capability.

Learning justification

Demand is justified as a bounded experiment or capability-building phase. A valid learning justification requires an objective, hypothesis, budget, time horizon, required evidence, stopping condition, and transition rule.

Strategic justification

Demand is strategically justified through resilience, security, sovereign capability, supplier diversification, military readiness, prevention of exclusion, or preservation of an option under uncertainty.

The strategic profile is:

SP=⟨Threat,Capability,Counterfactual,Adequacy,Duration,Authority⟩.

Strategic justification cannot remain immune from reassessment merely because its value is not reducible to current revenue.

16.3 Combined coding

A package may be coded:

Provt=Independent

and:

Justt={Commercial,Operational}.

Another may be:

Provt=Mixed

and:

Justt={Learning,Strategic}.

A third may have indeterminate provenance while its declared justification is strategic. The existence of a justification does not establish its adequacy. The presence of coupling does not negate the justification.

16.4 Conditional scalar attribution

A scalar decomposition may be used only where a credible counterfactual design exists:

Dtobs=Dtbase+ΔDtcpl,

where Dtbase is estimated demand absent the material coupling mechanism and ΔDtcpl is the estimated increment attributable to it.

This requires evidence such as incentive expiry, a contractual discontinuity, a matched uncoupled case, supplier substitution, a natural experiment, or another defensible counterfactual design. Without such evidence, the manuscript uses categorical provenance rather than an invented numerical allocation.

16.5 Governing non-equivalences

Provt=CouplingSupported⇏Vtext≤0.

Provt=Independent⇏Vtext>Ctfull.

Justt∋Strategic⇏Unlimited Expansion.

Justt∋Learning⇏Unbounded Continuation.

Provenance identifies how demand was produced. Justification identifies why it is defended. External-value analysis determines whether the defended commitment remains proportionate against a credible baseline.

17. Independent-Value Evidence Profile

Observed transaction maturity, external validation, and persistence after support are different empirical dimensions. They do not form one necessarily ordered sequence.

The canonical profile is:

IVEr=⟨TMr,EVr,PSr⟩.

No single score is calculated.

17.1 Transaction maturity

TM∈{TM0,TM1,TM2,TM3}.

Code	Evidence state
TM0	Non-binding intention, target, memorandum, or prospective arrangement
TM1	Binding commitment or legally operative obligation
TM2	Payment, financing, construction, procurement, delivery, or another material implementation step has begun
TM3	Supplier revenue has been recognized after disclosed customer consideration

TM concerns the transaction and supplier-side implementation. It does not establish payment or benefit outside the package.

Share-based consideration payable to a customer can affect revenue measurement. FASB ASU 2025-04 clarifies the accounting for such arrangements and purchase-volume conditions. The update is effective for annual reporting periods beginning after December 15, 2026, with early adoption permitted; it should therefore be treated at the July 25, 2026 cutoff as an authoritative clarification, not as a rule necessarily mandatory for every entity. Company-specific disclosures remain primary for the anchor cases (Financial Accounting Standards Board 2025).

17.2 External validation

EV∈{EV0,EV1,EV2}.

Code	Evidence state
EV0	No identifiable payment or outcome outside the package in the reviewed public record
EV1	Identifiable external payment, use outcome, productivity effect, capability benefit, or other result outside the package
EV2	Comparative external net value is supported against a credible baseline and complete-burden profile

EV1 establishes that the signal crosses the package boundary. It does not establish that the result exceeds complete cost.

EV2 requires a domain-, actor-, baseline-, and horizon-specific comparison. It cannot be assigned from revenue, utilization, user counts, backlog, benchmarks, or strategic rhetoric considered separately.

17.3 Post-support persistence

PS∈{PS0,PS1,PS2}.

Code	Evidence state
PS0	No material observation after the relevant support declined, expired, or became economically less important
PS1	Support declined and demand, renewal, or utilization weakened materially
PS2	Material demand, renewal, or utilization persisted after support declined

PS1 and PS2 require a defined support mechanism, a before–after observation, and controls for material changes unrelated to the support.

Post-support persistence is not identical to external value. A package can persist after support while remaining costly; it can also produce strong external value before any support-expiry observation becomes available.

17.4 Non-ordinal interpretation

The dimensions are not collapsed because:

TM3 can occur before EV1;
EV1 can occur without public supplier revenue;
PS2 can be observed without a defensible EV2;
and EV2 can be estimated before a support mechanism expires.

The profile:

⟨TM3,EV0,PS0⟩

therefore means implemented supplier-side activity without publicly identified outside-package validation or post-support observation. It does not mean failure.

17.5 Current anchor profile

At the observation cutoff, the public evidence supports:

Case	TM	EV	PS
AMD–OpenAI	TM1	EV0	PS0
AMD–Meta	TM1	EV0	PS0
Cerebras–OpenAI	TM3 for delivered services and net supplier revenue; future components remain TM1 – TM2	EV0	PS0
Amazon–Anthropic	Component-specific TM1 – TM2	EV0	PS0
Amazon–OpenAI	Funded equity TM2; future equity and commercial commitments TM1	EV0	PS0
Microsoft–NVIDIA–Anthropic	TM0 – TM1 by component	EV0	PS0
NVIDIA–OpenAI	TM0	EV0	PS0

The table records public evidence availability. It does not deny external value or predict future persistence.

The strongest current conclusion is that the anchor set contains several mature contractual and implementation signals but does not yet provide public EV1, EV2, PS1, or PS2 evidence at the package level.

18. Net Revenue, Downstream Payment, Renewal, and Portability

Independent-value analysis requires operational tests that separate the size of an announced relationship from the strength of its value evidence.

18.1 Adjusted revenue

Where the supplier provides material consideration to the customer, gross revenue should not be interpreted without that consideration.

Radj=Rgross−Wamort−Credits−Rebates−CustomerIncentives−FinancingConcessions.

This is an analytical structure, not an alternative accounting standard. Accounting treatment supplies an indispensable starting point—particularly where share-based consideration is linked to customer purchases—but the research adjustment serves a broader economic identification purpose (Financial Accounting Standards Board 2025). It identifies the complete economic cost of acquiring and sustaining demand. A reduction from gross to adjusted revenue does not imply fictitious revenue.

18.2 Downstream-payment ratio

A downstream-payment test can be represented as:

DPP=CashRevenueoutsidepackageFullAttributableCost.

The denominator may include compute hardware, data-center construction, financing, networking, energy, cooling, software, model operation, human supervision, verification, governance, and customer acquisition.

The ratio is not expected to be complete in early deployment phases. Its function is to expose which variables are missing when a headline contract is treated as proof of independently supported value.

18.3 Renewal

Renewal is stronger than initial procurement because it occurs after the customer has acquired information about performance, integration cost, operational value, demand, and alternatives. Renewal while the same warrant, credit, financing facility, exclusivity privilege, or equity relationship continues may remain coupling-supported.

18.4 Utilization

Utilization determines whether infrastructure performs work. It is necessary but insufficient. A system can be highly utilized because workloads were transferred from another provider, internal experimentation expanded, low-price use was encouraged, strategic redundancy was maintained, or processes were reorganized around available capacity.

The relevant sequence remains:

Delivery→Utilization→Output→External Outcome.

Each transition requires separate evidence.

18.5 Portability

Portability tests whether demand is tied to the workload’s value or to continuation of a particular relationship.

PV=WorkloadRetainedaftersubstitutionWorkloadbeforesubstitution.

A high ratio suggests that underlying demand survives supplier change. A low ratio may indicate genuine supplier-specific advantage, switching costs, software dependence, contractual restrictions, or demand partly sustained by the original package. Portability is therefore both a demand test and a dependency measure.

19. External Value and Complete Burden

The article rejects a zero-value thesis. Contemporary AI already produces substantial commercial activity.

Microsoft reported in April 2026 that its AI business had surpassed an annual revenue run rate of approximately $37 billion, up substantially year over year, and reported more than 20 million paid Microsoft 365 Copilot seats. It also stated that continued AI-infrastructure investment and growing AI-product usage exerted pressure on cloud gross-margin percentages (Microsoft 2026). The same record contains evidence of monetization, demand, infrastructure burden, and margin pressure.

Alphabet reported strong Google Cloud growth, a large cloud backlog, millions of paid Gemini Enterprise seats, and very large planned capital expenditure for 2026 (Alphabet 2026). These facts establish large-scale commercialization and infrastructure expansion. They do not isolate complete AI-specific return or allocate that return to individual packages.

The correct inference is:

Real AI Commercial Value Exists.

The incorrect stronger inference is:

Every Increment of AI Capital and Compute Is Efficiently Allocated.

Revenue measures payment received by one actor. External value asks: What benefit is produced, for whom, relative to which credible alternative, over what period, and with what allocation of capital, risk, labor, infrastructure burden, dependency, knowledge, and authority?

The external-value profile is:

Vd,a|b,Text=⟨Ben,Ret,Prod,Qual,Str,Lrn,Util⟩,

where Ben is externally realized benefit; Ret, net commercial return; Prod, productivity; Qual, quality, reliability, or capability; Str, strategic and resilience value; Lrn, learning and knowledge value; and Util, user or institutional utility.

The complete burden is:

Cd,a|b,Tfull=⟨Cap,Op,En,Grid,Lab,Meta,Risk,Dep,Gov,Opp⟩.

The vectors remain disaggregated because benefits and burdens can be borne by different actors and some dimensions are not reliably commensurable. A supplier can recognize revenue; a model company can bear market risk; a cloud provider can obtain equity exposure; enterprise users can perform verification; workers can absorb workflow changes; and local infrastructure can bear energy or grid costs.

The relevant comparison is often not AI versus no AI, but the current configuration versus a credible simpler alternative. The RATIUM.AI configuration framework requires benefit, labor, risk, knowledge, authority, and exit dependence to remain visible (Dunavich 2026a).

Where common valuation is defensible, continuation may be supported where:

Vd,a|b,Text*>Cd,a|b,Tfull*.

Where common valuation would erase materially different interests or constraints, the decision should use component thresholds, vector dominance, multi-criteria comparison, and non-compensatory limits.

Commercial revenue should not automatically compensate every infrastructure burden. Strategic value should not automatically compensate unlimited dependency. Aggregate productivity should not erase burdens transferred to actors who lack corresponding authority or benefit.

20. Energy, Infrastructure, and Physical Commitment

Compute demand is converted into physical infrastructure. The relevant denominator therefore extends beyond chips and cloud invoices.

The International Energy Agency estimated that data centers consumed approximately 415 TWh of electricity in 2024 and projected substantially higher consumption by 2030 under its base case, with accelerated servers associated primarily with AI accounting for a large part of the projected increase (International Energy Agency 2025). The IEA also emphasized substantial uncertainty and materially different outcomes based on efficiency, AI uptake, and energy-system bottlenecks.

These projections do not establish that AI electricity use is excessive. Global share alone also does not capture local concentration, grid constraints, or infrastructure timing.

The governance-relevant asymmetry is temporal:

Compute Deployment Time<Energy-System Adaptation Time.

A data center may become operational faster than new generation, transmission, and local grid infrastructure can be planned, approved, financed, and constructed. This creates a possible mismatch:

Financial and Technical Commitment Velocity>Physical Correction Velocity.

Valuations, demand forecasts, and model architectures can change rapidly. Data-center buildings, grid interconnections, generation capacity, cooling systems, high-capacity networks, and geographic clusters cannot always be reversed or repurposed at the same speed.

A gigawatt is neither evidence of value nor evidence of waste. It is a material commitment whose justification depends on utilization, external outcome, opportunity cost, asset transferability, regional infrastructure, time horizon, and the credible alternative.

The relevant baseline may be build now versus stage construction; one supplier versus a diversified portfolio; dedicated versus transferable capacity; new infrastructure versus improved utilization; or full scale versus a bounded learning tranche.

21. Learning, Maturity, and Convergence

Weak early returns do not establish failure. Large technological transitions can require complementary investment, workflow redesign, employee learning, product iteration, customer adoption, and organizational reallocation.

Current firm-level evidence supports a mixed picture rather than a settled verdict. Recent executive surveys report substantial AI adoption alongside heterogeneous and often limited measured productivity effects to date, with expectations of larger future gains (Yotzov et al. 2026). Other firm-level research reports positive but uneven effects and a gap between perceived and measured gains (Baslandze et al. 2026). Reviews of available datasets emphasize that different sources measure invention, adoption, internal capability building, outsourcing, realized activity, and investor perceptions differently (Babina 2026).

These 2026 NBER sources are working papers rather than settled peer-reviewed consensus. They are used as contemporaneous empirical evidence and measurement input, not as definitive estimates of economy-wide AI productivity.

The appropriate conclusion is neither that AI has failed to raise productivity nor that a productivity transformation is complete. The evidence supports meaningful value in some firms, products, tasks, and sectors; heterogeneous adoption and effects; limited measurement comparability; and uncertainty concerning wider convergence.

The manuscript distinguishes four lifecycle phases:

Setup — initial construction, procurement, integration, and organizational preparation.
Stabilization — bounded correction and learning after deployment.
Routine value production — sustained operation with proportionate maintenance and measurable outcomes.
Persistent reconfiguration — continuing expansion or modification without convergence, bounded learning, or terminal acceptance.

The RATIUM.AI framework states that high burden during setup or stabilization is not sufficient evidence of persistent failure; the relevant test is movement toward stable external-value production (Dunavich 2026a).

A valid learning phase should specify the learning objective, testable hypothesis, resource budget, time limit, scope, required evidence, stopping rule, and transition condition.

Bounded Learning≠Unbounded Continuation Under Uncertainty.

