National Value Model

V U R A Wo r k i n g P a p e r S e r i e s N o . 1 0 — L ay e r Z e r o ( N a t i o n a l S t r u c ‐ t u r e ) National Value Models: A Theory of Resource, Transformation, and Utilization for Nations in the Age of AI, with Critical-Tier Governance 国家価値モデル ― AI時代における資源・変換・活用の国家理論と臨界ガバナ ンス Naoki Kadowaki VURA Capital Innovation Holdings, Inc. Version 1.0 (Working Paper) — August 2026 This paper is a working paper and has not undergone journal peer review. Please note this when citing. Abstract This paper is a general theory, not an argument about any one country. Its apparatus — the Nine-Cell Matrix, geoeconomic leverage, the dynamics of transition, critical-tier governance, and value-definition capability — applies to every state that does not belong to the two poles of the Resource-Producing Model. AI is reorganizing the structure of relations among states as a "strategic general-purpose resource" resembling oil, but no single analogy holds. Resource characteristics differ by capability tier: the commodity tier corresponds in part to oil and electricity, the frontier tier to managed strategic materials, and the critical tier to nuclear technology. This paper neither discards nor abuses analogy; its methodology is a discipline of analogy that states explicitly which properties transfer. As a matter of comparative design, this paper uses a contemporaneous comparison with the oil market of 2026 in addition to the diachronic comparison with 1973 — observation at a single point in time removes era effects from the difference as a common term and grounds transfer judgments in observation of an ongoing present (Sections 3.9 and 6.11). The 2026 supply disruption event is described only as market fact, in accordance with the editorial policy set out in Section 1. The Nine-Cell Matrix is the product of the three types of national value model of the oil era (M1 Resource-Producing, M2 Transformation, M3 Utilization) and the three AI capability tiers (C1/C2/C3). The tiers are defined by capability distance alone; the differentiation of market structure and of governance form is not a consequence of the definition but a dependent variable of Propositions 2 and 2b. The cells are non-equivalent in their institutions, their conditions of viability, and their modes of failure; national strategy is therefore not the choice of a single cell but a portfolio. The Nine Cells describe the mode of value generation, but they do not describe whether a state can push back when its conditions are changed from outside. This paper introduces a second axis, geoeconomic leverage (Definition 15), with two components: indispensability (the cost and the degree of malfunction that arise if others attempt to bypass or exclude the state in question) and desirability (the degree to which other states voluntarily seek engagement). Position and leverage are independent variables and do not coincide (Proposition 22). National strategy therefore has two objective functions — optimization of position and maximization of leverage — and the two do not call for the same policies. Furthermore, indispensability grounded in a chokepoint does not depreciate while it is merely held; it begins to depreciate the moment it is exercised, because exercise induces a search for alternatives — building inventories, designing bypasses, developing substitute sources of supply, investing in domestic production (Proposition 23). What the Transformation Model can export falls into three kinds: capability, products, and integrated systems. What withstands compression is the export of integrated systems (Definition 20), protected by the wall of integration cost. On the side of desirability there is no such paradox: the more an integrated system is adopted, the more conformity investment accumulates on the recipient side, and desirability 2 appreciates together with switching costs. Indispensability depreciates when exercised; desirability appreciates the more it is used (Proposition 38). What can be exported is determined not by the jurisdiction with the highest capability but by the jurisdiction able to separate the system from its own institutions (Proposition 39); on the importing side the same variables govern the division of labor among three modes — construction within the home jurisdiction, procurement of capability, and procurement of integrated systems (Proposition 40). By way of this axis, standard-setting power is recovered inside the theory not as a fourth value model but as leverage on the side of desirability. This paper gives this configuration a name. The type that does not itself produce frontier capability but procures it from outside, converts it into an operable system by means of the complementary assets, national brain capital, and trust infrastructure of its own jurisdiction, and supplies that system outward as an integrated system, is called the AI Foundry Model (Definition 21); a state that adopts this type is called an AI Foundry State. The name derives from the correspondence with the structure of a semiconductor foundry, which owns not the design but the process capability. The correspondence is limited, however, to the structure of "taking value at the process stage without holding the design"; the indispensability that a semiconductor foundry retains through capital specificity and the difficulty of reproducing its processes does not transfer — to give a name and, in the same act, to state where the metaphor fails to transfer is this paper's discipline of applying the discipline of analogy to its own act of naming. Two questions that this paper had carried within itself remain at this point. First, the deep institutional embeddedness required by Propositions 4 and 18 and the separability from the institutions of the home jurisdiction required by Proposition 39(iv) appear to be contradictory demands upon one and the same system. They coexist only if the system is separated into a jurisdiction-specific layer and a portable core, with the interface between them explicitly defined (Proposition 41) — the design principle is not to make embedding shallow but to confine the locus of embedding to the outside of the interface. Second, does the height of switching costs, where an integrated system is deeply embedded, amount to substantive indispensability? It does not: lock-in is not indispensability (Proposition 42). Indispensability is a property concerning whether a third party can bypass the actor in question; lock-in is a property concerning whether a party already engaged can leave. A high level of lock-in is not evidence of indispensability unless it is accompanied by an indicator of supplier concentration. And the self-reinforcement of desirability has an upper bound, because a rise in switching costs simultaneously raises the recipient's incentive to institutionalize in-house production, multi-sourcing, and requirements of portability. The Nine