Inflation and Macrostability of Negentropic Value Currency: A Conditional Theory of the Full Monetary Life Cycle

1. Introduction

The first paper of this program (Cheng and Cheng, 2026a, 2026d) did three things: it migrated the monetary value anchor from scarcity to net order creation under an explicitly normative premise; it constructed the value equation Wτ = √(Eτ·Tτ·Iτ) together with its axiomatized incentive structure; and it supplied component-level correlational evidence. It also stated, without qualification, that the macrostability of a scarcity-free anchor is the program’s central open problem. The present paper takes up that problem.

The historical evidence makes the problem sharp. Every successful stabilization of hyperinflation on record — the Rentenmark of 1923, the four cases studied by Sargent (1982) — ultimately relied on some credible nominal anchor: precious metal, foreign currency, fiscal discipline, or institutional commitment. If the ontology of monetary value is no longer scarcity but the accounting of net order creation, then stability can no longer rest on the physical constraint of scarcity. It must rest on the integrity of the accounting and consensus processes themselves. This is a new stability problem, and the existing literature offers no ready-made answer.

Our answer comes in three layers. The first is the life-cycle layer. Issuance solves only half the problem: it specifies how money is born, but not how it dies. If the negentropy created is consumed while the corresponding money keeps circulating, the money stock outgrows the surviving value stock, the M/V ratio decouples, and the inflationary channel reopens through the back door. We therefore specify the complete cycle — creation accounting, platform issuance, distribution to creators, circulation, aggregation at the platform clearing pool, and extinction — in which the death of money mirrors the death of value. The stock identity M(t) ≡ ks·V(t) then holds at every instant, not merely on average. The second layer is the principle layer: five mechanisms that explain why inflation has no structural locus of generation in such a system, rather than merely being counteracted by policy. The third layer is the failure model: whatever inflation can still occur is shown to decompose into four identifiable integrity failures — accounting falsification, consensus distortion, issuance corruption, and extinction failure — each of which is an auditable object rather than a macroeconomic mystery.

Three methodological declarations precede the argument, and the first has been strengthened for this revision. The conditional register is maintained throughout: the claim is that, granted the NVC normative premises and structural assumptions, inflation and stability exhibit the following structure; we do not claim that actual economies already operate this way. Within that register, we further distinguish two objects that earlier drafts conflated: the accounting unit, whose constancy is indeed a construction identity (Proposition 0), and the experienced price level of households, whose behavior depends on the dual-price mechanism and is analyzed on its own terms in Section 4.7. The distinction costs the paper its most quotable slogan and buys it defensibility.

Second, the relationship to the first paper is a division of labor within one program. The first paper established the value ontology and the microeconomic incentives; this paper handles macroeconomic issuance, circulation, extinction, and stability; the two share one symbol system (Wτ, ατ, CU, ks, δ). Every definition or proposition inherited from the first paper is restated at the point of use rather than merely cited, so that no load-bearing element of the present argument requires access to the companion text; where a companion paper’s role is institutional rather than technical — the audit committee’s appointment procedure, the parliament’s double majority — a one-sentence restatement is given in place and the design details are left to the governance paper (Cheng and Cheng, 2026c).

Third — the scope discipline of the series — this paper does not re-derive the value equation, does not defend the normative premise, and does not design the institutions that guard the integrity conditions it identifies. The first two tasks belong to the first paper, the third to the third paper. What this paper claims is exactly the middle layer: granted the ontology and before any constitution, the macroeconomic behavior of the anchor has the structure derived here.

Section 2 positions the paper in the literature. Section 3 presents the four-layer price-formation structure and the full monetary life cycle. Section 4 gives the principle-level mechanisms and states the structural proposition with its exact scope. Section 5 formalizes the failure model and states three further propositions. Section 6 treats the cycle form and the four embedded stabilizers. Section 7 applies the framework to three contemporary monetary problems. Section 8 offers historical mappings as illustrations, not tests. Section 9 lists falsifiable hypotheses and verification designs. Section 10 states limitations. Section 11 concludes. Appendices C and D report the computational execution of five hypotheses; Appendix E specifies the complete pre-analysis plan for the sixth, the only one that engages real-world data, and Appendix F reports its baseline execution under the pre-registered decision rules.

2. Literature Positioning

2.1. Theories of Inflation: From Money Quantity to Expectation Management

The quantity theory traced inflation to an excess of money relative to output (Fisher, 1911), and Friedman (1968) pushed the claim to its limit: inflation is always and everywhere a monetary phenomenon. This tradition correctly identified the long-run correlation between money supply and the price level, but it never answered a decisive empirical puzzle: why does monetary expansion sometimes appear as consumer-price inflation, sometimes as asset-price inflation, and sometimes — as in the quantitative easing after 2008 — as almost no price movement at all? The New Keynesian Phillips curve grounds inflation dynamics in nominal rigidity and expectation management (Clarida et al., 1999); its policy implication concentrates on central-bank credibility and interest-rate rules, while the structural composition of inflation — which sector’s prices are rising and why — is absent from the model. Sargent (1982) showed that the termination of four big inflations required a credible switch of the fiscal-monetary regime, an insight that already approaches “inflation as institutional failure,” yet the insight remained at the level of commitment credibility and never touched value accounting itself. The present model can be read as a deepening of Sargent’s insight: commitments are incredible because the anchor itself rests on promises; when the anchor migrates to independently recomputable accounting, the commitment problem is replaced by a measurement-integrity problem.

One further tradition must be engaged, because it is the closest to this paper’s diagnosis. The conflict theory of inflation (Lavoie, 2014; Rowthorn, 1977) locates inflation in distributional struggle: workers and firms each claim a share of output, and when inconsistent claims exceed the available product, the price level arbitrates. The present framework can be read as radicalizing this insight one step further. Distributional claims that outrun measured creation are, in our vocabulary, unaccounted α-assignments — the market’s pricing of asset speculation before 2008 was a captured α in this sense — so conflict inflation becomes a special case of consensus distortion (Mode B). What the conflict tradition lacked was an accounting layer in which the distortion could be measured; what the present framework adds is instrumentation: the deviation αdi − αti is in principle observable, auditable, and attributable, which converts distributional struggle from an irreducible macroeconomic fate into a governable — though still political — object.