21.1 Evidence sufficiency

The evidence requirement remains a componentwise profile:

𝐄𝐕𝐆t=Etreq⊖Etext,

where ⊖ denotes unresolved requirements rather than arithmetic subtraction.

For a declared decision rule:

EVSt={1,Etextsatisfies the predeclared requirement,0,otherwise.

Insufficient evidence does not automatically justify stopping. Continued experimentation may remain rational where uncertainty is visible, learning value is material, the increment is bounded, dependency remains controlled, and the next decision is explicitly conditional.

21.2 Three forms of Commitment–Evidence Divergence

A commitment can exceed a defensible envelope in three analytically different ways.

Ex ante divergence

CEDtEA=1

where the proposed commitment violates a threshold, budget, scope, review date, or stopping rule declared before the decision.

External divergence

CEDtEX=1

where the commitment violates an independently defined legal, engineering, financial, infrastructural, rights-based, or strategic boundary.

Retrospective divergence

CEDtR=1

where later evidence indicates that the commitment exceeded one or more defensible envelopes, but no applicable ex ante or external rule was fixed before the decision.

Retrospective divergence is epistemically weaker because the analyst can select an envelope after observing the outcome. It therefore supports only an underidentified B2 candidate unless the result is robust across a disclosed range of plausible thresholds.

Every CED coding must report:

threshold provenance;
timestamp;
authority or source;
uncertainty allowance;
sensitivity range;
and whether the threshold was selected before or after outcome evidence.

Prospective decisions must separate prior investment from the justification for the next increment:

Prior Investment⇏Continuation Authorization.

Part III establishes the demand and external-value framework. It does not estimate demand provenance, establish EV1 or EV2, or code post-support persistence for the anchor cases.

Part IV — Relative Acceleration and Dependency

22. Role-Defined Players and Strategy Space

The capital–compute commitment system is strategically interdependent. A model developer deciding whether to reserve another tranche of compute cannot evaluate the decision solely through current product revenue. It must consider whether competing laboratories will continue scaling, whether hardware availability will tighten, whether capital providers will interpret restraint as weakness, whether cloud partners will allocate capacity elsewhere, and whether delay will impair future technical or strategic options.

The same structure appears from other positions. A semiconductor supplier may accept an unusually demanding commercial package because securing a frontier-model customer can affect product adoption, software-ecosystem development, market credibility, future customer acquisition, and competitive position. A cloud provider may invest in a model company while supplying its infrastructure because the relationship generates potential returns through cloud consumption, proprietary-chip utilization, distribution, product differentiation, equity appreciation, and strategic option value. A state may support capacity whose short-term commercial return remains uncertain because dependence on a foreign or rival infrastructure provider is treated as a separate cost.

The actors are represented by role rather than legal identity:

𝒩={LAB,HW,CLOUD,INFRA,FIN,PUB}.

One organization may occupy several roles. Incomplete-contract, property-rights, transaction-cost, and platform theories explain why ownership, integration, and cross-channel subsidy can be rational responses to complementary investment and coordination problems (Grossman and Hart 1986; Hart and Moore 1990; Williamson 1985; Rochet and Tirole 2003). The relevant payoff boundary may therefore be wider than one transaction or business unit:

Transaction-Level Return≠Portfolio-Level Return.

The reduced strategy space is:

𝒜i={ACC,COND,RET},

where ACC is Accelerate, COND is Condition, and RET is Retrench.

22.1 Accelerate

An actor chooses Accelerate when it approves the next material capital, capacity, procurement, financing, distribution, or integration increment before uncertainty concerning independent external value has been fully resolved.

Acceleration is not synonymous with recklessness. It can be rational where capacity is scarce, learning requires deployment, infrastructure has a long construction period, scale reduces unit cost, rival expansion threatens exclusion, or strategic option value is high.

22.2 Condition

An actor chooses Condition when it continues participating but makes the next increment dependent on specified evidence, thresholds, scope limits, portability protections, expiry rules, or review.

Conditioning can include phased deployment, lower initial capacity, evidence-linked tranches, limited exclusivity, utilization thresholds, shorter duration, or preservation of credible alternatives.

COND≠RET.

Its objective is to preserve valid value while reducing the irreversible commitment placed ahead of evidence.

22.3 Retrench

An actor chooses Retrench when it cancels, materially reduces, transfers, exits, or reverses an existing or proposed commitment. Retrenchment becomes relevant after adverse evidence, failed conditioning, technical or contractual failure, strategic revaluation, or emergence of a superior alternative.

The central game primarily compares ACC and COND. The immediate governance problem is usually not whether all AI development should stop. It is whether the next marginal increment should proceed unconditionally, proceed under limitations, or wait for specified evidence.

23. Actor Payoffs and the Restraint Penalty

Actors do not evaluate the next commitment through one common payoff function. A reduced-form payoff is:

ui=πi+αiΔVi+βiΩi+γiΣi+ηiCPLi−Ki−λiBi−ρiGovRiski−ξiXi,

where πi is expected operating profit or cash return; ΔVi, equity or investment-value change; Ωi, technological, commercial, or organizational option value; Σi, sovereign, security, resilience, or competitive-strategic value; CPLi, benefits specific to the coupling structure; Ki, direct capital and operating cost; Bi, other burdens borne by the actor; GovRiski, governance, legal, reliability, and correction risk; and Xi, dependency and exit exposure.

The coefficients differ by role. A frontier laboratory may assign high weight to capability, continuity, scarce compute, and the option value of retaining a frontier position. A hardware supplier may assign high weight to ecosystem formation, software adoption, and roadmap credibility. A cloud provider may internalize returns across infrastructure, proprietary chips, distribution, applications, and equity holdings. A public actor may assign greater weight to strategic autonomy, resilience, or defense capability.

The same package can therefore be attractive to several actors for different reasons. Financial theory also shows that relative-performance concerns can make actors reluctant to move against a collectively expanding position even when they recognize downside risk (DeMarzo, Kaniel, and Kremer 2008).

23.1 Restraint Penalty

The Restraint Penalty is actor- and rival-specific. For actor i relative to strategically relevant horizontal rival k:

RPi∣k(t)=𝔼[ui(ACCi,ak,Zt)∣ℐi,t]−𝔼[ui(CONDi,ak,Zt)∣ℐi,t].

Where several rivals matter, the aggregate expected penalty may be represented as a belief-weighted profile rather than a single universal number:

𝐑𝐏i(t)={RPi∣k(t):k∈Rivalsi}.

The identity of k, the competitive dimension, the expected rival action, and the time horizon must be specified. A customer–supplier contractual incentive is not by itself evidence of a laboratory–laboratory, cloud–cloud, supplier–supplier, or state–state restraint penalty.

When:

RPi∣k(t)>0,

the actor expects unilateral conditioning to be privately costly. When RPi∣k(t)<0, the actor expects cost savings, risk reduction, or preserved flexibility to exceed the relative loss.

The Restraint Penalty is not the social cost of restraint and is not evidence that acceleration produces greater external value. It is the actor’s expected difference between two strategies under specified expectations concerning others.

A positive Restraint Penalty can coexist with a socially preferable conditioned outcome. A negative penalty can coexist with socially undesirable retrenchment.

The penalty may be decomposed as:

RPi=Licap+Litech+Limarket+Lifin+Lival+Licontract+Listrat−Sicost−Sirisk−Sioption.

The first group captures expected loss of capacity, technology, market position, finance, valuation, contractual rights, or strategic position. The second captures expenditure saved, risk avoided, and option value preserved by conditioning.

23.2 Evidence levels

Grade	Evidentiary state
RP0	No transaction-specific evidence that conditioning is costly
RP1	A stated competitive, strategic, or contractual incentive favors acceleration
RP2	Conditioning would forfeit an identifiable right, financing opportunity, capacity position, or material benefit
RP3	An actor conditions or retrenches and then suffers a causally identified relative loss

The anchor transactions support RP1-RP2. Procurement-linked warrants can create an identifiable cost of reducing purchases. Capacity-delivery milestones can create an identifiable cost of slowing infrastructure provision. Customer-financed buildout can create bilateral exposure whose unwinding affects several connected assets.

The cases do not establish RP3. Contract structure shows that a penalty can exist. It does not establish its magnitude or prove that it changed behavior.

24. The Core Two-Strategy Game

Consider two strategically comparable actors choosing between Accelerate and Condition.

New Field	Other conditions	Other accelerates
Actor conditions	g,g	\ell,t
Actor accelerates	t,\ell	a,a

Here, g is the payoff from mutual conditioning; t, the payoff from accelerating while the other conditions; ℓ, the payoff from conditioning while the other accelerates; and a, the payoff from mutual acceleration.

A strict relative-acceleration dilemma exists if:

t>g>a>ℓ.

Under this ordering, each actor prefers acceleration when the other conditions because it obtains a relative advantage; each prefers acceleration when the other accelerates because unilateral conditioning produces the laggard payoff; mutual acceleration is the unique Nash equilibrium; and both would receive a higher payoff under mutual conditioning.

The quantity a−ℓ represents the loss from unilateral restraint when the other actor accelerates. The quantity g−a represents the gain available under credible mutual conditionality.

This payoff ordering is not an empirical finding about the AI sector. It is a candidate structure whose conditions must be tested.

Other orderings are possible. If a≥g, mutual acceleration may be privately and collectively preferred. If g≥t, conditioning may be stable without external coordination. Where actors have asymmetric positions, the interaction may resemble bargaining, entry deterrence, vertical foreclosure, platform competition, or coordination rather than a symmetric prisoner’s-dilemma structure.

A valid classification requires actor-specific payoffs, feasible alternatives, response expectations, and unilateral deviation costs.

25. Repeated Interaction and Acceleration Expectations

Capital–compute decisions are repeated. Actors observe financing rounds, infrastructure announcements, chip reservations, model releases, customer commitments, public procurement, strategic alliances, and valuation changes. They update their beliefs and decide whether to reserve capacity, issue financing, expand infrastructure, offer incentives, or deepen integration.

Repeated interaction creates the possibility that mutual conditionality could be sustained through future consequences.

The following illustration assumes:

indefinitely repeated interaction;
stationary stage-game payoffs;
sufficiently observable actions;
a credible trigger strategy;
reversion to mutual acceleration after unilateral deviation;
a common effective discount factor δ.

Under these assumptions, mutual conditioning can be sustained where:

g1−δ≥t+δa1−δ,

or:

δ≥t−gt−a.

The inequality is not a general empirical threshold for the AI sector. Repeated-game results depend materially on monitoring, actor asymmetry, horizon, information, and credible response structures (Fudenberg and Maskin 1986; Radner, Myerson, and Maskin 1986; Fudenberg, Kreps, and Maskin 1990).

Mutual conditioning becomes more difficult where the decision horizon is short, monitoring is weak, private commitments are difficult to observe, actors can accelerate indirectly through affiliates, sanctions are not credible, product cycles are rapid, or strategic shocks increase the perceived cost of delay.

25.1 Acceleration expectations

Let:

μi,t=Pri(a−i=ACC)

represent actor i’s belief that relevant others will accelerate. Under the candidate dilemma ordering:

∂RPi∂μi,t>0.

The more likely the actor believes others are to accelerate, the greater the expected cost of conditioning.

This creates an expectation channel:

Observed or Announced Rival Commitment→Higher Belief in Continued Acceleration→Higher Expected Restraint Penalty→Further Commitment.

Public announcements may matter before every announced transaction is completed because they can affect beliefs about scale, scarcity, financing availability, technological direction, and commitment. The NVIDIA–OpenAI PCI case is not evidence of implemented procurement or completed investment, but it may contribute to the information environment in which other actors form expectations.

The causal effect remains a hypothesis. Demonstration requires evidence that an announcement changed another actor’s decision rather than coinciding with a decision already under consideration.

25.2 Shared expectations

A strategic equilibrium does not require identical beliefs. It requires sufficiently shared expectations for the relevant strategy to remain stable.

Empirical questions include whether laboratories expect competitors to continue scaling; suppliers expect frontier customers to reward capacity commitments; investors penalize visible restraint; public authorities expect strategic competitors to continue building; and actors believe coordinated conditioning is infeasible.

Public statements reveal some expectations but do not necessarily reveal operative beliefs used in boards, investment committees, procurement, or state planning. Shared expectations remain an empirical requirement.

26. From Vertical Package Coupling to Horizontal Rivalry

The anchor mechanisms are predominantly vertical. They connect customers, suppliers, cloud providers, infrastructure operators, investors, and model laboratories inside specific commitment packages.

The core relative-acceleration game is horizontal. It concerns strategically comparable actors such as:

rival model laboratories;
rival cloud providers;
rival semiconductor suppliers;
rival capital providers;
or rival states.

A vertical package does not automatically establish a horizontal acceleration dilemma. The analytical bridge must be shown.

26.1 Layer V — the vertical package game

For contractual partners i and j:

𝒱ij:Γij→⟨Δui,Δuj,ΔXi,ΔXj⟩.

This layer asks how PCE, CFC, CCF, ICL, MCN, or PCI changes:

contractual rights;
financing;
capacity;
option value;
dependency;
and the payoff from continuing or conditioning the relationship.

The anchor cases directly support this layer at different maturity levels.

26.2 Layer H — the horizontal rivalry game

For strategically comparable actors i and k:

ℋik:{ACC,COND}i×{ACC,COND}k.

This layer asks whether actor i’s vertical package changes the relative payoff of conditioning while rival k accelerates.

The required bridge is:

Γij→ΔRPi∣k→Strategyi.

A valid bridge claim must identify:

the vertically coupled package Γij;
the horizontal rival k;
the competitive dimension;
the transmission channel;
the relevant timing;
and the counterfactual payoff without the package.