Cells are not a static classification but a field of transitions. Upward transition requires the accumulation of complementary assets, national brain capital, computing infrastructure, and electricity, and its time constant is longer than the time constant of policy decision. Downward transition requires no accumulation and occurs passively, through the relative depreciation of existing accumulations alone (Proposition 15). "Doing nothing" is not "holding position" but "descending." As AI becomes critical infrastructure, it gives rise to a new systemic risk in the form of correlated supply stoppage — "AI outage," a coinage of this paper formed in correspondence with power outage in elec‐ 3 tricity. A state requires a sovereign minimum guarantee level corresponding to oil stockpiles; but AI capability cannot be stockpiled in barrels and depreciates at the speed of the frontier, so the guarantee is not a requirement that is achieved once but holds only as continuous construction. Tier C3 (the critical tier) is an unrealized anticipatory category, and what follows is a conditional design argument for the case in which it arrives. Across five regimes — nuclear, chemical, biological, missile, and cyber — verification mechanisms came into being only where the object of control was accompanied by a measurable physical correlate (the verification anchor hypothesis, Proposition 9). In AI only compute, electricity, and facilities can serve as anchors; and because an anchor depreciates with a half-life, critical-tier governance is sustained only if it has continuous downward revision of thresholds built into it. Concerning Layer Zero (national structure), this paper derives two consequences. First, because the advantage obtained through efficiency gains from capability that has descended to C1 diminishes as the cost of imitation falls, the residual that makes a difference shifts from efficiency to definition — to "the capability to select what is to be aimed at and to realize it" (Proposition 17). To design AI policy as efficiency policy is a systematic error. Second, the substrate of the defensibility of the Transformation Model is national brain capital. AI capability can be imported, but tacit knowledge on the ground, judgment embedded in language and culture, trust in institutions, and long domain experience cannot be imported (Proposition 18). The two consequences converge upon the common constraints of middle powers: states outside the two poles of the Resource- Producing Model are subject, regardless of region, income, or political system, to three constraints — energy, data sovereignty, and value-definition capability (Proposition 21). This paper makes no predictions, but it supplies instruments of identification. There are at least three branches in the advance of AI capability — [S1] Fragmentation, [S2] Diffusion, [S3] Stagnation (Definition 13). This paper does not state which will occur; it supplies leading indicators (Definition 14) that identify the branch before its consequences appear, together with a set of no-regret actions that carry positive expected value in all three branches — national brain capital, exclusive domain data, value-definition capability, and operational readiness (Proposition 20). Owning frontier-class computing infrastructure outright does not belong to this set: it has high value under S1, but under S2 it is overinvestment and under S3 a stranded asset. The Nine Cells are not, however, a uniform lattice. The M axis and the C axis are not orthogonal, and the higher the capability tier, the narrower the set of positions a state may occupy (the feasible region, Definition 18) becomes (Proposition 29). And recommendations have costs. Because domestic guarantees run counter to economies of scale, they generate a sovereignty premium (Definition 19) and are justified not as efficiency but only as insurance — only where the total premium is less than the expected value of the losses avoided (Proposition 30). A requirement of redundancy lowers capital efficiency at Layer Three; its benefits accrue to the system as a whole while its costs are borne by individual actors, so it holds only if it is designed together with an allocation of that cost (Proposition 31). The diagnostic framework itself also consumes administrative capacity, and so has no implementability unless it is accompanied by a minimum indicator set 4 (Proposition 36). Section 19, "The Cost of Sovereignty," treats these together, and thereby fixes, by this paper's own hand, the range within which its recommendations hold. The application treated in greatest detail is Japan (Section 18). None of the conditions for the success of the postwar processing-trade model transfers unmodified to the age of AI, and the viable portfolio is limited to a set of three: transformation protected by integration cost (M2′), the compounding of depth of utilization (M3), and a sovereign minimum guarantee level narrowed to three functions. This position does not coincide, however, with the position on the leverage coordinates — Japan is an application of Proposition 22, not the purpose of the theory. Japan's half-century of oil also supplies one general structure: a policy that reduces exposure in aggregate does not reduce dependence if supplier concentration rises in the remaining portion (Proposition 37). Reducing exposure and reducing concentration are separate policy objectives, and a design that pursues only the former may improve the aggregate while worsening the degradation that occurs upon interruption. This paper claims no comprehensiveness. The subjects deliberately not treated, and the reasons for not treating them, are declared in Section 20 — the post-truth condition and the redesign of democracy, the state as a provider of existential purpose, and the civilizational-historical debate over the multipolarity of intelligence. The Position of This Paper This paper is the tenth in the VURA Working Paper Series. The series has so far carried out the work of redefinition for the enterprise (Layer Three), society (Layer Two), and capital (Layer One). This paper extends that work to the state (Layer Zero) and turns the national conditions that the three lower layers have treated as given into the object of analysis. This paper is written in Japanese, and treats the Japanese case in detail in Section 18, because Japan is the country whose primary sources — official statistics, statutes, advisorycouncil materials, and practice on the ground — the author can approach most closely, and not because the framework itself is specific to any one country. The thickness of the case study is not intended to narrow the generality of the theory; it is intended as a worked example by which readers elsewhere can see how an analysis of comparable thickness might be assembled for their own country. In reading Section 18, attention is best directed not at the Japanese figures described but