2.2. Anchors of Money: Endogenous Money, Sovereign Money, Physical Standards, and Mission Orientation

Post-Keynesian endogenous-money theory established that the money supply is created endogenously by credit demand (Lavoie, 2014), correctly dissolving the myth of the exogenous money multiplier, but it left unsolved the matching problem between endogenous money and value creation — credit can flow into speculative assets while corresponding to no order creation at all. Modern Money Theory locates the ontology of sovereign money in tax-driven mechanics (Kelton, 2020; Wray, 2015); its policy implication of functional finance is fundamentally asymmetric between reserve-issuing and non-reserve-issuing countries.

The physical-standard lineage is the closest structural relative and must be confronted head-on. Soddy (1926) proposed anchoring money to the flow of available energy; the technocracy movement’s energy certificates (Technocracy Inc., 1934) carried the proposal to a concrete denomination; Kümmel (2011) later showed that exergy input earns its place in estimated production functions. The present framework shares the premise that money should answer to physics and rejects the shared conclusion that energy throughput is the right physical quantity: energy consumed is as compatible with waste as with order, so the anchor must be the net order increment, with energy as one factor and the ecological entropy debt of its source deducted at the accounting point (the operationalization is Definition 1 of Section 3, inherited from Cheng and Cheng (2026d, Section 4.2), and restated there in place). Gesell’s (1916) stamped scrip, discussed sympathetically by Keynes (1936, ch. 23) and tested briefly at Wörgl in 1932–33 (Douthwaite, 1996), supplies the ancestor of our metabolism rate δ; the differences are that δ is constitutionally bounded, calibrated through democratic procedure, and avoidable through the Civilization Time Bank rather than unconditionally levied (Section 4.6 and Section 6.2). Mazzucato (2018), finally, made the case for mission-oriented public investment, with the state as risk-taker and direction-setter; the GPF mechanism of Section 6 is closely aligned with that position and can be read as a globalization of mission-oriented capital at the level of the value anchor. Against all four traditions, the present framework differs in the origin of money creation: money is created neither by credit demand (post-Keynesian) nor by sovereign fiscal authority (MMT), nor against raw energy throughput (the physical standards), but by consensus-weighted net order creation itself — value creation creates money, not credit demand.

2.3. The Measurement-Critique Tradition: The GDP Dispute and Value Accounting

The critique of national accounts shows that a dominant system of value measurement can itself become a source of economic failure: GDP records destructive activities and remedial expenditure as equal contributions and records ecological overdraft at zero cost (Coyle, 2014; Stiglitz et al., 2009). The present paper shares with this tradition the premise that measurement determines governance, but moves in the opposite direction. The GDP critique points at the falsity of existing measurement; we ask the converse question — if the measurement system were honest, taking recomputable order creation as its object, could macroeconomic pathologies such as inflation be eliminated at the level of causation rather than managed at the level of symptoms? In other words, we rewrite inflation theory from “aggregate dynamics under a given measurement system” into “the dynamics of the measurement system’s integrity.”

3. The Analytical Framework: A Four-Layer Price-Formation Structure and the Full Monetary Life Cycle

The task of this section is to lift the microeconomic value theory of the first paper (Cheng and Cheng, 2026d) into a macroeconomic price-formation framework. The system consists of four layers — measurement, calibration, issuance, and extinction — and the failure of each layer corresponds to one class of inflationary causation. Together the four layers support the complete life cycle of the currency. In keeping with the self-containment declaration of Section 1, every inherited element is restated where it enters.

Definition 1 (measurement layer). The Contribution Real-time-accounting Network (CRN) computes, for each value-creation event τ, the negentropic value Wτ = √(Eτ·Tτ·Iτ), where Eτ is the net negentropy flow (physical efficiency net of ecological entropy debt), Tτ is non-equilibrium maintenance time, and Iτ is structural information gain, measured counterfactually as the normalized Kullback–Leibler (KL) divergence closed by the event: Iτ = max{0, D_KL(p_cf‖p_ref) − D_KL(p_final‖p_ref)}/H_ref, where D_KL(·‖·) is the KL divergence, p_cf the distribution the field would have realized under the no-intervention counterfactual, p_final the realized post-event distribution, p_ref the accepted knowledge-base reference distribution, and H_ref its entropy. For a discovery, the counterfactual coincides with the pre-event distribution; for a maintenance event, the divergence that would have accumulated absent the intervention counts as gain. The unit of evaluation is the activity event within a time window, and events are aggregated over disjoint activity sets and non-overlapping windows under the aggregation axiom (Axiom 3) of the first paper, the approximation error of any residual interaction terms being bounded by ε·n(n − 1)/2. The output of the measurement layer is an objective quantity in the following precise sense: any third party can independently recompute it under stated public conventions. (This restates the operationalization of Cheng and Cheng (2026d, Section 4.2), including the counterfactual construction of Iτ, the open positive orthant domain of the value function with its continuous boundary extension, and the minimax calibration a = 1/2; the construction of the three factors and their error budget are not re-derived here.)

Definition 2 (calibration layer). The consensus coefficient ατ ∈ [0, 2] is determined by the Civilization Progress Preference Algorithm (CPPA) through a three-stage procedure of Delphi survey, agent-based simulation, and parliamentary review, expressing society’s relative preferences among categories of value creation. The output of the calibration layer is a democratic quantity: it carries value judgments, and its legitimacy derives from procedure rather than objectivity. (The α normalization convention used below — α is a weight vector, W-weighted and normalized to unit mean — is stated here for self-containedness; it is inherited from the first paper’s general-equilibrium section.)