26.3 Bridge channels

A vertical package can alter a horizontal rivalry game through several candidate channels.

Capacity scarcity

A procurement or finance package may reserve capacity that a rival cannot obtain promptly. Conditioning can then expose the actor to a relative capability delay.

Financing and valuation

A package may improve financing access or perceived strategic commitment. Conditioning can affect the actor’s financing position relative to a rival.

Customer and ecosystem migration

Distribution, integration, or proprietary tooling may attract customers and developers. Conditioning can permit a rival ecosystem to expand.

Supplier learning and roadmap influence

Large commitments can affect supplier engineering attention, software optimization, or product roadmaps. A conditioning actor may lose influence relative to an accelerating rival.

Sovereign capability comparison

A public actor may evaluate restraint relative to another state’s compute, defense, or industrial capability rather than against a purely commercial baseline.

These channels are hypotheses. They require evidence of actual substitution, response, or strategic deliberation. Simultaneous capital expenditure is not sufficient.

26.4 Mechanism-specific vertical effects

Purchase-Contingent Equity

Under PCE:

ACC→Q+W,

while conditioning can reduce both procurement and potential equity rights. This establishes a vertical contractual effect. It affects a horizontal rivalry game only if the resulting capacity, finance, ecosystem position, or valuation changes the actor’s payoff relative to an identified rival.

Customer-Financed Compute

Under CFC:

Fcustomer→Buildsupplier→Qcustomer.

The package can increase bilateral exposure and capacity assurance. It changes horizontal rivalry only where that capacity or exposure affects the customer’s competitive position against another actor.

Capacity-Contingent Finance

Under CCF:

Qdelivered→Favailable.

This directly changes the vertical provider–customer relationship. The horizontal effect depends on whether delayed finance changes the customer’s relative capability or whether provider resources are reallocated to a rival.

Investment–Commercial Linkage

Under ICL:

ui=uiequity+uicloud+uichips+uidistribution+uiproduct+uistrategic.

The consolidated relationship can make conditioning privately costly. A horizontal acceleration claim still requires evidence that the consolidated loss is relative to an identified rival’s continued expansion.

Multiparty and prospective structures

MCN can transmit incentives across several vertical edges. PCI can alter expectations before final implementation. Neither is evidence of a horizontal game until the rival pair and transmission effect are observed or independently supported.

26.5 Evidentiary boundary

The anchor cases establish vertical package effects and candidate bridge channels. They do not establish:

the horizontal actor pair for every package;
the magnitude of ΔRPi∣k;
the payoff ordering t>g>a>ℓ;
or an observed horizontal equilibrium.

The correct current sequence is:

Verified Vertical Coupling→Candidate Horizontal Transmission→Unvalidated Relative-Acceleration Game.

27. Dependency, Portability, and Exit Cost

Capital–compute commitments change the state in which future decisions are made. Dependency can arise through dedicated infrastructure, financing, software integration, data architecture, exclusive distribution, organizational specialization, and strategic reliance.

Dependency is not assumed to be linear, monotonic, or always harmful. The canonical transition is:

Xt+1=𝒳(Xt,Qt,Ft,Λt,Atspec,Portt,Altt,Stdt,SecMktt),

where:

Qt = relationship-specific compute;
Ft = linked financing;
Λt = technical and distribution integration;
Atspec = asset specificity;
Portt = portability;
Altt = availability of credible alternatives;
Stdt = interoperability and standards;
SecMktt = secondary-market or redeployment depth.

The sign and magnitude of each marginal effect are conditional.

Scale can finance interoperability. A large standardized deployment can improve portability. Integrated tooling can reduce dependence on scarce personnel. Financing can diversify suppliers. Specialized assets can retain value where secondary markets or alternative workloads exist.

27.1 Technical dependency

Technical dependency can arise through hardware-specific optimization, proprietary software stacks, model architecture, networking design, data locality, and operational tooling. A technically superior system may rationally create dependency. The relevant question is whether feasible substitutes, migration paths, and transferable competence remain available.

27.2 Contractual and financial dependency

Financial dependency can arise through customer loans, security interests, cross-default exposure, warrant conditions, minimum purchases, reserved capacity, and long-duration obligations. Reducing the compute relationship may affect financing, ownership, repayment, and contractual rights.

Linked finance can also reduce dependency where it funds a second supplier or transferable infrastructure. The direction must be coded from the actual package.

27.3 Institutional and strategic dependency

Institutional dependency can arise when a product line depends on one model provider, a laboratory depends on one cloud, a state depends on one private infrastructure network, or a supplier’s roadmap depends on concentrated customers. Strategic dependency concerns the ability to preserve critical capability under geopolitical, legal, or supply disruption.

27.4 Portability and alternatives

Portability preserves feasible alternatives through workload migration, interoperable software, supplier diversity, transferable contracts, reusable facilities, alternative financing, standardized interfaces, and retained human competence.

A dependency warning requires more than integration:

Etextremains insufficient∧Xt↑∧Altt↓.

High exit cost establishes neither current failure nor current superiority. Prior investment and current dependency cannot by themselves authorize the next avoidable increment (Arthur 1989; David 1985; Liebowitz and Margolis 1995; Dunavich 2026a).

The relevant comparison is prospective and vector-valued:

⟨ExpectedBenefit,AvoidableCost,AdditionalDependency,TransitionExposure,Portability⟩.

Where exit cost is already high, immediate termination may be inferior to staged restriction. A conditioned strategy can preserve service while restoring alternatives, increasing portability, reducing exclusivity, and preventing further dependency growth.

28. Local Rationality, Distributed Impact, and Rival Explanations

The framework does not require irrational actors. A system-level problem can emerge from decisions that are locally rational within each actor’s payoff boundary.

The manuscript does not aggregate actor utilities into one welfare scalar. The relevant utilities are not shown to be cardinally comparable, and effects outside the package can be positive as well as negative.

The canonical distributed-impact profile is:

𝒲t=⟨Utinside,Btoutside+,Btoutside−,Distt,Rightst,Authorityt⟩,

where:

Utinside = actor-specific benefits and burdens internal to the package, retained as a profile;
Btoutside+ = positive benefits realized outside the package;
Btoutside− = external burdens;
Distt = distribution of benefits and burdens;
Rightst = non-compensatory rights or legal constraints;
Authorityt = which institution is entitled to make the relevant tradeoff.

Potential outside benefits include scientific progress, consumer utility, ecosystem innovation, security, resilience, and knowledge spillovers. Potential outside burdens include grid and public-infrastructure costs, public guarantees, systemic financial exposure, displaced investment, downstream verification burdens, labor-market adjustment, concentration, and dependency borne by actors without corresponding authority.

The valid conclusion is:

Local Rationality⇏Collective Optimality.

The framework does not claim a calculated social-welfare deficit unless a study declares a defensible valuation rule, affected population, distributional treatment, and authority for making compensatory tradeoffs.

Pareto inferiority likewise requires a feasible alternative, actor-level preference evidence, inclusion of relevant parties outside the package, and proof that at least one actor would be better off without making another worse off.

28.1 Efficient project finance

Customer finance, long-term commitments, and staged financing may solve genuine capital constraints. They can allocate construction risk to the party best able to bear or observe it. Evidence favoring this explanation includes coherent risk pricing, timely delivery, high utilization, development of additional customers, and continued demand after temporary support declines (Biais and Gollier 1997; Petersen and Rajan 1997; Klapper, Laeven, and Rajan 2012).

28.2 Genuine scarcity and diversification

Large reservations and advance commitments may reflect a real shortage of frontier compute. Evidence includes sustained utilization, rising replacement prices, inability to obtain comparable capacity elsewhere, and profitable reallocation of released capacity.

28.3 Efficient vertical integration

Role overlap may reduce coordination cost and internalize complementary investments. An investor–cloud–distribution relationship can be efficient where separate contracting would produce hold-up, incompatible technical roadmaps, duplicated investment, or slower commercialization (Grossman and Hart 1986; Hart and Moore 1990; Williamson 1985; Rochet and Tirole 2003).

28.4 Productive general-purpose-technology investment

Capital expenditure may run ahead of current productivity because organizational adaptation and complementary investment take time. Evidence includes improving unit economics, wider diffusion, post-support persistence, expanding third-party revenue, and transition from setup to routine value production (Brynjolfsson, Rock, and Syverson 2021).

28.5 Strategic insurance

States and firms may rationally build spare, redundant, or currently underutilized capacity to reduce dependence and preserve future capability. This explanation requires a defined threat, capability requirement, adequacy threshold, and stopping point.

28.6 Ordinary path dependence

Persistence may result from sunk assets, long contracts, migration time, organizational routines, or legal constraints without constituting a strategic equilibrium (David 1985; Arthur 1989; Liebowitz and Margolis 1995).

The distinction is:

Past Commitment Constrains Present Choice

versus:

Actors Reproduce Commitment Because They Anticipate the Relative Cost of Conditioning.

The second is the stronger game-theoretic claim.

Observed pattern	Stronger ordinary explanation	Stronger relative-acceleration interpretation
Long contract and dedicated facility	Project finance and asset specificity	Contract links raise unilateral conditioning cost across channels
Capacity reserved before use	Scarcity or long planning period	Rival acceleration expectations make delay privately costly
Investor also supplies cloud	Efficient integration	Portfolio benefits transmit into a horizontal rival disadvantage
Customer receives supplier equity	Adoption incentive	Procurement and equity rights increase actor-pair-specific RP_{i\mid k}
Strategic capacity exceeds current demand	Rational insurance	Adequacy threshold is absent and justification expands indefinitely
High switching cost	Ordinary path dependence	Actors expect unilateral exit to cause a relative strategic loss
Continued investment after weak results	Bounded learning	Predeclared thresholds are crossed while dependency rises

The framework adds value only where it explains facts that ordinary accounts do not explain adequately. It must identify the horizontal rival, transmission channel, restraint counterfactual, and failed correction path.

Part IV establishes verified vertical coupling and candidate horizontal transmission channels. It does not establish the sector’s payoff ordering, RP3, or an observed equilibrium.

Part V — Correction, Political Agency, and the CEP Boundary

29. Three Levels of Correction

The capital–compute system contains extensive governance in the ordinary sense. Its transactions are structured through definitive agreements, financing conditions, purchase milestones, delivery obligations, service levels, vesting schedules, repayment provisions, termination clauses, accounting controls, board approvals, and regulatory reporting. Accountability and risk-management structures can produce explanation, questioning, judgment, documentation, and response obligations without necessarily changing the permission state of the governed object (Bovens 2007; Koppell 2005; National Institute of Standards and Technology 2023; Dunavich 2026e).

The institutional problem is whether those controls govern the same object as the article’s external-value inquiry.

A contractual mechanism may govern whether a party performed what it promised. The article asks a different question:

Can credible evidence concerning demand provenance, complete burden, dependency, strategic adequacy, or comparative value change the operative permission state of the next material capital–compute commitment?

That question requires a distinction among three levels of correction.

29.1 Contract correction

Contract correction determines whether the parties complied with the legal and operational terms of an agreement. It may ask whether required capital was transferred, capacity delivered, technical specifications satisfied, a purchase milestone reached, a warrant vested, payment made, a service-level failure occurred, a closing condition failed, or a party may terminate or seek damages.

Contract correction is real governance. It can alter payment, delivery, ownership, vesting, liability, timing, and continuation of the specific agreement.

Its limitation is one of decision object. A contractual gate usually governs performance under an existing arrangement. It does not necessarily determine whether the complete package continues to serve the external objective that justified it.

29.2 Package correction

Package correction evaluates the combined capital–compute relationship rather than an individual clause. The package may include equity investment, procurement, customer incentives, infrastructure finance, cloud consumption, distribution, product integration, revenue, valuation exposure, strategic dependence, and exit conditions.

Package correction asks whether the combined arrangement still justifies its next increment, whether independent-value evidence has strengthened, whether the coupling mechanism has become less necessary, whether external value is converging, whether dependency has grown faster than value, whether a bounded learning phase has become continuing expansion, and whether a smaller or more transferable alternative is now superior.

A package can remain legally compliant while becoming economically weak, strategically redundant, excessively concentrated, insufficiently reversible, or unsupported at its next scale:

Contract Compliance⇏Package Adequacy.

29.3 System permission correction

System permission correction determines whether a defined activity should remain authorized at the level at which its broader consequences are produced. The decision may concern the next data-center phase, gigawatt, financing draw, warrant tranche, exclusivity renewal, public guarantee, grid connection, sovereign procurement increment, or dependency-producing integration.

The possible permission states are:

{SHIP,RESTRICT,HOLD,ROLLBACK}.

System permission correction does not necessarily replace private contracting. It determines whether the next defined increment may proceed under the complete evidence state.

The three levels are non-equivalent:

Contract Correction≠Package Correction≠System Permission Correction.

A system may possess strong contract correction and weak package correction. It may possess internal package review and no cross-institutional permission path. It may also possess a public authority capable of stopping one infrastructural component without possessing the evidence required to judge the complete package.

The central problem is not the absence of governance functions. It is whether the required functions are connected at the correct permission object.

30. The Capital–Compute Permission Profile as a Correction Graph

For a bounded permission object o, the Capital–Compute Permission Profile identifies the functions required for correction:

No={τ,St,Ev,Fo,Jd,Ga,Im},

where τ is trigger recognition; St, standing; Ev, evidence access; Fo, competent forum; Jd, judgment; Ga, operative gate determination; and Im, implementation.

Real correction architectures can contain parallel evidence channels, recursive review, appeals, several gate authorities, and multiple implementation agents. The canonical representation is therefore a directed graph:

𝔾o=(No,Eo).