at the procedure by which figures are translated into position and constraint. The diagnostic instruments for applying the same procedure are set out separately in Appendices D, E, F, and G. An English edition of this paper is to be prepared in due course, preserving the content of the Japanese edition. The author is a practitioner at an investment holding company and is presently engaged in business and investment in the domains on which this paper makes recommendations. This position gives the paper two characteristics. First, sensitivity to practical constraints: the author stands closer, as a participant rather than as an analyst, to constraints such as the feasibility of policy, the time constant of corporate decision-making, and the years required for accumulation. Second, a structural conflict of interest: if the recommendations of this 5 paper were adopted, the author's business opportunities may expand. Readers should read the policy recommendations of this paper together with this fact. Because of this position, the author presents the claims of this paper both as "recommendations" and as "hypotheses whose verification the author undertakes to bear." Stating the conflict of interest rather than concealing it is the condition for writing from this position. The details of the disclosure are placed in Section 2.7, and the acknowledgment of limitations in Section 20. Editorial Policy of This Paper — Political Neutrality This paper takes the state as its unit of analysis and not as an object of evaluation. What it describes are observed institutions, measures, and supply structures, together with the structural consequences these have for the options available to states. The content and dates of published policy documents and statutes, and the fact that suppliers and productive capacity are concentrated in particular countries or regions, are described, because they are indispensable to the analysis. On the other hand, this paper makes no judgment about the motives behind measures, the appropriateness of policies, or the legitimacy of political systems. Measures can be observed; intentions cannot. Nor does this paper endorse any camp or issue any call to counter one. This position carries costs. First, this paper cannot treat normative questions — which allocation is just, which form of governance is preferable. Second, since motives are placed outside the object of analysis, this paper's explanatory power with respect to why the same measure is taken at one moment and not at another extends only to the description of structural conditions. These two constraints are accepted in order to separate analysis from advocacy. When analysis is mixed with the defense of a particular position, what is lost is not the persuasiveness of the advocacy but the falsifiability of the analysis. Accordingly, when readers use this paper in judgments about their own country or organization, normative judgment is reserved to the reader. What this paper supplies is a map of options and of their structural consequences, not an answer as to which should be chosen. This policy is reaffirmed in Section 20 (the acknowledgment of limitations). JEL classification: F52, F51, F13, F02, O33, O38, O25, L13, L51, L86, L94, K23, Q34, H54 Keywords (17): national value models; AI capability tiers; strategic general-purpose resource; discipline of analogy; resource curse; transformation value; AI outage; sovereign minimum guarantee level; critical-tier governance; compute governance; geoeconomic leverage; trust infrastructure; feasible region; national brain capital; AI Foundry Model; national redefinition; Layer Zero Contents 1. Cover, Abstract, Editorial Policy, and Contents (this section) 6 2. Introduction 2.1 The Autumn of 1973 — Making Dependence Visible and the Redefinition of a National Model 2.3 Research Questions (four sub-problems) 2.4 The Contributions of This Paper (eight; one of which is "treating the supply side and the procurement side as two faces of a single framework") 2.6 The Structure of This Paper 2.7 Disclosure of Conflicts of Interest and of Observational Position 3. Methodology: The Discipline of Analogy 3.4 Decomposing the Analogy — Bundles of Properties and the Correspondence Table 3.7 Proposition 1 — Formulating the Core of the Methodology 3.9 Contemporaneous Comparison — Controlling for Era Effects 4. Theoretical Background: Resources and the State 4.9 Where Is Value Captured? — Global Value Chains, the Smile Curve, Trade in Value Added, and Economic Complexity 4.10 Network Power and Regulatory Power — Value Positions Not Based on Production 5. A Theory of AI Capability Tiers 5.1 Definition 2 and Its Operationalization 5.5 Propositions 2 and 2b — The Covariation of Tier and Governance, and Its Dynamic Character 6. The Three Types of National Value Model 6.7 Definition 3 — National Value Models 6.9 Development into the Nine Cells — Proposition 3 6.10 Non-Orthogonality of the Axes and the Feasible Region — The Nine Cells Are Not a Uniform Grid (Definition 18, Proposition 29) 6.11 The Oil Market in 2026 — A Contemporaneous Observation 7. The Nine-Cell Matrix I — Row C1 (Commodity Tier) 8. The Nine-Cell Matrix II — Row C2 (Frontier Tier) 9. The Nine-Cell Matrix III — Row C3 (Critical Tier) and Critical-Tier Governance 9.4 Comparison of Control-Group Regimes — Chemical, Biological, Missile, and Cyber (the section that raises Proposition 9 from an induction on a sample of one to a comparative proposition across four regimes) 9.7 The Half-Life of the Verification Anchor — Integrating Proposition 8 and Proposition 9 9.9 The Stability of Deterrence — The Conditions for MAD and Incentives to Pre-empt in AI 10. Focal Analysis: The M2×C2 Cell — Conditions for High-Value-Added Transformation 10.3 Condition I — The Four Indicators of Complementary Assets Made Concrete at C2 10.4 Condition II — National Brain Capital as the Substrate (Definition 11, Proposition 18) 10.5 Failure Modes Specific to This Cell 7 10.6 The Minimum Engagement With the Higher Tier Needed to Hold the Position 10.9 Verification by Contemporaneous Comparison — The Petroleum Market in 2026 11. Geoeconomic Leverage — Indispensability and Desirability (Definitions 15 and 17; Propositions 22, 23, 25, and 28) 11.1 Why Position Alone Is Not Enough (Definition 15) 11.2 The Sources of Indispensability 11.3 The Sources of Desirability (Definition 17, Proposition 25) 11.4 Resolving the M4 Problem — Not Exclusion but Recovery 11.5 The Non-Identity of Position and Leverage (Proposition 22) 11.6 The Paradox of Leverage Exercise (Proposition 23) 11.7 Non-State Actors and the Residual Functions of the State (Proposition 28) 11.8 The Institutional Treatment of Military and Dual-Use Questions 11.9 Summary — The Move to Dual Coordinates 12. The AI Foundry Model — Export and Procurement of Integrated Systems (Definitions 20 and 21; Propositions 38, 39, and 40) 12.1 What Does the Transformation Model