Definition 3 (issuance layer). Money issuance follows the proof-of-contribution principle:

M = (Σi Wi × αi) × ks, ks ∈ [0.95, 0.98]

(1)

where ks is the macrostability coefficient, whose function is to smooth the short-run purchasing-power fluctuation that an explosive growth of W output under technological breakthrough could induce (a value buffer pool). The only legitimate inputs of the issuance layer are the outputs of the measurement and calibration layers; any issuance deviating from equation (1) is issuance corruption.

Definition 4 (extinction layer). The death of money mirrors the death of value: negentropy is born in creation and dies in consumption and depreciation; money is born in issuance and dies in the clearing of consumption events. Extinction proceeds along three paths according to the type of value. First, consumption-triggered extinction: when a consumer purchases a final consumption good or service through the platform, the money paid is not transferred to the producer — the producer’s remuneration was already issued at the moment of creation — but is canceled at the platform’s clearing node. For example, a designer completes a design with Wτ = 4×10⁴ √(J·s), and the platform issues 4.4×10⁴ NVC to her (ατ = 1.1); when a consumer buys the product at its civilization cost price and consumes it, the money the consumer pays is canceled by the platform. Money lives and dies with value in a closed cycle of “issued at creation, canceled at consumption.” Second, amortized extinction of durables: the negentropic value of durable goods and infrastructure erodes with physical depreciation, and the corresponding money is canceled in installments on the same depreciation schedule — a building that provides fifty years of housing service has its corresponding money extinguished over fifty years, in step with the physical erosion of the value stock. Third, persistence of non-rival value: knowledge and ecosystems undergo no consumptive death, and the corresponding money persists, accumulating in step with civilization’s value stock. The intrinsic metabolism rate δ (Section 6.2) serves above these paths as the basal-metabolism backstop, absorbing the extinction demand of residual off-platform circulation, untracked depreciation, and hoarding motives. The issuance layer and the extinction layer together constitute the complete life cycle of the currency — a bionic closed loop of photosynthesis and decomposition.

A walkthrough of the closed loop in six stages. Taking the end-to-end demonstration of the Global Brain Science Program from the first paper (Cheng and Cheng, 2026d, Section 11.2; restated here in outline: a research team completes a theoretical model, the CRN computes its three factors, audit cross-validates the inputs), the complete life cycle of money closes along six stages:

Stage 1, creation and accounting. A research team completes a theoretical model. The CRN perception layer computes Eτ (green-power server energy and itemized metering of fMRI, EEG, and optogenetics rigs), Tτ (flow-state time computed under trusted-execution-environment privacy computing), and Iτ (the structural information gain of the theoretical model, measured against the no-intervention counterfactual of the field’s knowledge base), yielding Wτ = √(Eτ·Tτ·Iτ). The audit layer cross-validates energy reports against laboratory logs, and highly controversial results go to interpretive-community review.

Stage 2, platform issuance. The platform issues M = Wτ×ατ×ks according to equation (1) — in the demonstration, basic research enters the α ≥ 0.9 regime by CPPA consensus, with ατ = 0.95 — and credits the creators’ accounts; the issuance record is committed to the chain.

Stage 3, distribution to creators. The issued amount belongs in full to the creating individual or team. Where AI participates deeply in the creation, the 70/30 protocol applies (70% to the designers, trainers, and maintainers of the AI system, 30% compulsorily allocated to the Global Public Value Fund in return for the data commons and the open-source ecology). No tax is withheld — the system has abolished the tax instrument.

Stage 4, circulation. The holder puts the money to three uses: purchasing means of life and production within the platform at the dual price of civilization cost price (CCP) plus a market floating price (MFP) bounded to ±30%; depositing in the Civilization Time Bank (CTB), converting it into a revenue share of long-horizon strategic projects (patient capital); or subscribing to equity certificates of high-α projects.

Stage 5, aggregation at the platform. In every consumptive purchase, the money paid by the buyer is aggregated into the platform’s clearing pool — not transferred to the seller, because the seller’s remuneration was completed at issuance. The platform is thereby the estuary of money.

Stage 6, extinction. The clearing pool cancels the aggregated money along the three paths of Definition 4 — cancellation upon consumption, amortized cancellation on depreciation schedules, and no cancellation for knowledge-type value; the δ metabolism rate absorbs the untracked residual.

The loop thus returns to Stage 1: the issuance space vacated by extinction is filled by new value creation, and the money stock satisfies the stock identity (1′) at every instant. Of the six stages, the first two are the birth of money, the middle two its career, and the last two its death — birth, career, and death are all anchored to the real physical process of value. This is the morphological dividing line between the present system and every historical form of money.

The stock identity. Let I(t) be the issuance flow in period t (= ks·Σ over creation events of Wα), X(t) the extinction flow (= ks·Σ over consumption and depreciation events of Wα), and V(t) the surviving negentropic value stock. The event-mirroring of issuance and extinction gives dM/dt = I(t) − X(t) = ks·dV/dt, and hence, at every instant t,

M(t) = ks·V(t)

(1’)

The correspondence between the money stock and the value stock holds not merely as a single-period flow but as a stock, at every point in time. This supplies the stock foundation for the quantity-identity mechanism of Section 4.2 and for Proposition 0. If there were issuance without extinction, the money stock would accumulate monotonically while the value stock does not, and M/V would decouple again — the extinction layer is precisely the structural component that seals this residual inflationary channel.

The policy meaning of the four-layer structure is immediate: stabilizing the general price level does not require regulating “the money supply”; it requires maintaining four integrity conditions — the measurement layer unfalsified, the calibration layer uncaptured, the issuance layer uncorrupted, and the extinction layer unfailing. Conventional monetary policy faces a black box, with an untraceable transmission chain between money and prices; the present framework faces a white box, in which every deviation of the price level can be located in one failure of one layer. This is the exact meaning of the shift from aggregate regulation to integrity maintenance.