Correction completeness requires at least one timely and authorized path:

∃p:τ⤳Im

subject to:

evidence integrity;
forum competence;
lawful authority;
procedural legitimacy;
and completion before effective irreversibility.

30.1 Minimal canonical path

The serial sequence:

τ→St→Ev→Fo→Jd→Ga→Im

is retained as the minimal canonical path. It is a completeness test, not the only permissible architecture.

A system can satisfy the profile through parallel paths. For example, technical and financial evidence can reach different forums before a joint judgment. An appeal can return the process from gate determination to judgment. Several authorities can issue component gates that jointly determine implementation.

The decisive question is whether at least one complete path can change the bounded permission object.

30.2 Nodes are insufficient

A system does not possess a complete correction architecture merely because all functions exist somewhere.

A trigger may exist without a party authorized to invoke it. A party may possess standing without access to evidence. Evidence may reach a forum lacking competence. A forum may issue an advisory judgment without operative authority. A binding gate may be issued without an implementation mechanism capable of changing infrastructure, finance, procurement, or deployment.

The Stable Governance Layer formalizes the distinction between node presence and valid derivation relations. It treats a metric without a failure mechanism as orphaned, a threshold without rationale as administrative, a gate without authority as symbolic, and a decision without implementation as non-operative (Dunavich 2026c).

30.3 Bounded permission object

The graph must be attached to a bounded object. The object cannot be “AI,” “the AI industry,” “innovation,” or “national competitiveness” without further specification.

A usable object identifies the activity, actors, domain, material commitment, baseline, decision period, and implementation instruments. Examples include authorization of a second 500MW construction phase, release of a financing tranche, renewal of an exclusive distribution right, vesting of a warrant tranche, or approval of a sovereign capacity increment.

The same evidence can justify different states for different objects. Weak independent-value evidence may justify continued operation of deployed capacity, RESTRICT on a new build phase, and HOLD on additional exclusivity.

30.4 Assurance layer

Accountability, appeal, remedy, audit, expiration, changed-circumstances review, and reauthorization surround the core graph. They do not substitute for a trigger-to-implementation path (Bovens 2007; Koppell 2005; Jasanoff 2003; National Institute of Standards and Technology 2023).

A system may provide explanation and appeal while lacking correction power. Conversely, an actor may possess stopping power while lacking reviewability or remedy. Both defects must be coded separately.

31. From Trigger to Implementation

The subsections below describe the minimal canonical path through the correction graph. Real systems may contain parallel evidence channels, recursive review, appeals, multiple forums, and several implementation agents. Completeness requires at least one timely, lawful, and operative route from trigger to implementation; it does not require one exclusively serial bureaucracy.

31.1 Trigger recognition - τ

A trigger is an event, threshold crossing, or evidence change sufficient to reopen the permission state. It does not predetermine the outcome.

Triggers may include material underutilization after an agreed ramp period, failure of downstream monetization to reach a threshold, non-renewal after an incentive expires, a material difference between gross and adjusted revenue, a large increase in grid burden, loss of portability, increased concentration or dependency, strategic adequacy being reached, a change in the strategic threat, financing distress, technical failure, breach, or emergence of a superior alternative.

A trigger must be specified sufficiently to resist selective reinterpretation. If every adverse signal can be redescribed as temporary, confidential, part of learning, strategically necessary, or irrelevant to the next commitment, the trigger layer cannot constrain continuation.

31.2 Standing - St

Standing identifies who may initiate the correction process. Potential holders include contractual counterparties, boards, lenders, shareholders, designated employees, customers, public auditors, energy authorities, regulators, defense institutions, and affected communities where the burden is materially external.

Standing is not equivalent to a veto. It may confer the right to submit evidence, require a response, trigger review, demand escalation, participate in questioning, or initiate appeal.

The location of standing should reflect the location of evidence and burden. A cloud provider may observe utilization. A downstream enterprise may observe productivity and verification burden. A grid authority may observe infrastructure constraints. A model company may possess technical-necessity information. A public institution may define the strategic objective.

The actor that can observe the trigger may not be entitled to activate review. That mismatch is a central source of correction failure.

31.3 Evidence access - Ev

No single actor necessarily possesses the complete evidence profile. Technology-governance scholarship emphasizes that uncertainty, vulnerability, framing, and distribution can be visible to different participants and institutions (Jasanoff 2003). A model developer may know workload composition, model economics, utilization, customer revenue, and capability plans. A hardware supplier may know pricing, discounts, warrant economics, shipments, and bottlenecks. A cloud provider may know reservations, consumption, infrastructure cost, migration behavior, and concentration. An investor may know valuation, liquidity, and financing conditions. A public authority may know strategic purpose, energy constraints, public guarantees, and legal limits. Affected third parties may know local burdens and downstream human costs.

The problem is not merely that evidence is missing. Evidence can exist while remaining institutionally fragmented.

Public Disclosure≠Decision-Relevant Observability.

Commercially sensitive or classified evidence need not be published, but it must be accessible to a forum authorized and competent to judge the object.

31.4 Competent forum - Fo

A competent forum must integrate the dimensions required by the decision, potentially including technical necessity, commercial demand, accounting, financing, infrastructure cost, strategic purpose, energy, dependency, reversibility, and uncertainty.

A purely technical forum may be unable to judge strategic legitimacy or public burden. A purely financial committee may omit infrastructure effects, rights, long-term dependency, or strategic adequacy. A defense body may overvalue resilience while underweighting commercial or infrastructure cost. A contractual dispute forum may be competent to determine breach but structurally incapable of judging whether the next package increment remains externally justified.

Competence is matched to the permission object. It is not a general property of an institution.

31.5 Judgment - Jd

Judgment converts evidence into a reasoned determination. It should state the objective, baseline, available and missing evidence, material threshold, competing interpretations, burden distribution, strategic rationale, reversibility profile, and recommended permission state.

Judgment is not merely a score. A composite metric can conceal a non-compensatory legal limit, concentration, strategic dependency, severe local burden, or evidence held by an actor outside the primary beneficiary’s accounting boundary.

31.6 Operative gate determination - Ga

The gate specifies:

Ga(o)∈{SHIP,RESTRICT,HOLD,ROLLBACK}.

A recommendation to consider a gate is not the gate. An advisory report may be epistemically valuable while lacking operative authority.

The relevant question is: Which actor or coordinated structure is legally and institutionally empowered to determine the permission state of this object?

The answer may differ by component. A board may control capital. A contracting officer may control procurement. A lender may control a draw. A grid authority may control connection. A public authority may control a guarantee. A private operator may control deployment. Where several decisions are jointly necessary, the architecture must specify how distributed determinations combine into one operative result.

31.7 Implementation - Im

The path is incomplete until the determination changes operational reality. Implementation may require withholding capital, changing a notice to proceed, reducing procurement, preventing vesting, modifying exclusivity, transferring workloads, suspending construction, imposing a capacity limit, denying a guarantee, or executing termination rights.

Gate Determination≠Implemented Permission State.

An institution can issue HOLD while construction continues because the contractual notice, financing transfer, or technical deployment was not changed. An organization can possess a formal exit right while lacking a replacement supplier, migration capability, political permission, or financing capacity to exercise it.

Right to Correct≠Effective Correction Capacity.

31.8 Assurance layers

The core path must be surrounded by accountability, audit, appeal, remedy, expiration, changed-circumstances review, and reauthorization.

A HOLD without a deadline can become indefinite paralysis. A SHIP decision without expiration can become permanent authorization by inertia. A ROLLBACK without remedy can impose unjustified burden on actors who relied on the prior permission.

A gate architecture requires both a core operative path and an assurance and revision layer.

32. Correction Audit of the Anchor Mechanisms

The anchor cases contain meaningful local correction mechanisms. The relevant question is which object each mechanism governs.

Mechanism	Publicly visible local gates	Object governed	External-value package gate	System permission path
PCE	Purchase milestones, vesting, share-price, technical, and commercial conditions	Procurement-linked equity rights	Not publicly demonstrated	Indeterminate
CFC	Delivery schedules, financing, repayment, credits, service levels, termination	Bilateral capacity and finance performance	Not publicly demonstrated	Indeterminate
CCF	Capacity-delivery milestones before finance becomes drawable	Availability of financing after delivery	Capacity-based, not demonstrated as external-value-based	Indeterminate
ICL	Investment milestones, expiry, commercial obligations, distribution, product integration	Separate investment and commercial components	Not publicly complete	Indeterminate
MCN	Announced procurement, intended investment, technical integration	Multiparty strategic package	Not publicly demonstrated	Indeterminate
PCI	Letter-of-intent and prospective deployment conditions	Proposed future partnership	Not mature enough to test	Not yet applicable

32.1 PCE correction

In PCE, non-purchase can prevent vesting. That is a real contractual consequence. The gate governs whether the customer earns equity rights under the procurement conditions. It does not necessarily ask whether the compute is independently monetized, whether the supplier remains comparatively superior, or whether the next increment is proportionate to complete burden.

The contractual gate can operate in an expansion-positive direction:

More Procurement→More Potential Vesting.

This is not evidence of weak contract governance. It shows that contract correction and external-value correction answer different questions.

32.2 CFC correction

The Cerebras–OpenAI structure contains comparatively developed bilateral correction through schedules, service requirements, financing, repayment, credits, refunds, vesting, and termination. It can respond to delayed infrastructure, service failure, payment failure, and contractual non-performance.

Its public structure does not demonstrate a gate of the form:

Weak Independent-Value Evidence→HOLD Next Capacity Tranche.

Contractual performance can succeed while broader economic justification remains unresolved.

32.3 CCF correction

The Amazon–Anthropic facility contains a clear capacity gate:

Compute Delivery Milestone→Finance Availability.

This protects against releasing the complete facility before capacity is supplied. It does not demonstrate that the draw is conditioned on downstream monetization, utilization, productivity, strategic adequacy, or complete cost.

32.4 ICL correction

ICL contains partially separate gates concerning investment conditions, expiry, cloud and chip obligations, distribution, and product integration. The difficulty is fragmented decision boundaries. One committee may evaluate equity; another cloud revenue; another chip adoption; another strategic positioning.

A system-level review must assemble the complete exposure without collapsing its components into one scalar.

32.5 Multiparty networks

In MCN, the path may cross several legal entities. A cloud provider may control capacity, a hardware supplier systems and engineering, an investor capital, and a model company demand. No single bilateral agreement necessarily contains authority over the complete package. The path may still be reliable, but public announcements do not demonstrate the required handoffs.

32.6 Evidentiary conclusion

The anchor mechanisms contain genuine local governance over performance, delivery, vesting, financing, breach, expiry, and termination. The public record does not yet demonstrate a causally complete cross-package path through which evidence concerning demand provenance, external value, complete burden, dependency, or strategic adequacy changes the permission state of the next material commitment.

This does not mean that no private process exists. The proper public classification is usually Indeterminate or Not Publicly Demonstrated, not Absent.

33. The Capital–Compute Correction Deficit

A Capital–Compute Correction Deficit exists where a materially consequential capital–compute arrangement lacks a specified, timely, and implementable path through which credible evidence can produce a binding change in the permission state of the relevant commitment package.

For permission object o:

CCDo=1

where the object is material, a relevant trigger domain exists, one or more indispensable core functions or handoffs are missing or non-operative, and the failure prevents evidence from changing the implemented state.

The deficit is narrower than a generic governance gap. It does not require that contracts be absent, boards ineffective, reporting weak, regulators inactive, or no actor possess any stopping power. A system can have extensive governance and still possess a correction deficit concerning one bounded object.

33.1 Structural deficit

A structural deficit exists before a material trigger occurs. Examples include no actor having standing over the complete package, evidence being unable to cross an institutional boundary, no forum owning package-level judgment, gate authority being unable to bind relevant actors, or implementation being too slow to precede irreversibility.

Structural deficit is an architectural finding. It does not prove that the system has already produced an adverse outcome.

33.2 Manifest deficit

A manifest deficit exists where a credible material trigger occurs, relevant evidence or judgment becomes available, a feasible correction path is required, and institutional blockage prevents a timely implemented change.

The manifest condition requires an actual correction episode rather than incomplete architecture alone.

33.3 Successful correction

Successful correction is necessary evidence for validating the framework. A system demonstrates correction capacity where a trigger occurs, evidence reaches the appropriate forum, judgment is produced, an operative gate is issued, the state changes, and justified value is preserved where possible.

The valid outcome may be SHIP. A trigger does not imply that restriction or rollback is required.

33.4 Indeterminate

Indeterminate is necessary where the public record cannot establish the path. Private contracts, confidential board processes, classified strategic review, or undisclosed implementation arrangements may contain relevant mechanisms.

Non-Observability≠Absence.

34. Political Agency Deficit Boundary

Not every Capital–Compute Correction Deficit is political. A bilateral private procurement arrangement may remain primarily commercial where its burdens are internalized, effects limited, and one actor can exercise the complete correction path.

A material political-effect predicate is:

PoliticalEffecto*=1

only where the bounded object satisfies at least one of the following:

coercive or legally binding public authority is exercised;
a material public subsidy, guarantee, grid allocation, tax preference, or public asset is committed;
a rights or essential-service threshold is implicated;
a non-consenting population bears a material external burden;
a critical sovereign, defense, or public-infrastructure dependency is created;
decision authority and material burden are structurally separated across institutions.

Every positive code must identify:

jurisdiction;
affected population;
materiality threshold;
duration;
and the relevant authority or legal basis.

The Political Agency Deficit relation is:

PADo=CCDo∧PoliticalEffecto*∧InstitutionalInterdependenceo.