Export? (export of capability / export of products / export of integrated systems. Definition 20. Section 12.1.6 gives the type its name [Definition 21; the discipline of notation], and Section 12.1.7 determines what transfers and what does not by contrast with semiconductor foundries [Table 27]) 12.2 Why It Is Bought Even Though It Costs More (three things thereby established: where responsibility lies, proof of conformity, and accountability to supervisory authorities) 12.3 Conditions for a State That Exports Integrated Systems (Proposition 39. Of the four conditions, portability is the most binding. Section 12.3.7 formulates the condition under which embedding and portability coexist, by making the interface explicit [Proposition 41]) 12.4 Types of Exporting State (described as combinations of conditions; no evaluation of particular states) 12.5 The Self-Reinforcement of Desirability (Proposition 38. Indispensability depreciates when exercised; desirability appreciates the more it is adopted. Sections 12.5.6–12.5.8 respond to the objection that lock-in amounts to substantive indispensability and formulate the upper bound of self-reinforcement [Proposition 42]) 12.6 The Procurement Portfolio of the Importing Side (Proposition 40. Three modes and three variables. Table 26) 12.7 The Risks Attending the Import of Integrated Systems (the situations in which Proposition 24 operates as a direct consequence of the procurement mode, and the design of mitigations) 12.8 The Asymmetry Between Exporting and Importing States (not adversarial, but their interests do not coincide) 8 13. AI as Infrastructure: Price, Scarcity, and AI Outage 13.3 A Theory of AI Outage — Definition 4 and Proposition 7 13.6 The Sovereign Minimum Guarantee Level — Correspondence with Oil Stockpiles and the Asymmetry 13.7 Rationing and Priority — Designing Allocation Institutions for Periods of Scarcity 13.10 The Performance of Buffers in 2026 — A Triple Buffer and the Blank in AI 14. Country Profiles (described in three coordinates: position on the Nine Cells, geoeconomic leverage, and the possibility of exporting integrated systems) 14.12 Small-State Strategy in General — Value Strategy Under Constraints of Scale 14.13 Common Constraints on Middle Powers — Three Constraints That Operate Independently of Region, Income, and Political System (Proposition 21) 14.14 Cross-Cutting Observations — Structure Visible in the Distribution (Section 14.14.3 treats the export of integrated systems as a third distribution) 15. The Dynamics of National Value Models 15.2 The Asymmetry of Transition — Ascent Requires Accumulation, Descent Does Not (Definition 10; Propositions 15 and 16) 15.3 Scenario [A] The Branching of the Transformation Model — Ascent and Fall 15.4 Scenario [B] Vertical Integration Across the Axes — From Market Allocation to Allocation Within Alliances 15.5 Scenario [C] Moving Upstream Through Capital — The Ladder and the Drilling Right 15.6 Scenario [D] Downward Transition Through Physical Constraints — A Path That Operates Independently of Intention 15.7 Conditions for a Third Pole — As an Analysis of Conditions, Not an Advocacy (Proposition 19) 16. World Scenarios and Leading Indicators (Definitions 13 and 14; Proposition 20 — the three branches [S1] Fragmentation / [S2] Diffusion / [S3] Stagnation, the leading indicators by which they are identified, and the no-regret actions that carry positive expected value in all three) 16.5 Leading Indicators 16.6 No-Regret Actions 17. Layer Zero and the Four-Layer Architecture — Value-Definition Capability and National Brain Capital 17.2 Proposition 11 — Three Channels of Inter-Layer Transmission 17.3 Diminishing Returns to Efficiency and the Residual of Value-Definition Capability — Proposition 17 (Definition 12, Proposition 32) 17.4 National Brain Capital — Connecting Layer Zero to the Human Substrate (Propositions 18, 24, 33, and 34. Section 17.4.5 makes the connection to the procurement of integrated systems) 9 17.6 National Redefinition — Proposition 14 and the Correspondence with the Five Dimensions 17.9 The Future Value of a State — Connection to Future Value Theory 17.10 The Institutional Time Constant — Governance Design at Layer Zero (Propositions 26 and 35) 17.11 The Relative Scarcification of Authentic Data — Rereading the First Indicator of Proposition 4 (Definition 16, Proposition 27) 18. Case Study: Japan — Generalization to Middle Powers (an application, not the purpose of the theory; the same procedure applies to any middle power) 18.3 Establishing the Present Position Empirically — Japan's Position With Respect to AI as a Resource (Proposition 37. Section 18.3.5 treats the reduction of exposure alongside the concentration of dependence) 18.5 What National Brain Capital Consists of in Japan — Four Components and Their Attrition 18.7 Proposition 13 — A Viable Portfolio for Japan 18.11 The Complementarity of the Three-Part Set, and Japan on the Leverage Coordinates (the application of Propositions 22, 23, and 25 to Japan) 18.15 Generalization to Middle Powers — Country-Independent Lessons Extracted from the Analysis of Japan 18.16 Applying the Conditions for an AI Foundry State to Japan — Assessment by the Four Conditions of Proposition 39 (Section 18.16.10 makes explicit that the bargaining power that may be expected lies on the side of desirability and not of indispensability) 19. The Cost of Sovereignty — Scale, Fiscal Capacity, Cost of Capital, and Institutional Coherence (Definition 19; Propositions 30, 31, and 36. The section that treats the costs and constraints carried by this paper's own recommendations) 19.1 Why a Section That Counts Costs Is Required 19.2 Diseconomies of Scale and the Sovereignty Premium (Definition 19, Proposition 30) 19.3 The Fiscal Ceiling 19.4 Frictions in the Cost of Capital and the Inter-Layer Conflict of Interest (Proposition 31) 19.5 The Process of Examining Institutional Coherence (not legal advice) 19.6 Graduated Treatment of Data 19.7 Administrative Capacity Constraints and the Minimum Indicator Set (Proposition 36) 19.8 The Total Cost, and the Part That Remains Justified 20. Objections and Limitations 20.8 The Absence of a Measurement Framework — Erecting Concepts Without Constructing Observables (ten items) 20.9 Incomplete Formalization — Signs Given, Magnitudes Not (nine items) 10 20.10 The Absence of Opportunities for Falsification, and the Thinness of the Evidence (ten items) 20.11 Failure to Reach Design — Where the Paper Stops at Noting a Need (six items) 20.12 Limitations Arising from the Choice of Framework, the Unit of Description, and the Observational Position (twelve items; 47 limitations in Sections 20.8–20.12) 20.14 What This Paper Does Not Cover — A Declaration of Explicit Exclusions (this paper claims no comprehensiveness) 20.15 The Conflict of Interest When a Practitioner Recommends Policies That Bear on His Own Business Opportunities (including an