4. The Principle-Level Mechanisms: Why Inflation Has No Locus of Generation in This Structure

Section 3 gave a static structural description; this section answers the deeper question — why anchoring to net order creation blocks inflation in principle, rather than merely supplying new instruments for managing it. We identify five mechanisms: the first four sever one deep transmission channel of traditional inflation each, the fifth separates relative prices from the price level, and a symmetric sixth seals the deflationary end. Together they support the strongest structural proposition of the paper (Proposition 0), whose exact scope — the accounting unit, not the experienced consumer price level — is stated with the proposition and analyzed in Section 4.7.

4.1. Temporal Synchrony: Ex-Post Issuance Eliminates the Value Gap

The inflationary seed of conventional credit money is buried in its temporal structure: credit issues money before value creation — money is a claim on future value, and whether that future value materializes is uncertain. When expected value fails to materialize, the total of monetary claims exceeds the total of realized value, and this value gap admits only two modes of settlement: default (financial crisis) or rising prices (inflation). Inflation and crisis are thus two expressions of the same gap. Proof-of-contribution issuance reverses this temporal order: money is issued after value creation has been verified by the CRN, and each unit of NVC is a certificate of completed order creation, not a claim on future value. Claims and value are generated synchronously; the gap does not exist in principle. This can be read as a strengthened form of the real bills doctrine: money corresponds not merely to real transactions but to verified real creation — behind the issuance stands not a bill but an order increment itself.

4.2. The Quantity Identity: The Quantity Theory Turns from Approximation Into Construction

Let the total real value supply, measured in negentropy units, be V = ΣiWti, and define the accounting-unit price as the money price of a unit of negentropic value, P = M/V. In conventional systems, M and V are driven by mutually independent processes — M by credit expansion and fiscal needs, V by production — their decoupling is the norm, MV = PY is only an approximation, and the fluctuation of P cannot be excluded from within the system. In the present system, issuance follows equation (1): M ≡ ks·Σi(Wti×αti). Under the CPPA normalization convention (α is a weight vector, W-weighted and normalized to unit mean; restated from the first paper in Definition 2 above), Σi(Wti×αti) = ΣiWti = V, and therefore P ≡ ks — a published constant. By the stock identity (1′) of Definition 4, this correspondence is lifted from the single-period flow to the stock at every instant: M(t) ≡ ks·V(t). The quantity theory thereby turns from an empirical approximation into a construction identity: the synchronization of the money supply with real value creation is not a policy target but a constructed feature of the system. Inflation of the accounting unit requires the decoupling of M from V, and the only channels of decoupling within the structure are accounting falsification (V falsely reported) and issuance corruption (M deviating from equation (1)) — which converts the inflation problem once and for all from a problem of policy discipline into a problem of integrity maintenance. What this identity does not by itself settle is the purchasing power of the unit over a changing basket of goods; Section 4.7 takes up that question.

4.3. Channel Excision: The Three Engines of Traditional Inflation do not Exist

Even granting the identity, the skeptic will ask whether the system retains the transmission channels of traditional inflation. Inspection shows that all three main engines are structurally removed. First, the fiscal-monetization channel: the issuance rule has no discretionary interface, public expenditure is allocated by the GPF from the already-issued stock, and no government can create money for spending — the inflation tax, the oldest and most concealed engine of inflation, is institutionally impossible. Second, the credit-multiplier channel: the system knows neither fractional reserves nor debt money, the money multiplier is identically one, and the chain of credit expansion, asset bubble, and debt crisis loses its starting point. Third, the interest-burden channel: interest on debt contracts is abolished in favor of revenue sharing under the creative-capital theory, and the compound-interest structure no longer compels the money supply to expand exponentially — the hidden inflationary pressure of scarcity-anchored money, in which interest demands continuous monetary growth on pain of cascading default, disappears with it. The removal of the three engines is not a regulatory prohibition, which can be evaded, but a structural absence: the corresponding institutional positions do not exist.

4.4. Expectation Self-Stabilization: Recomputability Replaces Commitment Credibility

The core transmission of modern inflation dynamics runs through expectations: inflation is self-fulfilling because the credibility of the anchor rests on institutional promises, and promises can always be doubted. Sargent’s (1982) lesson is precisely this — ending hyperinflation requires a credible regime switch. The present system substitutes recomputability for commitment as the basis of credibility: ΣW can be independently recomputed by any third party under public conventions, and any deviation of M from equation (1) is in principle immediately observable, auditable, and attributable. Expectation anchoring no longer depends on trusting that the authority will keep discipline; it depends on anyone being able to verify whether discipline has been kept — the object of trust shifts from institutional character to public computability. Expectation-driven amplifiers such as wage–price spirals and panic buying draw their fuel from the uncertainty that the anchor might drift; recomputability removes that fuel. This is the completed form of Sargent’s insight, stated in Section 2.1: the commitment problem is not solved by a better promise but eliminated.

4.5. The Separation of Relative Prices from the Price Level

Supply-shock inflation, as in the oil crises of the 1970s, propagates in conventional systems from cost push to a rise in the general price level. In the present system, a real shock changes the relative structure of W and α across sectors, and is expressed through the dual-pricing mechanism — the CCP anchor plus the MFP band of ±30% — as a relative-price adjustment, while the accounting unit is locked by the identity. Baumol-type structural inflation is handled the same way: intersectoral productivity differences are absorbed by α revaluation into relative-price signals rather than diffusing into aggregate inflation. The point of the distinction is that relative-price changes are information, the signals necessary for resource allocation, whereas price-level changes are noise, a distortion of the unit of account. The institutional design leaves the former entirely free and sets the latter to zero by construction — with the scope qualification of Section 4.7 kept in view.