A large project is not political merely because it affects labor markets, energy use, or distribution in some diffuse sense. The effect must cross a declared materiality or rights threshold.

Responsibility-gap, many-hands, governance-triangle, and group-agency literatures explain important features of distributed authority and attribution, but none alone specifies the complete transition from trigger to implemented permission (Thompson 1980; Abbott and Snidal 2009; List and Pettit 2011; Santoni de Sio and Mecacci 2021).

The RATIUM.AI Political Agency Deficit framework identifies the core failure as separation without integration, traceability, and correction. It defines a reliable path from trigger through standing, evidence access, review, judgment, gate authority, operative determination, and implementation, while preserving timeliness, enforceability, appeal, and reauthorization (Dunavich 2026d).

34.1 Distributed authority is not pathological

PAD is not an argument for one institution to control capital, technical evidence, public purpose, infrastructure, and implementation. Distributed authority may be necessary because technical knowledge is private and specialized, strategic authority is public, infrastructure authority is sectoral or local, judicial remedy is separate, and affected parties possess evidence formal decision makers do not.

The failure is not distribution. It is distribution without a complete, legitimate, and timely path at the permission endpoint.

34.2 Orphaned capital–compute inference

An orphaned capital–compute inference is one whose component judgments are distributed across actors but whose transition from external objective and evidence to implemented permission lacks an identifiable owner or coordinated structure.

For example, a model company defines technical necessity; a cloud provider controls utilization data; an investor evaluates valuation; an energy authority controls grid connection; the state defines strategic purpose; and contracting parties control commercial continuation. Each may perform its function competently while the complete inference remains institutionally unowned.

34.3 Standing and burden

A package may create material public infrastructure costs, local energy constraints, strategic dependency, or rights effects for actors who possess no standing in the correction process. Political agency includes the capacity of relevant public and affected actors to introduce valid evidence into a process capable of changing the operative state.

Standing does not imply an unrestricted veto. Its form must be proportionate to the affected interest and compatible with due process, confidentiality, and lawful institutional mandates.

34.4 Candidate status

The anchor cases are not sufficient to classify each arrangement as a manifest PAD. The record does not establish a complete system-level permission object, a trigger crossing an independently defensible political-effect threshold, a failed authorized correction attempt, or persistence after that failure.

The article may identify candidate correction deficits and possible political effects. It may not infer manifest or persistent PAD from transactional complexity alone.

35. B3, CEP, and S4: Discriminant Boundaries

A correction deficit does not establish a game-theoretic equilibrium. It may result from organizational omission, legal fragmentation, immature process design, confidentiality, ordinary path dependence, technical uncertainty, or one-time coordination failure.

The manuscript distinguishes four downstream constructs.

Construct	Object	Necessary evidence	What it adds
B2	Domain outcome	Strong or externally grounded CED, material coupling, repetition, rising dependency, weak conditionality	Coupling-sustained overextension
B3	Domain persistence	B2, actor-pair Restraint Penalty, sufficiently shared expectations, correction deficit, failed genuine correction opportunity	Locked bubble-like regime
CEP	General game structure over a defined system and time	Independently established closure, locally incentive-compatible continuation, meaningful deviation costs, shared expectations, persistence through correction opportunities	Cross-domain strategic-equilibrium diagnosis
S4	Ontological–epistemological configuration	Separate mapping of players, objectives, evidence, burdens, deviations, and correction authority	Cognitive and governance configuration

35.1 Can B3 exist without CEP?

Yes.

B3 is a domain-specific regime classification. It can be supported where a capital–compute domain exhibits overextension, actor-pair restraint penalties, shared acceleration expectations, and a failed correction path.

CEP requires additional proof that:

a closure regime is independently established rather than inferred from B3;
continuation is locally incentive-compatible across the defined relevant actor set;
deviation costs and preferences are mapped sufficiently for a game diagnosis;
and the reproduction rule generalizes beyond the observed domain-specific symptoms.

A B3 finding therefore does not authorize CEP where closure or full actor-level incentive compatibility remains underidentified.

35.2 CEP entry sequence

The analysis must first establish an independently evidenced closure regime through a recurrent reproduction rule, durable correction asymmetry, repeated continuation, and failure of simpler rival explanations.

Only then may it test:

CEPS,T=(CR,LIC,DC,SE,PC),

where CR is an independently established closure regime; LIC, locally incentive-compatible continuation; DC, meaningful unilateral deviation cost; SE, sufficiently shared expectations; and PC, persistence through genuine correction opportunities.

Closure regime — CR

The system repeatedly reproduces the relevant commitment structure. A single complex transaction or a B3 symptom profile is insufficient.

Locally incentive-compatible continuation — LIC

Relevant actors possess reasons to continue even if the complete system outcome remains uncertain or burdensome. Part IV supplies candidate microfoundations and a vertical–horizontal bridge, but does not establish this condition sector-wide.

Deviation cost — DC

Conditioning or exiting alone imposes an identifiable cost. The anchor cases support RP1–RP2 vertical mechanisms but not a causally demonstrated RP3 horizontal event.

Shared expectations — SE

Actors sufficiently expect others to continue accelerating, unilateral restraint to be costly, or correction attempts not to change the system. Public announcements may influence these beliefs, but shared expectations have not been demonstrated.

Persistence through genuine correction opportunities — PC

A genuine correction opportunity requires a credible trigger, feasible alternative, relevant evidence, an actor or path capable of initiating correction, and sufficient time before irreversible commitment. Persistence without such an opportunity is not evidence that correction was blocked.

35.3 CEP does not imply conspiracy

A CEP-consistent structure does not require covert coordination, bad faith, shared ideology, fraud, or a central planner. Actors may behave transparently and locally rationally. The claim is structural: continuation is rewarded more reliably than unilateral justified correction, and relevant actors anticipate that moving alone will impose an unacceptable local cost.

The canonical CEP source requires closure and rival-explanation testing before strategic persistence and directs classification to be narrowed or rejected where incentives, deviation costs, shared expectations, or correction opportunities cannot be established (Dunavich 2026b).

35.4 Pareto boundary

Even where all CEP components are supported, Pareto inferiority requires a separately specified feasible alternative and actor-level preference evidence. Local incentives, high burden, or correction difficulty do not prove that every relevant actor would be at least as well off under mutual conditioning.

35.5 S4 non-identity

S4 is not a synonym for coupling, persistence, lock-in, a bubble, a correction deficit, B3, or CEP.

Contractual Coupling⇏Capitalization Loop,

Capitalization Loop⇏B3,

B3⇏CEP,

CEP-Consistent Persistence⇏S4.

A valid S4 mapping requires a separate demonstration of the ontology and epistemology that define the players, objectives, recognized burdens, admissible evidence, available deviations, and correction authority. The current article has not completed that mapping.

35.6 Current classification

The evidence supports contractual coupling, replicated PCE, implemented CFC, capacity-contingent finance, investment–commercial linkage, candidate vertical Restraint-Penalty mechanisms, and a testable correction framework.

It does not establish a complete recurring loop, B2, B3, shared acceleration expectations, RP3, persistence through a failed genuine correction opportunity, CEP, or S4.

Part VI — Bubble-Like Regimes and Governance Design

36. From Productive Expansion to Locked Bubble-Like Persistence

The term bubble is frequently applied to AI through an accumulation of suggestive observations: rapidly rising valuations, exceptional capital expenditure, multi-gigawatt infrastructure announcements, model-company losses, supplier investment in customers, delayed productivity gains, and growing energy demand.

These observations may be relevant. They do not form one proposition.

An asset can be overvalued while the underlying technology creates substantial value. Infrastructure can be built ahead of current demand without becoming waste. A model developer can remain unprofitable while producing user or strategic benefit. Customer finance can solve a supplier’s capital constraint. A temporary overbuild can be rational where learning, scarcity, or construction cycles justify commitment before complete demand is observable.

The article therefore does not define a bubble through price, investment, delayed profit, coupling, or weak current productivity alone. It defines a bubble-like capital–compute regime as:

A dynamic condition in which recurrent commitments to finance, construct, procure, distribute, and integrate AI compute exceed an independently defensible commitment envelope, while material coupling and increasing dependency weaken the probability that adverse evidence will change the permission state of subsequent commitments.

This is a commitment-regime definition, not a substitute for an asset-price bubble definition. It identifies a real-investment and governance structure that may amplify bubble risk, coexist with financial mispricing, or arise without a demonstrated asset-price bubble.

Four states are distinguished:

B0,B1,B2,B3.

These states are not a chronological law. A domain can move forward or backward and can occupy different states across firms, regions, workloads, and infrastructure classes.

36.1 B0 — Productive Expansion

A B0 Productive Expansion regime exists where capital and compute commitments are supported by strengthening external-value evidence, bounded dependency, and working correction.

B0 can include failed experiments, temporary overcapacity, operating losses, and large upfront investment. The defining feature is not immediate positive return. It is convergence and discrimination: successful uses expand while weak uses can be reduced or redesigned.

36.2 B1 — Bounded Transitional Overbuild

A B1 Bounded Transitional Overbuild regime exists where commitments temporarily precede realized external value but remain within a predeclared or externally defensible envelope incorporating uncertainty, learning value, strategic adequacy, and time.

The divergence is governed where the learning objective is declared, hypothesis testable, budget bounded, scope limited, required evidence specified, review date fixed, and next increment conditional.

Investment Ahead of Return≠Commitment Without a Convergence Rule.

A valid transitional regime identifies how it will move from setup through stabilization to routine value production. The RATIUM.AI configuration framework treats high burden during setup or stabilization as insufficient evidence of persistent failure and requires bounded learning with an objective, hypothesis, budget, time limit, evidence, stopping criteria, and reauthorization (Dunavich 2026a).

36.3 Divergence predicates

The regime classifier distinguishes:

CEDEA=1 — an ex ante threshold, budget, scope, review date, or stopping rule was violated;
CEDEX=1 — an independently defined legal, engineering, financial, infrastructural, rights-based, or strategic boundary was violated;
CEDR=1 — later evidence indicates excess commitment, but no applicable ex ante or external rule was fixed.

Define:

CEDStrong=CEDEA∨CEDEX.

Retrospective divergence is underidentified unless robust across multiple disclosed envelopes:

CEDR⇒Candidate Classification Only.

Additional conditions are:

CPL*=1 — material coupling supports scale, timing, supplier choice, or continuation;
REP=1 — the pattern recurs across more than one material decision cycle;
DEP*=1 — dependency or irreversibility rises materially;
COND*=1 — the next commitment is governed by operative external-value conditionality;
RP*=1 — a material actor-pair Restraint Penalty is supported;
SE*=1 — sufficiently shared acceleration or correction-failure expectations are supported;
CCD=1 — a Capital–Compute Correction Deficit is supported;
PC=1 — persistence through a genuine correction opportunity is supported.

36.4 B2 — Coupling-Sustained Overextension

A strong B2 classification requires:

B2=1⇔CEDStrong=1∧CPL*=1∧REP=1∧DEP*=1∧COND*=0.

A retrospective-only candidate is:

B2C=1⇔CEDR=1∧CPL*=1∧REP=1∧DEP*=1∧COND*=0,

subject to sensitivity analysis across multiple plausible envelopes.

B2 does not require fictitious demand, fraud, irrationality, or universal operating losses. It can produce real revenue, useful products, strategic capability, and technical progress. The classification concerns recurrent commitment outside an independently defensible envelope while material coupling and dependency increase and operative conditionality remains absent or ineffective.

The current study does not establish strong B2 or B2C for the sector.

36.5 B3 — Locked Bubble-Like Regime

A strong B3 classification is:

B3=1⇔B2=1∧RP*=1∧SE*=1∧CCD=1∧PC=1.

Where only B2C is supported, the strongest downstream label is:

B3C=Locked-Regime Candidate / Underidentified.

B3 is not established merely because exit is expensive. It requires evidence that identified actors continue because unilateral conditioning is comparatively costly and the correction graph cannot produce a credible alternative through a genuine opportunity.

36.6 Regime profile

BRt=⟨Comt,IVEt,CPLt,Uset,Valt,FinDept,Xt,𝐑𝐏t,𝔾t⟩.

The profile remains multidimensional. A scalar bubble score would conceal important distinctions. High commitment and high value may indicate B0. High commitment and weak current value under strong bounded learning may indicate B1. Retrospective divergence with coupling but weak threshold provenance supports only a B2 candidate. Strong divergence, dependency, restraint costs, and failed correction are required for B3.

36.7 False-positive boundary

Large capital expenditure, current losses, long payback periods, supplier investment in customers, customer warrants, large backlog, high utilization, high electricity consumption, delayed productivity, strategic public support, persistence, and high exit cost are each insufficient by themselves.

High Cost⇏Disproportion.

Long Transition⇏Non-Convergence.

Path Dependence⇏Strategic Lock.

Coupling⇏Artificial Demand.

37. Differential Diagnosis, Validation Controls, and Falsification

A bubble-like diagnosis is credible only if the strongest ordinary explanations are tested first. Chapter 28 defined mechanism-level rivals. This chapter asks which regime-level pattern remains after those explanations are applied.

37.1 Productive general-purpose-technology buildout

The strongest rival is that firms and states are constructing infrastructure for a general-purpose technology whose value will diffuse over a long period. Under this account, current investment precedes organizational adaptation, complementary products and workflows are developing, productivity is measured with delay, early scarcity justifies precommitment, and failed individual projects remain compatible with high portfolio value (Brynjolfsson, Rock, and Syverson 2021).

This explanation strengthens where external payment, margins, diffusion, durable post-support persistence, capability gains, and transition to routine value production improve.