eighth item) 20.16 Acknowledgment of Five Weaknesses 20.17 The Limitations of This Section Itself 21. Conclusion and Research Agenda 21.2 Table 10 — The Map of the Verification of the Propositions (All 42 Numbers, 44 Statements) 21.7 Priorities in the Research Agenda (including the construction of a measurement framework for portability) 21.8 Concluding Remarks 22. References Appendix A. The Nine Cells in Detail (Tables A-1 to A-11) Appendix B. Nuclear–AI Governance Correspondence Table (Tables B-1 to B-2) Appendix C. AI Dependence Audit Protocol (Tables C-1 to C-8) Appendix D. National Diagnostic Checklist (Tables D-1 to D-8) Appendix E. The Cell-Transition Matrix and a Measurement Framework for National Brain Capital (Tables E-1 to E-8. Section E.7 sets out a provisional proposal for measuring portability [Table E-8]) Appendix F. Scenario Monitoring Indicator Table (Tables F-1 to F-5) Appendix G. Geoeconomic Leverage Diagnostic (Tables G-1 to G-7; seven tables, 113 items in total. Section G.9 places the diagnostic for making the interface explicit [Table G-6], Section G.10 the discrimination between lock-in and indispensability [Table G-7], and Section G.11 the order of implementation) Appendix H. Glossary (Japanese–English) (Table H-1. A list of the 21 definitions and the principal concepts) 11 Summary of the Definitions and Propositions (Definitions 10–21, Propositions 15– 42) What follows is a summary of those theoretical instruments used in this paper that are numbered Definitions 10–21 and Propositions 15–42. Definitions 1–9 and Propositions 1–14 are placed in the sections of the main text where they belong, and a list of all definitions appears in Appendix H (Table H-1). Definition 10 (Cell Transition) — Section 15. Defines the movement of the centroid of a state's portfolio weights across the Nine Cells, decomposed into three directions: horizontal (the M axis), vertical (the C axis), and cross-axis. Definition 11 (National Brain Capital) — Section 10. The whole of that part of the human capital of the country in question which AI cannot replicate or transfer at low cost (four components: tacit knowledge on the ground; judgment embedded in language and culture; the professional ethics and practical conventions that make trust in institutions possible; and the capacity for audit and verification grounded in long domain experience). Definition 12 (Value-Definition Capability) — Section 17. The capability to select for oneself the future state to be achieved and to realize it by translating it into allocation of resources, institutional design, and organizational structure. It is distinguished from efficiency in achieving an existing objective. Definition 13 (World Scenarios) — Section 16. Identifies the exogenous states of the world determined by combinations of the mode of advance of AI capability, supply structure, and physical constraints, as three states: [S1] Fragmentation, [S2] Diffusion, and [S3] Stagnation. The three states are neither exclusive nor exhaustive, and different states may hold simultaneously in different sectors and applications. Definition 14 (Leading Indicators) — Section 16. Observables that permit identification of which world scenario is coming into being, before the consequences of that scenario appear. Only those that satisfy three conditions — repeatable observability, discriminating power, and leadingness — are admitted. Definition 15 (Geoeconomic Leverage) — Section 11. Defines the power of a state to realize its own preferences in international negotiation and conflict as having two components: indispensability (the cost and the degree of malfunction that arise if other states attempt to bypass or exclude the state in question) and desirability (the degree to which other states voluntarily seek engagement with it). It is a variable independent of position on the Nine Cells (Definition 3). Definition 16 (Authentic Data) — Section 17. Data generated directly from human action or physical process, whose provenance is verifiable. It is distinguished from synthetic data derived from the outputs of generative models. Its scarcity is determined not by the total volume of what is produced but by the verifiability of provenance. 12 Definition 17 (Trust Infrastructure) — Section 11. The whole of the institutions that, with respect to harm arising from acts that use the outputs of AI, fix in advance where responsibility lies, compensate the harm, and have conformity certified by a third party (three elements: rules for allocating liability, conformity assessment, and insurance). Definition 18 (Feasible Region) — Section 6. The set of positions of value generation on the M axis that a state can in fact occupy at a given capability tier. The feasible region differs by tier; not all nine cells are equally stable occupiable points. Definition 19 (Sovereignty Premium) — Section 19. The difference between the unit price of use for compute, data, and models guaranteed domestically or within an alliance, and the unit price of use if procured from an unconstrained international market. It grows larger the further the guaranteed scale of supply falls below the minimum efficient scale, and for the domestic actors that use it has the character of an effective cost increase, that is, of an insurance premium. Definition 20 (Export of Integrated Systems) — Section 12. Transferring to an external jurisdiction neither AI capability itself nor products produced using AI capability, but the whole of the system that makes capability operable in a particular field of work — the five elements of (i) access to capability, (ii) the design of its incorporation into work processes, (iii) the arrangements for allocating responsibility, (iv) proof of conformity, and (v) the human capacity to operate and verify it. It is distinguished from both the export of capability and the export of products in that it involves embedding within the institutions, work, and personnel of the recipient. Definition 21 (AI Foundry Model) — Section 12 (Section 12.1.6). That configuration among national value models (Definition 3) in which a state does not itself produce frontier capability but procures it from outside, converts it by means of the complementary assets of its own jurisdiction (the four indicators of Proposition 4), national brain capital (Definition 11), and trust infrastructure (Definition 17) into a system operable in a particular field of work, and supplies that system to external jurisdictions as an export of integrated systems (Definition 20). It is thus the type that arises when M2 (the Transformation Model) takes C2 (the frontier tier) capability as its object and chooses integrated systems as the form of its output; a state that adopts this type is called an AI Foundry State. The name derives from the structural correspondence with a semiconductor foundry (a business form that owns not the design but the process capability), but