4.6. The Symmetric Mechanism: The δ Metabolism Rate Seals the Deflationary end

Stability is bidirectional: the symmetric failure of inflation is the hoarding-driven deflationary spiral. The zero storage cost of digital money makes indefinite hoarding possible, and a fall in velocity can amplify itself into a deflationary trap. The intrinsic metabolism rate δ, the basal layer of the extinction structure of Definition 4, imposes a mild, public, and avoidable holding cost on idle balances, keeping velocity in the active band; the CTB offers savings an exit that does not break the value correspondence — savings are converted into revenue shares of strategic projects rather than withdrawn from circulation as dead hoards. The inflationary end is sealed by the identity and the deflationary end by the metabolism rate; bidirectional stability is thereby closed.

Intellectual honesty requires locating δ in its lineage. A holding charge on idle money is Gesell’s (1916) stamped scrip, which Keynes (1936, ch. 23) judged to contain the germ of a sound idea, and which the Wörgl experiment briefly embodied in practice (Douthwaite, 1996). Three design features distinguish δ from its ancestor. First, avoidability: a holder can escape extinction entirely by depositing in the CTB, converting the charge from a tax on liquidity into a redirector of saving toward patient capital; Gesell’s stamp admitted no such exit. Second, boundedness: δ is constitutionally confined to a calibrated band (0.5%–1%) and adjustable only through the parliamentary procedure of the companion governance paper (Cheng and Cheng, 2026c) — restated in one sentence: parameter changes require a simple majority in each of two chambers, a randomly drawn citizens’ house and a peer-reviewed experts’ house. Third, embedding: δ does not stand alone but serves as the residual absorber beneath the three tracked extinction paths of Definition 4, a role no earlier demurrage currency contemplated because none had an extinction layer. The claim is continuity with redesign, not invention ex nihilo.

The mechanism also has a quantitative limit, which earlier versions left implicit and which we now state as a proposition, because it disciplines the role δ can play.

ΔX(t+1) = (1−δ)·ΔX(t) + ℓ·C(t)

(4)

Proposition 0a (viability condition for the metabolism backstop). Let a share ℓ of consumption spending escape platform tracking each period, generating an extinction gap that accumulates according to (4), with the value stock growing at rate gV and consumption C(t) = c·V(t). Then the overhang ratio d(t) ≡ ΔX(t)/V(t) converges to d∗ = ℓc/(gV + δ), and the deviation of the accounting-unit price from its constant, |P − ks|/ks = d/(1 + d), remains within a pre-registered tolerance ε if and only if ℓ ≤ ε(gV + δ)/c. Proof. Dividing (4) by V(t+1) = (1+gV)V(t) gives the contraction d(t+1) = ((1−δ)/(1+gV))·d(t) + ℓc/(1+gV), whose unique fixed point is d∗; the convergence factor (1−δ)/(1+gV) is below one whenever δ > −gV. □

The proposition quantifies what was previously a qualitative caveat. With δ = 1%, trend value growth gV = 2%, a consumption share c = 0.6, and a tolerance ε = 1%, tolerable untracked leakage is ℓ ≤ 0.05% of consumption spending. The δ backstop is thin: platform coverage, not metabolism calibration, is the load-bearing defense of the extinction layer, and a constitution implementing this system should specify coverage floors with the same seriousness as parameter bands. The fifth limitation of Section 10 is thereby converted from a caveat into a checkable engineering requirement.

Proposition 0 (constancy of the accounting unit, stock form). Under the integrity conditions (i)–(iv) (Section 5.3) and the α normalization convention, M(t) ≡ ks·V(t) holds for all t, and the accounting-unit price P(t) = M(t)/V(t) ≡ ks is a published constant; any persistent change of P occurs if and only if some integrity condition fails. Proof: the issuance–extinction mirroring of Definition 4 yields the stock identity (1′); substitution into P = M/V completes the proof. □

Scope of Proposition 0. The proposition is a construction identity about the unit of account, and we present it as exactly that. It asserts that the money price of one unit of measured negentropic value cannot drift while integrity holds; it does not assert that the money price of a basket of consumer goods is constant, because the negentropic content of a given basket changes with technology, preferences, and the composition of the value stock. Whether the experienced price level inherits the unit’s stability is a further question, taken up in Section 4.7, and the answer turns out to be conditional rather than definitional. Earlier drafts of this program blurred the two claims; the present version treats the distinction as load-bearing.

4.7. The Accounting Unit and the Experienced Price Level

Define the experienced consumer price level as a conventional index over consumption goods, CPI(t) = Σj ωj(t)·pj(t), where pj(t) = CCPj(t)·(1 + mj(t)) is the dual price of good j, CCPj is its civilization cost price denominated in negentropy units and converted to money at the unit price ks, mj ∈ [−0.3, +0.3] is the market floating premium, and ωj are expenditure weights. Three observations discipline the analysis. First, the MFP band bounds the contribution of premium movements: even if every mj swings from one rail to the other, the mechanical effect on CPI is bounded by the band width, roughly ±30% at the extreme and far less under independent movements; the band converts unbounded price-level drift into bounded relative-price noise. Second, the CCP anchor moves only when the measured negentropic content of goods changes — productivity gains lower CCPj as the same basket embodies less ordering effort per unit of service, so the dominant long-run force on the index is benign deflation of cost prices, the mirror of technological progress, rather than monetary debasement. Third, the composition condition is the real residual risk: if the value stock V(t) grows in directions distant from household consumption needs (say, an epoch of α-weighted megaprojects), the money stock grows with it while the consumption basket stagnates, and the CPI can then rise through premium congestion at the upper rail of the band even with P ≡ ks intact. We state this as a condition to be monitored — the alignment between the composition of α-weighted creation and the composition of consumption demand, itself an observable, auditable quantity — rather than as a defect discovered by critics. The governance implication lands in the calibration layer: consumption-relevance indicators belong in CPPA’s dimension mapping, and the companion governance paper assigns exactly this monitoring to the audit committee’s quarterly audits (Cheng and Cheng, 2026c).

What this section buys the framework is precision. The slogan “price-level constancy is a construction identity” survives only for the accounting unit; for the experienced price level the claim is weaker and empirical — bounded premium noise, technology-driven benign drift of cost prices, and one named residual risk with a named institutional monitor. We regard this division of claims as the minimum an honest macrostability theory owes its readers.