37.2 Efficient project finance

Customer finance, long-term purchase commitments, milestone-linked capital, and warrants can solve ordinary financing and coordination problems. This explanation strengthens where transferred risks are priced coherently, construction succeeds, capacity is utilized, independent customers emerge, and demand remains after temporary support declines (Biais and Gollier 1997; Petersen and Rajan 1997; Klapper, Laeven, and Rajan 2012).

37.3 Genuine scarcity and diversification

Advance procurement may reflect scarce frontier compute. This explanation strengthens where replacement capacity is unavailable, released capacity can be reallocated, utilization is high, and supplier diversification improves resilience or bargaining power.

37.4 Efficient integration and platform economics

Investment–commercial packages may internalize complementary value. This explanation strengthens where the package produces lower total cost, faster deployment, superior reliability, stronger downstream monetization, and preserved correction capacity (Grossman and Hart 1986; Hart and Moore 1990; Williamson 1985; Rochet and Tirole 2003).

37.5 Strategic insurance

States and firms may rationally maintain excess or redundant capacity where expected strategic loss avoided exceeds cost. Strategic insurance is credible only where the threat, required capability, counterfactual, adequacy threshold, duration, and stopping authority are specified.

37.6 Ordinary path dependence

Long contracts, sunk assets, migration time, and organizational routines can produce persistence without strategic equilibrium (David 1985; Arthur 1989; Liebowitz and Margolis 1995). Ordinary path dependence explains why change is costly. Relative acceleration additionally requires an identified horizontal rival and evidence that vertical coupling changes the cost of conditioning relative to that rival.

37.7 Regime differential-diagnosis matrix

Observed regime pattern	Productive or ordinary interpretation	Bubble-like interpretation
Commitments precede revenue	Bounded infrastructure investment	Ex ante or external thresholds are crossed repeatedly
Customer finance enables construction	Efficient project finance	Demand and capacity become mutually supporting without external validation
Warrants support procurement	Adoption incentive	Equity rights materially transmit into a horizontal restraint penalty
High utilization	Real operational need	Utilization fails to support comparative external value
Strategic overcapacity	Rational insurance	Strategic rationale lacks adequacy or stopping conditions
High integration	Efficient coordination	Alternatives and portability decline without corresponding value
Repeated new financing	Growth finance	Prior package signals materially enable the next commitment cycle
Continued expansion after weak evidence	Long learning phase	Predeclared boundaries are crossed and correction remains ineffective
No visible rollback	Stable value or unobserved review	A genuine correction opportunity fails

37.8 Classification ladder

Level	Classification
L0	Large AI investment or infrastructure activity
L1	Contractual capital–compute coupling
L2	Replicated or networked coupling
L3	Capitalization-loop candidate
L4	Confirmed recurring capitalization feedback
L5a	Retrospective B2 candidate / underidentified
L5b	Strong coupling-sustained overextension — B2
L6	Locked bubble-like regime — B3
L7	CEP-consistent persistence
L8	Validated S4 mapping

The current study supports L1, material evidence for L2, and an L3 candidate. It does not establish L4–L8.

37.9 Negative-control validation

The development taxonomy must be tested against cases expected not to satisfy the stronger classifications.

Control	Expected discriminant result
Large uncoupled commitment	L0 without L1
Coupled package with successful correction	L1 or L2 without CCD, B2, or B3
High-dependency / high-value package	High X without overextension
Strategic capacity with declared adequacy	B1 or B0 rather than open-ended B2

A classifier that labels these controls as bubble-like fails discriminant validity.

The current manuscript freezes the definitions and specifies the controls. It does not report a completed validation set and therefore does not describe the taxonomy as validated.

37.10 Evidence that would strengthen the framework

The framework would strengthen if the record showed:

recurrent financing feedback;
an ex ante or external divergence threshold;
material vertical-to-horizontal transmission;
RP3 events;
declining portability;
failed genuine correction opportunities;
and different outcomes across positive cases and negative controls.

The inference must rest on their conjunction, not any one indicator.

37.11 Falsification and reduction

The bubble-like account should be rejected or narrowed where:

customers continue substantial procurement after coupling support expires;
external monetization grows sufficiently relative to complete burden;
productivity and capability converge;
adjusted unit economics improve;
capacity and workloads remain transferable;
adverse evidence produces timely reduction or supplier change;
strategic actors define and respect an adequacy threshold;
expansion becomes supported increasingly by operating cash and outside demand;
vertical coupling does not alter actor-pair restraint penalties;
or ordinary theories explain the pattern more parsimoniously.

The framework must lose explanatory territory where ordinary mechanisms perform equally well.

38. Governance of the Marginal Commitment

The appropriate governance object is not AI as a whole. It is the next material commitment increment.

ΔΓt+1=⟨ΔK,ΔQ,ΔF,ΔW,ΔΛ,ΔX⟩.

The governing question is:

Does the current evidence justify this specific next material increment under the proposed conditions, and which institution is lawfully entitled to authorize it?

Treating the increment rather than the entire technological field as the decision object is consistent with real-options analysis of irreversible investment and staged commitment (McDonald and Siegel 1986; Dixit and Pindyck 1994).

The marginal approach permits different decisions for different layers of the same package. Current services may remain SHIP, new exclusivity RESTRICT, the next construction tranche HOLD, and a failed optional expansion ROLLBACK.

38.1 Materiality and aggregation

A commitment is material where it significantly changes financial exposure, physical scale, duration, concentration, exclusivity, financing dependence, strategic dependence, infrastructure burden, rights exposure, or reversibility.

Several formally small amendments must be aggregated where they share an objective, asset, counterparty, financing source, trigger, or correction path:

Aggregate(ΔΓ1,…,ΔΓn)≥M*.

The study must declare:

the lookback period;
related-party treatment;
aggregation rule;
and anti-slicing threshold.

38.2 Decision package

DPΔΓ=⟨Obj,Base,Ev,Bur,Unc,SP,X,𝐑𝐏,Auth,T⟩.

The components are external objective, credible baseline, external-value evidence, complete burden, uncertainty and learning value, strategic profile, dependency and reversibility, actor-pair Restraint-Penalty profile, authority and implementation map, and duration and review.

The package must state source provenance, assumptions, disagreements, minority interpretations, missing evidence, implementation owner, and reauthorization conditions.

38.3 Epistemic assessment

Evidence does not mechanically produce a gate. The epistemic assessment is:

Assesso=𝒜(Evidenceo,Burdeno,Uncertaintyo,Alternativeso).

It identifies what the evidence supports, which uncertainties remain, and which alternatives are feasible.

38.4 Legitimate authorization

The operative gate is a separate institutional act:

Gao=ℒ(Assesso,Mandateo,Rightso,Procedureo).

The authorization function incorporates:

legal mandate;
rights;
public and fiduciary duties;
legitimate risk tolerance;
distributional judgment;
due process;
and procedural competence.

LoopGuard-AI or another technical architecture may structure evidence, trace assumptions, and test consistency. It cannot supply political, legal, or corporate legitimacy by itself.

38.5 SHIP

SHIP authorizes the proposed increment under defined scope and conditions. It is appropriate where the objective is clear, baseline credible, benefit sufficiently supported, burden proportionate, strategic value specified, uncertainty bounded, and reassessment or exit feasible.

SHIP should specify authorized quantity, duration, assumptions, monitoring, triggers, reassessment date, and expiration. It is conditional authorization, not permanent validation (Dunavich 2026a).

38.6 RESTRICT

RESTRICT authorizes the valuable portion while narrowing the unsupported or excessive component. Restrictions may concern quantity, duration, exclusivity, geography, supplier concentration, financing, warrant vesting, public guarantees, portability, or construction staging.

Its logic is:

Preserve Valid Benefit−Remove Unjustified Burden.

38.7 HOLD

HOLD suspends the next material increment pending specified evidence, authority, or correction. A valid HOLD identifies what is paused, what may continue, which evidence is required, who must produce it, the reviewing forum, deadline, and consequence of continued failure.

An indefinite HOLD without a decision rule is not stable governance (Dunavich 2026a).

38.8 ROLLBACK

ROLLBACK returns the package to a prior, simpler, more transferable, or better-validated state. It can include cancellation of an unstarted tranche, capacity reduction, termination of exclusivity, supplier diversification, workload transfer, refinancing, non-vesting, repurposing infrastructure, or withdrawal of public support.

ROLLBACK does not mean abandonment of AI. It means reversal of the invalidated or disproportionate component.

38.9 Assessment-to-gate tendencies

Epistemic assessment	Possible authorization tendency
Strong external value, proportionate burden, credible baseline, preserved exit	SHIP
Positive value but unsupported scale, concentration, exclusivity, or dependency	RESTRICT
Major increment with missing provenance or value evidence	HOLD
Valid strategic objective but no adequacy threshold	RESTRICT or HOLD
High exit cost with weak comparative value	RESTRICT with transition plan
Negative comparative value and expired learning rationale	ROLLBACK
Material legal, rights, authority, or safety failure	HOLD or ROLLBACK
Stable post-support persistence	SHIP or reduced restriction
Strategic adequacy reached and marginal value is weak	RESTRICT or deny expansion

The table is not an algorithm. The same assessment can yield different lawful outcomes under different mandates and rights constraints. The reasoned authorization must state why the selected gate is legitimate for the bounded object.

39. Mechanism-Specific Governance, Legal Boundaries, and Governance Red-Teaming

The four gates must be translated into the legal and operational structure of each mechanism. A generic oversight committee that cannot alter the relevant contract, financing draw, construction notice, procurement order, or implementation state does not govern the package.

39.1 Purchase-Contingent Equity

A PCE decision package should separate product demand, customer consideration, equity value, and external utilization. It should include procurement milestones, warrant fair value, accounting treatment, effective economic purchase cost, utilization, post-support persistence, expiry and non-vesting rules, and limits on future vesting beyond the evidence horizon.

SHIP may be appropriate where independent-value evidence is converging; RESTRICT where procurement remains useful but the next vesting tranche is disproportionate; HOLD where provenance cannot be evaluated; and ROLLBACK through non-vesting or procurement reduction where conditions fail.

39.2 Customer-Financed Compute

A CFC package should identify construction milestones, loan draws, security, interest and waiver conditions, non-cash repayment, service credits, residual assets, alternative customers, portability, and transition obligations.

The central resilience test is whether the supplier, infrastructure, and workload can survive a material reduction in the bilateral relationship.

Construction and capacity decisions should be staged. Completion of a construction milestone should not automatically authorize the complete next capacity tranche where utilization, outside-package validation, or concentration has materially changed.

39.3 Capacity-Contingent Finance

In CCF:

Capacity Delivered→Capital Available.

A package-level design may add:

Capacity Delivered∧Declared Value or Learning Condition→Capital Available.

The condition should not demand mature profitability where finance supports a bounded learning phase, but the phase must remain observable and subject to a real next decision.

39.4 Investment–Commercial Linkage

ICL requires consolidated exposure review:

Exposurei=⟨Equity,Cloud,Chips,Distribution,Credit,Valuation,Dependency⟩.

The review must preserve component distinctions while preventing fragmented authorization. Weak margin in one channel does not invalidate a package where other channels generate legitimate complementary value; nor may one channel’s revenue conceal burdens or incentives elsewhere.

39.5 Multiparty networks

MCN governance must assign correction ownership across entities. Configurations can include a lead actor, federated gates, independent review with binding escalation, or a public–private protocol.

The architecture must specify who detects the trigger, compels evidence, judges the complete package, issues necessary component gates, resolves conflicts, and implements the state.

39.6 Strategic adequacy

Every strategic package should contain:

SP=⟨Threat,Capability,Counterfactual,Adequacy,Duration,Authority⟩.

Once the specified strategic requirement is reached:

Marginal Strategic Burden of Proof↑.

Further expansion requires a renewed strategic case rather than automatic extension.

39.7 Conditionality standards without competitor coordination

Governance may reduce first-mover restraint penalties through comparable evidence categories, accounting treatment, auditability, portability, or public-externality rules.

It must not coordinate:

prices;
output;
customers;
suppliers;
capacity quantities;
investment levels;
market allocation;
or competitively sensitive future plans

among horizontal rivals.

Competitors sometimes collaborate for legitimate innovation or efficiency purposes, but antitrust risk increases where collaboration reduces independent decision making or enables joint market power. As of the observation cutoff, the former U.S. competitor-collaboration guidelines had been withdrawn and the DOJ and FTC were considering updated guidance, reinforcing the need for case-specific legal review rather than reliance on a general safe harbour (Federal Trade Commission 2026; U.S. Department of Justice and Federal Trade Commission 2026).

Common standards should therefore be limited to matters such as:

evidence definitions;
public accounting treatment;
interoperability;
audit formats;
public infrastructure burdens;
and lawful safety or rights requirements.

Competitor-sensitive information should be handled, where lawful and necessary, by independent trustees, auditors, or public authorities. No incumbent-controlled standard should raise entry barriers beyond what the legitimate objective requires.

39.8 Time, expiration, and anti-slicing

A correction path must complete before the increment becomes effectively irreversible:

τc<τi.

Temporary permissions should expire unless reauthorized:

Permissiontemporary(t+τ)=0.

Transaction slicing is prohibited analytically. Amendments, affiliates, financing instruments, and connected commitments within the declared lookback period must be aggregated where they share an objective, asset, counterparty, financing source, or correction path.

39.9 Audit and replay

A gate decision should be reconstructable. A later reviewer should be able to identify the trigger, standing holder, evidence available and missing, threshold provenance, judgment, legal authority, implemented state, implementation date, and reauthorization condition.

Audit permits threshold revision, detection of inconsistent decisions, preservation of minority evidence, and replay under new information.