the correspondence is limited to the structure of "taking value at the process stage without holding the design," and the indispensability (Definition 15) that a semiconductor foundry retains through capital specificity and the difficulty of reproducing its processes does not transfer — the bargaining power of an AI Foundry State rests on the side of desirability (Proposition 38). The determination of what transfers is placed in Section 12.1.7 and Table 27. This paper always uses the qualified forms "AI Foundry State" and "AI Foundry Model," and does not use any form lacking the qualifier to denote the type introduced here (Section 13 12.1.6). The type-name used in this paper is unrelated to commercial products or services bearing the same or a similar name in the field of information technology. Proposition 15 (Asymmetry of Cell Transition) — Section 15. Upward transition requires accumulation and has a time constant on the order of years, whereas downward transition occurs passively, through the relative depreciation of accumulations alone. Proposition 16 (Pressure Toward Cross-Axis Transition) — Section 15. A rise in the level of capability generates pressure that irreversibly moves the logic governing the allocation of that capability from economics to national security. Proposition 17 (Diminishing Returns to Efficiency and the Residual of Value-Definition Capability) — Section 17. As capability descends to C1, the competitive advantage of efficiency gains diminishes with the falling cost of imitation, and the residual that makes a difference shifts to value-definition capability (Definition 12). This is the consequence, at the level of the state, of Future Value Theory (2026a). Proposition 18 (The Non-Replicability of National Brain Capital) — Section 10. The defensibility of the transformation margin at the C2 tier depends on the thickness of national brain capital; a strategy that aims at the Transformation Model while lacking national brain capital reduces to transformation without complementary assets (Proposition 4). Proposition 19 (Conditions for a Third Pole) — Section 15. States outside the two poles of the Resource-Producing Model can constitute an independent third pole only where three conditions are satisfied simultaneously: complementarity, mutual guarantees of access, and shared discipline. Proposition 20 (The Existence of No-Regret Actions) — Section 16. The set of investments carrying positive expected value irrespective of which scenario is realized is not empty; it consists of national brain capital, exclusive domain data, value-definition capability, and operational readiness. Owning frontier-class computing infrastructure outright is, by contrast, scenario-dependent. Proposition 21 (Three Constraints on Middle Powers) — Section 14. States that do not belong to the two poles of the Resource-Producing Model are subject in common to three constraints — the energy constraint, the data-sovereignty constraint, and the value-definition constraint — regardless of differences of region, income level, and political system. All three constraints are independent of the level of technological capability. Proposition 22 (The Non-Identity of Position and Leverage) — Section 11. Position on the Nine Cells and geoeconomic leverage are independent variables, and neither can be derived from the other. National strategy has two objective functions: optimization of position and maximization of leverage. Proposition 23 (The Paradox of Leverage Exercise) — Section 11. Indispensability grounded in the holding of a chokepoint depreciates through being exercised. Exercise induces a search for 14 alternatives on the side affected, and indispensability declines to the extent that this search succeeds. Proposition 24 (Self-Erosion of Brain Capital) — Section 17. To the extent that reliance on imported cognitive capability substitutes for the repetition of human practice, national brain capital (Definition 11) wears away and the four indicators of complementary assets in Proposition 4 decline. A strategy that deepens utilization while lacking transformation capability loses the basis for ascent through the very deepening of utilization. Proposition 25 (The Priority of Trust Infrastructure) — Section 11. The depth to which AI is deployed in regulated sectors is bounded above by the level of development of the trust infrastructure (Definition 17) of the jurisdiction in question. Trust infrastructure is a condition prior both to the depth of the Utilization Model (Proposition 5) and to the margin of the Transformation Model (Proposition 4). Proposition 26 (Institutional Time Constant) — Section 17. The effectiveness of governance depends on the ratio of the time an institution requires to reach a decision to the time the capability under control requires to change substantially. It is the general form of Definition 9 (the half-life of the verification anchor) and Proposition 9. Proposition 27 (Relative Scarcification of Authentic Data) — Section 17. As the proportion of public information space occupied by the outputs of generative models rises, the marginal value of authentic data with verifiable provenance (Definition 16) rises. This strengthens the exclusive data endowment of Proposition 4. Proposition 28 (Non-State Actors and the Residual Functions of the State) — Section 11. In domains where the compute, capital, and engineers of private actors exceed those of the state, the functions that the state still supplies irreplaceably converge upon three: legal finality, physical security, and permissions for siting and resources. Proposition 29 (Non-Orthogonality of the Axes and the Feasible Region) — Section 6. The M axis and the C axis are not orthogonal, and the higher the capability tier, the narrower the feasible region (Definition 18) becomes, owing to the rise in the class of externality. Proposition 30 (The Sovereignty Premium and the Lower Bound of Scale) — Section 19. Domestic guarantees enlarge the sovereignty premium (Definition 19) the further the guaranteed scale falls below the minimum efficient scale; they are not justified from the standpoint of efficiency and are justified only as insurance against a stoppage of supply. Proposition 31 (Inter-Layer Conflict of Interest and the Need for Compensation) — Section 19. The redundancy required by Layer Zero lowers capital efficiency at Layer Three. Because the benefits accrue to the system as a whole while the costs are borne by individual actors, this mismatch is not resolved by the market, and the requirement does not hold unless it is designed together with an allocation of that cost. Proposition 32 (Conditions for the Propagation of Value-Definition Capability) — Section 17. For value-definition capability (Definition 12) to be converted into national value, the value that has 15 been defined must be accepted outside the jurisdiction in question, and the channel for this is one