πCPIMFP ≤ m̄·(1 − A(t)), A(t) ≡ Σj min(sjc, sjd)

(5)

Proposition 0b (composition bound on experienced inflation). Let sjc be the α-weighted creation share of consumption class j and sjd its consumption-demand share, and define the alignment index A(t) ≡ Σj min(sjc, sjd) ∈ [0,1]. Suppose the market premium responds to class-level excess demand as mj = min(m̄, κ·max(0, sjd − sjc)) with sensitivity κ and band half-width m̄ = 0.3. Then the premium-driven component of experienced inflation satisfies (5), and the residual driver of CPI drift is the drift of civilization cost prices — negative under sustained technical progress. Proof. Since Σj sjc = Σj sjd = 1, the total shortfall mass is Σj max(0, sjd − sjc) = 1 − A; each shortfall class contributes at most m̄ to the premium component, weighted by its expenditure share. □ The bound is sharp in the limiting sense that full misalignment (A = 0) permits premium-driven drift up to the full band half-width — which is precisely why the composition monitor (the audit committee’s seventh duty, in the third paper’s terms: tracking the alignment between α-weighted creation and consumption demand) is a stability institution rather than an ornament.

Remark (domain of the composition bound, added after computational testing). The grid test of Appendix D.4 finds that bound (5) holds exactly in the domain κ·H ≤ m̄, where H = Σj (sjd)² measures demand concentration, and is violated exactly outside it; a sufficient general condition is κ·smaxd ≤ m̄, with the corrected bound πCPIMFP ≤ κ·smaxd·(1 − A(t)) applying where the condition fails. The composition monitor’s trigger is thereby set by demand concentration as well as by alignment — a strengthening of the monitor rationale, at the price of qualifying the bound.

5. Inflation as System Failure: The Formal Model

5.1. The Inflation-Rate Identity

Let the true negentropy creation of the period be {Wti} with true consensus coefficients {αti}; let the creation recorded by the accounting system, possibly including falsified components, be {Wfi + Wti}, and let the consensus coefficients actually in force, possibly distorted, be {αdi}. Define the inflation rate as the relative excess of distorted issuance over true issuance:

π = (Σi Wfi×αdi − Σi Wti×αti + ΔX) / (Σi Wti×αti)

(2)

where ΔX is the money that should have been extinguished but was not (the extinction gap). Equation (2) is an identity, not a behavioral equation: given the issuance structure P = αW, the deviation of the price level from its true-value benchmark equals by definition the deviation of the money stock from its true correspondence. The theoretical content lies in the causal analysis of the failure terms on the right-hand side (Section 5.2) and in the governability argument (Section 5.3). The inflation rate defined here pertains to the accounting unit; its translation into experienced CPI movements passes through the mechanism of Section 4.7.

5.2. Four Failure Modes

Mode A (accounting falsification, Wf > 0). The CRN suffers contamination, collusive attack, or design defects, and falsified negentropy creation obtains issuance. The epistemic basis is information asymmetry: without multi-node cross-validation, malicious agents can fabricate order creation. An illustrative scenario: an organization tampers with sensor data, fabricates an ecological-restoration negentropy of Wf = 5×10⁷ √(J·s), and obtains the corresponding issuance.

Mode B (consensus distortion, αd > αt in low-value domains). The α coefficients are captured by vested interests or fall into populist error, assigning excessive premia to rent-seeking, speculation, or low-value repetitive production. The theoretical basis is public-choice theory (Buchanan and Tullock, 1962): interest groups influence public decisions through lobbying and bend α away from the public interest. An illustrative scenario: the true coefficient αt = 0.2 of a heavily polluting chemical industry is raised to αd = 0.8, and the industry’s falsely weighted creation reaches 1×10⁸ √(J·s).

Mode C (issuance corruption). The issuance stage deviates from equation (1) — over-issuance for fiscal purposes (the residual temptation of the inflation tax) or political manipulation of ks. Mode C is excluded in principle by the design of a built-in issuance rule with no discretionary interface, but we do not assume it impossible — it corresponds to the link most difficult to eradicate in real institutional design, and is listed separately for that reason.

Mode D (extinction failure, ΔX > 0). Value has been consumed or depreciated while the corresponding money is not canceled: off-platform black-market transactions bypass the clearing node, depreciation schedules are manipulated, consumption records are concealed — each leaves the money stock in excess of the surviving value stock, producing overhang inflation. This is the only one of the four modes driven by stock dynamics rather than flow events. Its governance rests on the fact that the extinction layer and the measurement layer share one infrastructure: consumption-clearing records and CRN verification use the same blockchain notarization, and the extinction gap ΔX is itself an auditable quantity, with the δ metabolism rate continuously absorbing extinction demand that precise tracking misses.

5.3. Propositions

Proposition 1 (a sufficient condition for zero inflation). If the four-layer integrities hold simultaneously — (i) Wfi = 0 for all i (accounting unfalsified); (ii) αdi = αti for all i (consensus undistorted); (iii) issuance strictly follows equation (1) (issuance uncorrupted); (iv) ΔX = 0 (extinction unfailing) — then π = 0. Proof: by equation (2), the four conditions set the numerator to zero. □

Proposition 1 is elementary, and its significance is classificatory rather than mathematical: it converts the problem of inflation governance entirely into a problem of integrity maintenance — there is no fifth class of inflationary causation for the accounting unit. Every observed persistent rise of P must be locatable in one of (i)–(iv). The contrast with the quantity theory is instructive: in the quantity theory an untraceable transmission mechanism stands between “excess money” and “the real economy,” whereas every term of equation (2) corresponds to an auditable operational object.