39.10 Confidentiality, due process, and institutional law

Confidentiality does not require public disclosure of pricing, utilization, warrant valuation, financing, or classified strategic information. It requires observability to a competent and authorized forum.

Public Transparency≠Complete Decision Observability.

The governance architecture must be implemented through applicable legal and institutional constraints, including:

due process and reasoned decision requirements;
appeal and remedy;
fiduciary duties;
securities and disclosure law;
procurement rules;
confidentiality and trade-secret protection;
national-security classification;
judicial review where applicable;
and allocation of losses created by a changed permission state.

The framework supplies an architecture for asking these questions. It does not override the institution’s lawful mandate.

39.11 Governance anti-recursion

The correction layer can itself become a self-expanding commitment system. It can accumulate metrics, committees, reports, review stages, and approval dependencies without improving permission decisions.

It must satisfy:

Metric minimality: every metric serves a defined decision.
Rule traceability: every rule identifies purpose, trigger, authority, consequence, expiration, and review owner.
Governance budget: time, cost, and expert attention are bounded.
Simplification authority: an identified actor can remove unnecessary controls.
No automatic committee proliferation: a missing path does not automatically generate another advisory body.
Self-application: the governance regime measures its own burden and value.

39.12 Governance red-team matrix

Attack vector	Vulnerable node or edge	Detection indicator	Mitigation	Residual risk / rule rollback condition
Threshold gaming	Trigger and judgment	Repeated values immediately below thresholds	Cumulative and distributional tests	Remove threshold if it predictably distorts behavior
Transaction slicing	Evidence and materiality	Related increments avoid review individually	Lookback and aggregation rule	Suspend rule if aggregation becomes unbounded
Strategic relabelling	Objective and judgment	Commercial projects repeatedly reclassified as security	Independent adequacy and threat review	Narrow strategic exception
Selective disclosure	Evidence access	Material asymmetry between beneficiary and forum	Audit rights and adverse-inference rule	Reassess authorization if evidence remains unavailable
Forum capture	Forum and judgment	Stable one-sided expert or stakeholder composition	Rotation, conflict disclosure, plural review	Reconstitute forum
Expert monopolization	Evidence and forum	One provider controls indispensable expertise	Independent replication and capacity building	HOLD where claims cannot be independently tested
Delay as competitive weapon	Standing and procedure	Review requests cluster around rival milestones	Deadlines, standing tests, cost allocation	Dismiss abusive proceedings
Litigation freeze	Gate and implementation	Interim process becomes de facto permanent HOLD	Proportionate interim relief and expedited review	Expire interim gate
Incumbent standard capture	Evidence and gate	Compliance cost falls disproportionately on entrants	Technology-neutral standards and entry-impact test	Withdraw standard
Classification drift	All nodes	Definitions expand without formal revision	Versioned codebook and audit	Revert to last validated version

Governance rules are themselves subject to RESTRICT, HOLD, or ROLLBACK where they create more burden, capture, delay, or anticompetitive effect than the problem they were designed to correct.

39.13 LoopGuard-AI boundary

LoopGuard-AI can serve as a candidate implementation architecture for structuring the decision package, recording provenance, mapping triggers and thresholds, assigning authority, tracking implementation, preserving audit, and managing expiration.

It may support the epistemic assessment:

Assesso=𝒜(⋅).

It cannot independently supply:

Gao=ℒ(⋅),

because legitimate authorization depends on mandate, rights, and procedure.

This does not establish that LoopGuard-AI is technically complete, institutionally adopted, empirically validated, or optimal. The Stable Governance Layer distinguishes derivational completeness, substantive adequacy, operational completion, and reliable correction under repeated pressure (Dunavich 2026c).

Part VI establishes revised B0–B3 classifiers and a candidate governance architecture. It does not classify the sector as B2 or B3 or validate the intervention.

Part VII — Integrated Framework and Research Program

40. Integrated Causal Architecture

Within the framework developed here, the AI Capitalization Loop is not a claim that capital moves in a legally circular path, that every participant finances its own revenue, or that the contemporary AI sector has already entered a confirmed bubble. It is the candidate recurrent process through which prior commitment may help reproduce subsequent commitment.

The framework asks whether a network of capital providers, model laboratories, semiconductor suppliers, cloud platforms, infrastructure operators, customers, and public authorities can generate a recurrent process in which prior capital–compute commitments become material inputs into demand signals, valuations, financing capacity, strategic expectations, and institutional permissions supporting subsequent commitments.

The state is:

Zt=⟨Kt,Qt,Dt,Rt,Vt,Ft,Σt,Λt,Xt,𝒢t⟩.

The system evolves through commitment packages, actor strategies, information, and correction architecture:

Zt+1=Φ(Zt,Γt,at,ℐt,𝒢t).

The integrated framework contains six causally ordered layers.

40.1 Layer One — contractual coupling

The first layer concerns observable legal and economic relations. The anchor cases show that packages can connect procurement and equity rights; customer finance and supplier infrastructure; capacity delivery and financing availability; equity investment and cloud procurement; proprietary-chip consumption and distribution; and multiparty investment and infrastructure commitments.

Each package is coded through a multi-label mechanism vector:

𝐌r=⟨PCEr,CFCr,CCFr,ICLr,MCNr,PCIr⟩.

These relations establish that some variables are connected. They do not establish artificial demand, inefficiency, horizontal rivalry, or a loop.

40.2 Layer Two — demand and independent value

Demand is represented through provenance and justification:

𝒟t=⟨Provt,Justt⟩.

The independent-value evidence profile is:

IVEr=⟨TMr,EVr,PSr⟩.

Transaction maturity, external validation, and post-support persistence are not collapsed into one score.

The framework rejects both:

CouplingSupportedProvenance⇒0-value demand,

and:

BindingDemand⇒ComparativeExternalValue.

40.3 Layer Three — external value, burden, and divergence

External value and complete burden remain vector-valued:

Vd,a|b,Text=⟨Ben,Ret,Prod,Qual,Str,Lrn,Util⟩,

Cd,a|b,Tfull=⟨Cap,Op,En,Grid,Lab,Meta,Risk,Dep,Gov,Opp⟩.

Distributed impact is represented through:

𝒲t=⟨Utinside,Btoutside+,Btoutside−,Distt,Rightst,Authorityt⟩.

No aggregate welfare scalar is inferred without a declared valuation and authority rule.

Commitment–Evidence Divergence has three forms:

CEDEA,CEDEX,CEDR.

Only ex ante or independently external divergence supports a strong B2 classification. Retrospective divergence supports an underidentified candidate unless robust across several disclosed envelopes.

40.4 Layer Four — vertical coupling and horizontal rivalry

The game-theoretic layer has two distinct levels.

Vertical package level

𝒱ij:Γij→⟨Δui,Δuj,ΔXi,ΔXj⟩.

The anchor cases directly support several vertical effects.

Horizontal rivalry level

ℋik:{ACC,COND}i×{ACC,COND}k.

The bridge is:

Γij→ΔRPi∣k→Strategyi.

A horizontal claim requires an identified rival k, competitive dimension, transmission channel, timing, and counterfactual. The current cases establish candidate channels, not the payoff ordering:

t>g>a>ℓ.

40.5 Layer Five — dependency and correction

Dependency evolves through a conditional transition:

Xt+1=𝒳(Xt,Qt,Ft,Λt,Atspec,Portt,Altt,Stdt,SecMktt).

The signs are not assumed to be uniform. Scale and integration can increase or reduce dependency depending on specificity, standards, alternatives, transferability, and redeployment.

Correction is represented as a directed graph:

𝔾o=(No,Eo),

with a timely and authorized path:

∃p:τ⤳Im.

The epistemic assessment and legitimate authorization are separate:

Assesso=𝒜(Evidence,Burden,Uncertainty,Alternatives),

Gao=ℒ(Assesso,Mandateo,Rightso,Procedureo).

40.6 Layer Six — regime outcome

The system can occupy B0 Productive Expansion, B1 Bounded Transitional Overbuild, B2 Coupling-Sustained Overextension, or B3 Locked Bubble-Like Regime.

The complete candidate sequence is:

Contractual Coupling→Demand and Value Interpretation→Possible Financing or Valuation Feedback→Vertical-to-Horizontal Payoff Transmission→Dependency and Correction Stress→Possible Bubble-Like Persistence.

Each arrow is an independent empirical burden.

40.7 Canonical definition

An AI Capitalization Loop is:

A repeated capital–compute network process in which capital provision, compute procurement, infrastructure construction, distribution, supplier revenue, valuation, and financing capacity reinforce one another across partially overlapping actors, such that prior commitment becomes a material input into the financing, evidentiary justification, or authorization of subsequent commitment.

The minimum recurrent structure is:

Kt→Qt→DtorRt→VtorFt→Kt+1→Qt+1.

The current classification remains:

Capitalization-Loop Candidate.

40.8 Integrated claim boundary

Directly supported claims include material vertical coupling, PCE replication, implemented customer-financed compute, capacity-linked financing, multichannel investment–commercial relationships, and local contractual gates.

Mechanistically supported candidates include external-value identification problems, vertical effects on private payoff, possible horizontal transmission, conditional dependency growth, and correction-graph incompleteness.

Unestablished claims include:

a recurrent complete loop;
quantitative provenance shares;
EV1, EV2, PS1, or PS2 for the anchor packages;
vertical-to-horizontal causal transmission;
RP3;
B2 or B3;
CEP;
S4;
and governance effectiveness.

41. Formal Propositions and Empirical Research Program

The integrated framework is reduced to eight canonical propositions. Each contains a claim, observable implication, strongest rival explanation, and falsification or narrowing condition. A later proposition cannot be inferred solely from support for an earlier one.

Proposition 1 — Contractual Coupling

Where a capital–compute package materially connects two or more of capital, compute, finance, equity rights, distribution, revenue, or valuation, the connected variables cannot be treated as fully independent transaction signals.

Observable implication: a change in one component alters rights, financing, delivery, procurement, integration, or returns elsewhere in the package.

Strongest rival: the linkage is administratively present but economically immaterial.

Falsification or narrowing: the connected component is immaterial or comparable uncoupled arrangements produce the same behavior.

Proposition 2 — Demand-Provenance Constraint

The evidentiary strength of observed demand as evidence of independent provenance declines where the same quantity, timing, supplier choice, duration, or renewal is materially supported by equity, financing, distribution, or investment inside the package.

Observable implication: the most informative evidence shifts from headline contract value toward the multidimensional profile:

IVEr=⟨TMr,EVr,PSr⟩.

Strongest rival: coupling finances independently valuable demand without materially altering its steady-state scale or allocation.

Falsification or narrowing: procurement and outside-package value remain stable after support changes, or a credible counterfactual shows that the coupling mechanism did not materially affect demand.

Proposition 3 — Financing Feedback

Where prior procurement, infrastructure delivery, backlog, revenue, or valuation materially increases subsequent financing capacity, the system contains a financing-feedback link:

Qt,Dt,Rt,orVt→Ft+1.

A recurrent loop additionally requires:

Ft+1→Kt+1→Qt+1.

Observable implication: subsequent financing identifies prior contracts, capacity, backlog, revenue, or valuation as enabling factors.

Strongest rival: later financing reflects independent technological information, market conditions, collateral, or operating performance unrelated to the earlier package.

Falsification or narrowing: financing is explained adequately without the prior package signal; the loop claim fails if no recurrent next commitment follows.

Proposition 4 — Vertical-to-Horizontal Restraint Transmission

A vertical package affects the relative-acceleration game only where it changes the expected payoff of conditioning relative to an identified horizontal rival:

Γij→ΔRPi∣k→Strategyi.

Observable implication: capacity access, financing, customer migration, ecosystem adoption, supplier learning, valuation, or sovereign capability changes actor i’s relative position against rival k.

Strongest rival: the package changes bilateral returns but has no material effect on horizontal competition.

Falsification or narrowing: no rival pair or transmission channel can be identified; actors condition without relative loss; or the alleged loss is caused by the adverse information that motivated restraint rather than restraint itself.

RP3 requires an observed event and causal identification.

Proposition 5 — Conditional Dependency Transition

Dependency evolves through:

Xt+1=𝒳(Xt,Qt,Ft,Λt,Atspec,Portt,Altt,Stdt,SecMktt).

Observable implication: exit cost rises where asset specificity, linked finance, integration, and concentration increase while portability, standards, substitutes, and redeployment decline.

Strongest rival: scale or integration improves portability, finances diversification, or creates liquid alternative uses.

Falsification or narrowing: workloads remain transferable, capacity redeployable, financing separable, standards effective, and supplier change occurs without disproportionate loss.

Proposition 6 — Correction-Graph Completeness

Adverse evidence can change the operative permission state where the correction graph contains at least one timely, competent, lawful, and implementable trigger-to-consequence path:

∃p:τ⤳Im.

Observable implication: complete graphs exhibit shorter signal-to-consequence latency, clearer ownership, lawful gate authority, and better preservation of justified value than review-only arrangements.

Strongest rival: informal management, market discipline, or ordinary contracting performs equally well without a formal graph.

Falsification or narrowing: incomplete structures correct equally well, or the formal architecture adds burden, capture, or delay without changing state.

Proposition 7 — Bubble-Like Transition

A strong B2 classification requires:

B2=1⇔CEDStrong=1∧CPL*=1∧REP=1∧DEP*=1∧COND*=0.

A retrospective-only divergence supports:

B2C=Candidate / Underidentified.

A locked regime additionally requires:

B3=1⇔B2=1∧RP*=1∧SE*=1∧CCD=1∧PC=1.

Observable implication: recurrent commitments cross an ex ante or external boundary while coupling and dependency grow, identified actors face restraint penalties, and a genuine correction opportunity fails.