of three: market size, incorporation into standards, or connection to existing international frameworks. Proposition 33 (Asymmetry in the Mobility of National Brain Capital) — Section 17. National brain capital (Definition 11) cannot be acquired by import, but can be lost through outflow. Its level is determined by the net increase obtained by subtracting the rate of outflow from the rate of formation. Proposition 34 (Mismatch of Time Scales) — Section 17. The time constant required for the formation of national brain capital exceeds the time constant of change in capability tiers by more than an order of magnitude. The speed at which a complementary good is formed is structurally slower than the speed at which the object it complements changes. Proposition 35 (Hysteresis of Securitization) — Section 17. Once a capability has been placed under the logic of national security, the framework of control is not relaxed at a speed corresponding to any subsequent descent of that capability through the tiers. Cross-axis transition (Proposition 16) proceeds at different speeds on the outward and the return path. Proposition 36 (Administrative Capacity Constraints and the Minimum Set for Monitoring) — Section 19. Implementing a framework of diagnosis and audit consumes administrative capacity. Where administrative capacity is constrained, a requirement of comprehensive monitoring leads to non-implementation, formalism, or delay; a framework must therefore be accompanied by a minimum indicator set to be maintained as a priority under constraints of administrative capacity. Proposition 37 (Reduction of Exposure and Concentration of Dependence) — Section 18. A policy that reduces aggregate exposure (Definition 4) to a given resource does not reduce dependence if supplier concentration rises in the portion that remains. Reduction of exposure and reduction of concentration are separate policy objectives, and a design that pursues only the former may produce the outcome of improvement in the aggregate together with worsening in the degradation that occurs upon interruption. Proposition 38 (Export of Integrated Systems and the Self-Reinforcement of Desirability) — Section 12. The two components of geoeconomic leverage (Definition 15) carry opposite signs with respect to exercise. Indispensability depreciates through being exercised (Proposition 23), whereas the desirability formed through the export of integrated systems appreciates the more it is adopted, because the recipient's conformity investment raises switching costs in proportion to the depth of adoption. Proposition 39 (Conditions for a State That Exports Integrated Systems) — Section 12. The export of integrated systems occurs only where four conditions are satisfied simultaneously: (i) domain-specific national brain capital, (ii) trust infrastructure, (iii) an operating record within the home jurisdiction, and (iv) portability. The most binding is (iv): the capacity to export is 16 determined not by the height of capability but by the looseness of the coupling between capability and the institutions of the home jurisdiction. Proposition 40 (Portfolio of Procurement Modes) — Section 12. Procurement on the importing side has three modes — (A) construction within the home jurisdiction, (B) procurement of capability, and (C) procurement of integrated systems — and the domains to which each is suited are determined by three variables: the severity of the consequences of failure, the domain-specificity of judgment, and reversibility. Because in a domain where (C) is chosen the opportunity to form national brain capital in that domain is lost (Proposition 24), that choice must be made explicitly, domain by domain. Proposition 41 (The Condition Under Which Embedding and Portability Are Compatible) — Section 12 (Section 12.3.7). The institutional embeddedness and linguistic-contextual specificity of Proposition 4 defend the transformation margin, while the portability of Proposition 39(iv) requires separability from the institutions of the home jurisdiction. The two appear to be contradictory requirements, but they coexist only where the system is separated into (a) a jurisdiction- specific layer and (b) a portable core, with the interface between them explicitly defined. In a system whose interface is not made explicit, deeper embedding diminishes portability; in a system whose interface is made explicit, embedding is confined to the outside of the interface and the cost of transplanting the portable core becomes independent of the depth of embedding. What is to be adopted is not the shallowing of embedding but the confinement of the locus of embedding to the outside of the interface. Proposition 42 (Upper Bound of Self-Reinforcement; Lock-in Is Not Indispensability) — Section 12 (Sections 12.5.6–12.5.8). The self-reinforcement of desirability in Proposition 38 is bounded in two respects. (i) Lock-in is not indispensability — indispensability is a property concerning whether a third party can bypass the actor in question, whereas lock-in is a property concerning whether a party already engaged can leave. So long as multiple alternative suppliers exist, the exporting side may hold a strong position in an individual relationship while remaining substitutable within the system; a high level of lock-in is therefore not evidence of indispensability unless it is accompanied by an indicator of supplier concentration. (ii) An upper bound exists through counteraction on the recipient side — because a rise in switching costs simultaneously raises the incentive to institutionalize in-house production, multi-sourcing, and requirements of portability, desirability reaches its upper bound at the point where the recipient prefers to "recover autonomy even at the price of switching costs." The level of that bound is a function of the national brain capital remaining on the recipient side in the domain in question, the existence of alternative suppliers, and the severity of the consequences of failure. The theoretical apparatus of this paper consists of 21 definitions, 42 numbered propositions (44 statements, counting the splits of Proposition 2b and Propositions 6a/6b), and three hypotheses, together with 13 figures and 27 tables in the main text and 51 tables in the appendices (Tables A-1 to A-11, B-1 17 to B-2, C-1 to C-8, D-1 to D-8, E-1 to E-8, F-1 to F-5, G-1 to G-7, and H-1); the map of verification is gathered in Section 21 (Table 10), and the acknowledgment of limitations together with the declaration of what this paper does not cover in Section 20. "Exporting state" and "importing state" denote structural positions specific to a domain, not classifications of states — no assessment is made that a particular jurisdiction can or cannot be an exporting state (the editorial policy of Section 1). With respect to requirements concerning the handling of data, and with respect to platform operators, this paper likewise makes no judgment either about the appropriateness of the requirements or about the operators — what is described extends only to the structural fact that such requirements and such actors exist, and to the consequences this has for portability and for the differentiation of layers (the editorial policy of Section 1). The 2026 supply disruption event is likewise described only as market fact — volumes of supply, volumes of transport, prices, and inventories — without entering into causes, background, or parties. This paper claims no comprehensiveness: stating what it does not treat does not weaken the claims made about what it does treat, but is a procedure for calibrating their strength correctly. 