Proposition 2 (monotonicity and structure of consensus distortion). Suppose only Mode B occurs (Wf ≡ 0). Then π is a weighted linear function of the distortions (αdi − αti) across domains, with weights equal to each domain’s share of true weighted creation in the total; and the partial derivative of π with respect to any domain’s distortion is non-negative. Proof: direct partial differentiation of equation (2). □

A corollary of Proposition 2 deserves emphasis: the sensitivity of the inflation rate to distortion concentrates in high-weight domains. A distortion of 0.1 in a domain accounting for 30% of total issuance is equivalent to the same distortion in thirty domains of 1% each. This yields an allocation principle for regulatory resources: consensus audits should be ordered by domain issuance weight, not spread uniformly across domains by count.

Proposition 3 (existence of a buffering bound for ks). Let the true creation total grow at rate g in some period owing to a technological leap (a disruptive technology raising ΣW by g×100%), with issuance following equation (1) and ks adjustable within [0.95, 0.98]. Then for any g ≤ (1 − ks)/ks there exists a value of ks such that the money-supply growth rate does not exceed the level implied by 1 − ks; specifically, the issuance growth rate equals (1+g)·ks − 1, and issuance does not expand when ks ≤ 1/(1+g). For larger shocks with g > (1 − ks)/ks, the buffering capacity is exhausted and the residual fluctuation must be absorbed by the calibration layer (the pacing of α adjustment) and the functional anchor (countercyclical GPF investment). Proof: direct computation from equation (1). □

Proposition 3 delimits the capacity of ks: it can absorb output shocks on the order of 2% to 5.3% (ks = 0.98 corresponds to g ≤ 2.04%; ks = 0.95 to g ≤ 5.26%); shocks beyond this range require an institutional response. Stating this boundary honestly matters — we do not claim that ks is an all-purpose stabilizer; it is the first and the smallest line of defense.

ks∗ = Π 0.95, 0.98

(6)

Proposition 3a (optimal buffering under stochastic shocks). Let the technological-shock rate g be random with finite second moment, and take as the loss of a buffering choice the expected squared deviation of gross issuance growth from unity, L(ks) = E[((1+g)ks − 1)²]. Then L is strictly convex in ks, and its unique minimizer, projected onto the constitutional band, is given by (6). Proof. L is quadratic in ks with leading coefficient E[(1+g)²] > 0; setting the derivative to zero gives the unconstrained minimizer E[1+g]/E[(1+g)²], and projection onto [0.95, 0.98] preserves uniqueness. □ The band earns its keep in the result: when the unconstrained optimum falls below 0.95, shocks are too large for the first line of defense, and the residual passes to the calibration layer exactly as Proposition 3 describes.

6. Macrostability Mechanisms

6.1. The Cycle form Reconstructed: The Technology–Consensus Co-Evolution Cycle

In the present system the traditional financial–debt cycle loses its basis, since there is no interest and no credit-expansion mechanism built on debt contracts. The dominant form of fluctuation is reconstructed as the technology–consensus co-evolution cycle:

cycle amplitude = f(ΔT, Δα) = k1ΔT + k2Δα + k3ΔT×Δα

(3)

where ΔT ∈ [0, 2] is the intensity of technological paradigm revolution (1 for baseline progress, 2 for disruptive revolution) and Δα ∈ [0, 1.5] is the amplitude of consensus adjustment (1 for routine adjustment, 1.5 for major reorientation). The interaction term k3ΔTΔα captures the mechanism by which technological revolution forces consensus revaluation — a breakthrough in strong AI revalues the W of traditional labor — while the lag of consensus revaluation amplifies the structural pains of the technological shock. Compared with real business cycle theory (Kydland and Prescott, 1982), the present model grants technology shocks their central place but rejects the setting in which the shock is a purely exogenous physical event: the economic consequence of a technology shock depends on the response function of social consensus, and the consensus response can be smoothed by institutional design, namely the three-stage procedure.

A minimal linear reduction gives the claim quantitative content. Let a technology shock decay at rate λT, and let consensus adjust toward the level the shock implies at speed η, with coupling coefficient k3 from (3). The linearized (ΔT, Δα) system oscillates if and only if (λT − η)² < 4ηk3ΔT̄, where ΔT̄ is the mean shock intensity: slow consensus adjustment relative to shock-coupling strength produces oscillation, and sufficiently fast — though not instantaneous — adjustment damps it. The three-stage pacing of α adjustment thereby acquires a stability-theoretic meaning: its conservatism is a damping parameter, and the oscillatory regime corresponds to the non-monotone labor-supply scenario of the first paper’s general-equilibrium analysis (Cheng and Cheng, 2026d, Section 8, Scenario 2) — restated here: if learning effects bend an activity’s labor-supply curve backward, α-adjustment oscillates with amplitude entering the welfare-loss bound quadratically — rather than to an unspecified malfunction.

6.2. Four Embedded Stabilizers

The objectivity anchor (accounting). Wτ rests on the cross-validation of physical energy data, time records, and information gain, and depends on neither financial expectations nor subjective judgment. The causal path: objective accounting → truthful value information → undistorted resource allocation → fewer sources of fluctuation. This is the first line of defense, corresponding to condition (i) of Proposition 1.

The procedural anchor (consensus prudence). Adjustment of α passes through the three-stage procedure of Delphi survey, ABM simulation, and parliamentary review, preventing sharp-turn consensus swings. The causal path: prudent adjustment → stable incentive signals → stable expectations → smooth resource allocation. This corresponds to condition (ii) of Proposition 1 and acts directly on the Δα term of equation (3) — the function of the procedure is to confine the rate of change of Δα within the system’s absorptive capacity.

The functional anchor (countercyclical GPF investment). In periods of consensus disorientation or structural adjustment, the Global Public Value Fund expands countercyclical investment in high-α strategic domains such as basic science and ecological restoration. The resemblance to Keynesian countercyclical policy is superficial: the Keynesian instruments are fiscal expenditure and the interest rate, addressed to an undifferentiated aggregate demand, whereas the GPF’s instrument is directed investment ordered by α, addressed to the value-creation capacity of strategic domains. The causal path: countercyclical investment → stability of strategic domains → uninterrupted creation incentives → structural adjustment does not escalate into crisis.