Strongest rival: productive GPT investment, efficient project finance, scarcity, integration, bounded learning, strategic insurance, or ordinary path dependence.

Falsification or narrowing: thresholds are post hoc only, value convergence strengthens, support expires without demand collapse, portability remains high, vertical coupling does not transmit into horizontal restraint, or correction works.

Proposition 8 — CEP Entry and Downstream Classification Boundary

A Capitalization Loop, B2, B3, and CEP are analytically distinct.

CEP entry is admissible only where:

CEPS,T=(CR,LIC,DC,SE,PC).

B3 can be established without CEP where the domain-specific locked regime is supported but independently established closure or full actor-level incentive compatibility remains underidentified.

B3⇏CEP,

and:

CEP-Consistent Persistence⇏S4.

Falsification or narrowing: closure is absent; ordinary path dependence suffices; deviation costs or shared expectations are unsupported; or no genuine correction opportunity occurred (Dunavich 2026b).

41.1 Research Stream A — Development and validation census

Objective: estimate prevalence and test discriminant validity after taxonomy freeze.

Development set: the seven anchor packages.

Validation set: newly coded cases selected without requiring positive coupling and including:

a large uncoupled commitment;
a coupled package with successful correction;
a high-dependency / high-value package;
strategic capacity with a declared adequacy threshold.

Unit: a materially bounded package reconstructed under a fixed lookback and aggregation rule.

Output: the Evidence Vector, multi-label mechanism vector, component maturity, and source provenance.

The taxonomy cannot be called validated until independent coders apply the frozen rules to the validation set.

41.2 Research Stream B — Demand provenance and independent value

Objective: identify provenance and code:

IVEr=⟨TMr,EVr,PSr⟩.

Evidence: adjusted supplier revenue, outside-package payment or outcomes, utilization, post-support persistence, margins, concentration, and portability.

Designs: incentive-expiry analysis, matched coupled and uncoupled packages, contractual discontinuities, supplier substitution, and deployment cohorts.

The dimensions remain separate until construct validity supports aggregation.

41.3 Research Stream C — Financing and valuation feedback

Objective: test:

Prior Commitment→Reported Signal→Financing or Valuation Decision→New Commitment.

Data: financing documents, board records where available, lender materials, valuation reports, investor communications, and contemporaneous decision evidence.

Chronology alone is insufficient. The financing decision may reflect independent technology or demand information.

41.4 Research Stream D — Vertical-to-horizontal transmission and RP3

Objective: identify the rival pair and estimate whether a vertical package changes the cost of conditioning.

Candidate events: delayed capacity, declined investment, supplier switch, reduced exclusivity, procurement reduction, or cancellation.

Outcomes: capacity access, pricing, financing, customer retention, valuation, technical delay, strategic position, migration cost, and residual-asset loss.

The effect of restraint must be separated from the adverse condition that caused restraint.

41.5 Research Stream E — Dependency and correction graphs

Objective: estimate conditional dependency transitions and determine whether evidence reaches implemented permission.

Dependency variables: specificity, standards, alternatives, portability, financing separability, and secondary-market depth.

Correction object:

𝔾o=(No,Eo).

Outcomes: complete successful correction, structural deficit, manifest deficit, publicly indeterminate, or no relevant trigger.

The study must distinguish declared authority, legal authority, operational control, monitoring, enforcement, implementation, appeal, and remedy.

41.6 Research Stream F — Divergence and regime classification

Objective: distinguish B0, B1, B2C, B2, and B3.

Every CED coding must report:

ex ante, external, or retrospective status;
threshold provenance;
timestamp;
authority;
uncertainty allowance;
and sensitivity range.

No strong B2 classification may rest solely on a threshold constructed after the outcome.

41.7 Research Stream G — Governance intervention

Objective: test whether marginal permission governance improves correction while preserving justified value and lawful competition.

The intervention separates:

Assesso=𝒜(⋅)

from:

Gao=ℒ(⋅).

Comparators include ordinary corporate governance, contractual milestones, advisory review, and a complete correction graph.

Outcomes: signal-to-consequence latency, preserved value, dependency, unnecessary delay, legal error, anticompetitive effect, and governance burden.

A strong falsifier is that the proposed architecture adds cost, delay, capture, or coordination risk without improving decisions.

41.8 Research Stream H — Comparative, international, CEP, and S4 tests

Research must extend to non-US semiconductor and cloud ecosystems, sovereign AI projects, public infrastructure finance, joint ventures, military procurement, open-source ecosystems, and cases containing strong independent review.

CEP testing begins only after recurrence, closure, actor-level incentives, deviation cost, shared expectations, and correction opportunities are supported. S4 testing begins only after CEP entry and a separate ontological–epistemological mapping.

“Insufficient evidence” remains a valid terminal result.

41.9 Validation requirements

Before prevalence or prediction claims are made, the program requires:

content validity;
discriminant validity;
inter-rater reliability;
temporal stability;
negative controls;
out-of-sample cases;
and sensitivity analysis.

The following constructs must remain distinct:

component maturity;
external validation;
post-support persistence;
coupling;
financing feedback;
vertical transmission;
Restraint Penalty;
dependency;
correction deficit;
B2;
B3;
CEP;
and S4.

41.10 Current Study Limitations

The present study is subject to eleven principal limitations.

Purposive development sample: the seven cases identify mechanisms rather than prevalence.
No completed validation set: negative-control classes are specified but not yet independently coded.
Institutional concentration: the anchor set is concentrated in large, predominantly US-linked technology relationships.
Public-disclosure boundary: the analysis lacks complete access to board deliberations, utilization, package-level economics, alternative bids, strategic assessments, and private correction procedures.
Dynamic maturity: future tranches, options, letters of intent, and multiyear performance can change after the cutoff.
No causal estimation: the study does not estimate procurement caused by warrants, financing caused by valuation, horizontal behavior caused by vertical packages, or losses caused by restraint.
No prevalence estimate: the article does not establish how common the mechanisms are.
Unvalidated measures: the Evidence Vector, mechanism vector, provenance classifier, IVE profile, RP grades, correction graph, CED variants, B0–B3, CEP entry profile, and S4 mapping remain candidate instruments.
Single-coder development: no inter-rater reliability test has been conducted.
Working-paper evidence: recent 2026 productivity evidence remains contemporaneous working-paper evidence rather than settled consensus.
Unvalidated governance intervention: the four-gate architecture has not been tested comparatively for effectiveness, legality, competition effects, or institutional burden.

These limitations prohibit sector-wide or predictive promotion. They do not negate verified transaction structures or the article’s function as a falsifiable theory-building framework.

42. Maturity Statement and Conclusion

42.1 Maturity matrix

Dimension	Current status
Research object	Defined
Conceptual architecture	Integrated
Contractual microfoundations	Verified in anchor cases
Mechanism taxonomy	Frozen development taxonomy; multi-label; not yet validated out of sample
PCE replication	Verified within development set
Sectoral prevalence	Unknown
Demand provenance	Not causally estimated
Transaction maturity	Component-specific TM coding completed
External validation	No package-level EV1 or EV2 established in anchor set
Post-support persistence	No PS1 or PS2 established
Financing feedback	Partially supported; full recurrence not established
Vertical package effects	Verified in several mechanisms
Horizontal transmission	Candidate; not causally established
Restraint Penalty	RP1–RP2 candidate mechanisms; RP3 not established
Dependency transition	Theoretically specified; not estimated
Correction architecture	Directed graph defined and testable
System-level correction in anchor cases	Predominantly indeterminate
Strong B2	Not established
B3	Not established
CEP	Not established
S4	Mapping deferred
Governance design	Advanced candidate; empirically and legally unvalidated
LoopGuard-AI	Candidate epistemic and traceability architecture; not an independent source of legitimacy

The proper maturity label is:

Integrated Theory-Building Framework with Verified Contractual Microfoundations.

It is not a validated sector-wide game-theoretic theory.

42.2 Theoretical contribution

The primary contribution is a bounded research object: capital–compute packages in which procurement, finance, equity, infrastructure, distribution, revenue, valuation, and strategic positioning can become analytically interdependent. The cases verify several such relations. Whether they form a recurrent process that reproduces commitment through partially endogenous signals and horizontal acceleration incentives remains an open empirical question.

42.3 Empirical and measurement contribution

The article contributes the following instruments:

an Evidence Vector;
a multi-label mechanism vector;
a two-dimensional demand framework;
the IVE=⟨TM,EV,PS⟩ profile;
actor-pair RP grades;
a conditional dependency transition;
a directed correction graph;
ex ante, external, and retrospective CED distinctions;
B0–B3 regime classifications;
and an L0–L8 maturity ladder.

Together, these instruments convert broad claims of circular financing or an AI bubble into separable empirical questions. They remain development instruments pending negative-control and out-of-sample validation.

42.4 Game-theoretic contribution

The relative-acceleration framework separates vertical package coupling from horizontal rivalry. Its candidate bridge is:

Γij→ΔRPi∣k→Strategyi.

The cases verify several vertical effects capable of creating transmission channels, but not the rival pair, causal effect, payoff ordering, or equilibrium. The framework therefore specifies what must be shown before a package can serve as a microfoundation for a relative-acceleration game.

42.5 Institutional contribution

The article distinguishes contract correction, package correction, and system permission correction. Correction requires at least one timely, competent, lawful, and implementable path through the directed graph, while epistemic assessment remains distinct from legitimate authorization:

Assesso≠Gao.

The Capital–Compute Correction Deficit names failure of that operative path. The Political Agency Deficit boundary applies only where a material political effect is independently supported.

42.6 Governance contribution

The governance response is not a universal compute ceiling. It is a differentiated architecture attached to the next material commitment:

ΔΓt+1=⟨ΔK,ΔQ,ΔF,ΔW,ΔΛ,ΔX⟩.

Its outputs—SHIP, RESTRICT, HOLD, and ROLLBACK—must be issued by a legitimate authority after a traceable assessment and remain compatible with competition, fiduciary, securities, procurement, confidentiality, due-process, appeal, and national-security requirements. The objective is to preserve correction capacity without making coordination, review, or delay a new source of harm. #### 42.7 Final integrated thesis

The contemporary AI capitalization problem is not adequately described by high valuations, infrastructure expenditure, or reciprocal-investment rhetoric considered separately. It consists of an emerging family of capital–compute commitment packages through which procurement, infrastructure finance, customer incentives, equity exposure, cloud distribution, supplier revenue, valuation, and strategic positioning become analytically interdependent. These arrangements can produce real commercial, operational, learning, and strategic value. Their systemic significance lies in the possibility that prior commitments also become material inputs into the financing, evidentiary justification, and authorization of subsequent commitments. The public record verifies several vertical coupling mechanisms but does not yet establish their causal transmission into horizontal rivalry. Strong coupling-sustained overextension requires recurrent commitment across an ex ante or independently external boundary, material coupling, rising dependency, and ineffective conditionality. A locked bubble-like regime additionally requires actor-pair Restraint Penalties, sufficiently shared expectations, a correction deficit, and persistence through a genuine correction opportunity. The current evidence establishes contractual coupling, replication, implemented financing mechanisms, partial feedback, and candidate transmission channels. It does not establish a complete capitalization loop, strong B2, B3, CEP, or S4.

42.8 Final governance thesis

The appropriate response to capital–compute coupling is not a general presumption against AI expansion. It is a causally complete and legally legitimate permission architecture attached to the next material commitment. Such an architecture authorizes acceleration where external value and strategic adequacy support it, restricts unsupported scale and dependency, holds irreversible expansion where justification remains incomplete, and restores a more transferable state where comparative value fails. Its function is not to prevent commitment. It is to preserve the capacity of evidence to change commitment before prior commitment removes the practical possibility of correction.

42.9 Final classification

The article has established:

L1:Contractual Capital–Compute Coupling

and material support for:

L2:Replicated or Networked Coupling.

It has developed:

L3:Capitalization-Loop Candidate.

It has not established L4–L8.

The bubble claim remains:

Contemporary AI Bubble Risk,

not:

Confirmed Contemporary AI Bubble.

The CEP gate remains closed. The S4 mapping remains deferred.

42.10 Conclusion

AI capitalization should not be evaluated through a choice between technological triumph and speculative collapse. The contemporary system can contain genuine demand, real revenue, useful infrastructure, strategic value, and substantial overcommitment at the same time.

The central analytical challenge is to distinguish:

Continuation Because Value Is Converging

from:

Continuation Because Prior Commitment Has Made Conditioning Costly.

The distinction cannot be recovered from contract size, user counts, capacity, valuation, or strategic rhetoric considered alone. It requires:

demand provenance;
independent-value evidence;
external value and complete burden;
vertical package effects;
horizontal rivalry;
dependency;
correction authority;
and the permission state of the next increment.

A capital–compute system becomes governable when it can explain why the next commitment is justified, which evidence could change that judgment, who has standing to introduce the evidence, who can lawfully issue a binding gate, how the gate changes operational reality, and when the decision must be reopened.

Without that architecture, evaluation can accumulate while commitment continues by default. With it, acceleration remains possible without becoming institutionally irreversible.

The decisive question is therefore not whether AI should continue. It is whether the system can still distinguish justified continuation from continuation reproduced by its own commitments.

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This article belongs to the public essay layer of RATIUM.AI. For readers who want to move from this article into the broader source, technical, and orientation layers of the project, the following pages provide the relevant entry points.

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The articles page gathers the public essay layer of RATIUM.AI, including arguments on stable AI governance, decision-control architecture, visible governance versus real authority, universal reason, technical competence, purpose governance, and the doctoral-scale framing of CEP.