18 2. Introduction The intended readership of this paper. This paper is written with all states outside the two poles of the Resource-Producing Model — the small number of states that produce frontier-class AI capability within their own territory — in view. The readers specifically envisaged are, first, the policymakers of such states: those responsible for industrial policy, energy policy, economic security, and digital policy, who must decide where their own country stands with respect to AI as an input, which constraints bind it, and which accumulations it should prioritize. Second, those responsible for strategy at multinational firms, who must assess how the conditions of AI access, the regulation of data, and the constraints on electricity in each jurisdiction where they operate delimit the set of redefinition options open to the firm. Third, international organizations: those in a position to design multilateral frameworks for the allocation of access, the verification of capability, and the guarantee of supply. Fourth, academic readers who study national strategy, international political economy, and technology governance. This specification of readership carries one implication. The framework of this paper is not specific to any one country. The Nine-Cell Matrix, the dynamics of cell transition, the assessment of the transplantability of critical-tier governance, and the identification of value-definition capability and national brain capital as the substrate are all constructed so as to be applicable by the same procedure — whether to a middle power in Europe, an oil-producing state in the Gulf, an industrial state in East Asia, a hub state in Southeast Asia, or a populous state of the Global South. This paper treats Japan in detail in Section 18 because Japan is the country whose primary sources the author can approach in greatest detail, not because the purpose of the theory lies in the analysis of Japan. So that readers may perform the same work for their own country or firm, the diagnostic instruments have been separated from the main text and placed in the appendices: Appendix D (National Diagnostic Checklist) gives the procedure for identifying present position, target position, and missing accumulations; Appendix E (The Cell-Transition Matrix and a Measurement Framework for National Brain Capital) gives the measurement of transition possibilities and of national brain capital and value-definition capability; and Appendix F (Scenario Monitoring Indicator Table) gives quarterly monitoring of the leading indicators of the world scenarios — each in an operable form. It is possible to begin from the appendices without reading the main text; in that case, however, it should be noted that the interpretation of the diagnostic results depends on the propositions of the main text. 19 2.1 The Autumn of 1973 — Making Dependence Visible and the Redefinition of a National Model This paper begins from a single historical case. It is presented, however, not as the story of a particular country but as a general case in which an external resource shock forced the redefinition of a national value model. The oil crisis of 1973 is the most fully documented instance of the half-century that followed, and almost all of the structures with which this paper is concerned are contained in it: dependence on a general-purpose input, supplier concentration, the correlation of supply interruptions, the lag in measuring dependence, and institutionalization as a response. What matters is the fact that responses to the same shock diverged systematically across countries. Importing countries redesigned their conversion efficiency and their input mix (the Japanese example examined below); groups of importing countries jointly constructed multilateral buffer institutions (the IEA and national strategic stockpiles); and producing countries diverged to opposite outcomes according to whether or not they possessed fiscal institutions for converting production flows into permanent stocks (the contrast between Norway and Venezuela, Section 4). Readers may read what follows by substituting their own country's response — or non-response — to past resource shocks. What this section follows in greatest detail is the Japanese response, but that is a choice dictated by the availability of sources and does not imply the superiority of that response as a type. A detailed analysis of the Japanese response is placed in Section 18 (the case study); this section extracts only its structure. In October 1973, following the 1973 supply disruption event, oil-producing states in the Middle East restricted the supply of crude oil and raised prices substantially. This is what is known as the first oil shock. The position Japan occupied at that time is worth confirming in figures. In fiscal 1973, oil accounted for 75.5% of Japan's domestic supply of primary energy. Moreover, dependence on the Middle East within its crude oil imports reached 77.5% (Agency for Natural Resources and Energy, 2023). The energy self-sufficiency ratio had fallen sharply from 58.1% in fiscal 1960 over the course of the high-growth period, and Japan had built the world's second-largest economy within a structure that depended on foreign sources — and on one particular region — for nearly all of the basic inputs of its economy. Holding no oil fields at home, importing crude oil, and turning it into export value through a chain of transformation running from refining to petrochemicals, steel, shipbuilding, and automobiles, the postwar Japanese processing-trade model was a national value model that took an extreme form of "zero production, specialization in transformation." This structure was not the product of accident but of choice. Postwar Japan's energy transition — the fuel switch from domestic coal to imported oil — was a choice of industrial policy that, on the premise of cheap and stable Middle Eastern crude, sited industrial complexes along the coast and built an agglomeration of transformation running from refining to materials and from materials to final goods. The sharp fall in self-sufficiency is the obverse of that choice. In place of self-sufficiency from domestic resources, the country