The social anchor (UBI as demand floor). Unconditional basic income guarantees the basic life of individuals; it is funded by the issuance corresponding to negentropic value created by or with AI — not by taxation or debt — and its amount adjusts dynamically with civilization’s total negentropy creation. The causal path: the UBI floor → basic needs met → stable basic consumption → fluctuations cannot amplify themselves along the spiral of shrinking demand and shrinking creation.

The four stabilizers cooperate as layered defenses: the objectivity anchor reduces the sources of fluctuation, the procedural anchor smooths the process of adjustment, the functional anchor absorbs structural shocks, and the social anchor blocks crisis transmission. The theoretical dialogue is with the binary opposition of Keynesian demand management and neoclassical spontaneous equilibrium: the present system replaces that opposition with consensus guidance on the supply side (α) plus institutional floors on the demand side (UBI and the GPF), and it accords with the notion of resilience in complex-systems science (Holling, 1973) — stability is not the maintenance of a static equilibrium but the dynamic capacity of a system to preserve its core functions under shock.

6.3. The Transition Window: When the Structural Absences are not yet Structural

Section 4.3 and Section 6.1 describe a system in which the three traditional engines of inflation — credit multiplication, interest-rate transmission, and discretionary issuance — do not exist. During any realistic transition, however, the new unit coexists with legacy money, and the engines are absent only in proportion to adoption. Let σ(t) ∈ [0,1] denote the share of transactions settled in the new unit. The hybrid economy’s effective credit multiplier is then μeff = σ + μold(1−σ), the interest channel operates on the legacy share, and the integrity claims of Section 5 apply only to the new-unit circuit.

dσ/dt = σ(1−σ)·(uN(σ) − uT), uN(σ) = u0 + βσ − δω

(7)

Proposition 4 (transition tipping point). Suppose adoption follows the replicator dynamic (7), where uN(σ) is the utility of transacting in the new unit — comprising a base utility u0, network benefits βσ, and the holding-cost burden δω, with ω the average idle-balance share — and uT is the utility of the legacy alternative. If β > 0 and u0 − δω < uT < u0 + β − δω, there exists a critical coverage σc = (uT − u0 + δω)/β ∈ (0,1) such that adoption converges to full coverage whenever σ(0) > σc and collapses to zero whenever σ(0) < σc. Proof. The dynamic has equilibria at σ = 0, σ = 1, and σ = σc; the sign of dσ/dt on each side of σc gives instability of the interior equilibrium and stability of the two corners. □

Corollary (transition policy). The metabolism rate enters the tipping point positively: ∂σc/∂δ = ω/β > 0. During the transition window, δ should therefore sit at the bottom of its band — or be suspended by explicit constitutional clause — until coverage passes σc, after which it can be phased in. Symmetrically, anchor demand created by public procurement and GPF disbursement in the new unit raises u0 and lowers σc: the state’s own settlement choices are the cheapest credibility investment available in the transition.

The corollary formalizes a point the trilogy’s political-economy discussion had left at the level of intuition (Cheng and Cheng, 2026d, Section 14 — restated: the blocking coalition’s expected return turns negative once pilot success probability passes a threshold, so transition viability is a coverage race with a computable tipping point): the design parameters that are virtues in steady state — the holding cost above all — are liabilities before it.

7. Integrity Sealing as Constitutional Engineering

7.1. Integrity is a Maintained Stock, not an Assumed State

The failure-mode inventory of Section 5 has a design implication that distinguishes this framework from both commodity-money nostalgia and fiat-money conventionalism: integrity is not a property a unit either has or lacks at birth, but a stock that depreciates unless continuously maintained. Formally, let Q(t) ∈ [0,1] denote the integrity stock of the unit’s issuance-measurement chain, depreciating at rate ρ under adversarial pressure and replenished by maintenance expenditure m(t) (audit capacity, sensor redundancy, ledger reconciliation):

dQ/dt = −ρQ + φm, Q(0) = 1

(8)

The four failure modes are then states of the world indexed by the level and distribution of Q across the chain’s links: Mode A is low Q at the measurement link, Mode B low Q at the calibration (consensus) link, Mode C low Q at the issuance link, and Mode D low Q at the extinction link. The structural seals of this section are constitutional devices for keeping φm cheap relative to the rents that deception would create — that is, for keeping the adversary’s incentive constraint, rather than the auditor’s budget constraint, the binding one.

This reframing matters for how the seals should be evaluated. A seal is not a rule that makes fraud impossible — no rule does — but a rule that makes fraud unprofitable ex ante and detectable ex post. The three seals below are each justified by showing that they move one or more failure modes across exactly that threshold.

7.2. Three Structural Seals

Seal 1 — Birth-locking (issuance is downstream of measurement). New units may be minted only against a verified increment of measured negentropy, Wτ, recorded on the Canonical Record of Negentropy (CRN) and ratified through the bicameral procedure restated in Section 4.6. The mint has no discretionary balance sheet: it cannot issue ahead of measurement, cannot lend the unit into existence, and cannot purchase assets with newly created units. Birth-locking directly removes the ledger link’s capacity for autonomous expansion — the mechanical precondition of Mode C — by making the ledger a record of measurement events rather than a source of them. It also converts Mode A from a monetary event into a measurement event: a falsified negentropy claim mints units, but those units are traceable to the specific measurement record, so detection and clawback are accounting operations rather than macroeconomic ones.

Seal 2 — Proliferation ban (no credit multiplication of the unit). Intermediaries may hold and transfer the unit, but may not create claims denominated in it that exceed their holdings; the unit circulates on a full-reserve basis by construction. This is the strongest seal and the one most likely to be criticized as sacrificing the credit-creation function of banking. The defense is architectural rather than nostalgic: under a stock identity M(t) ≡ ks·V(t), privately proliferated money-like claims are issuance outside the rule — the boundary form of Mode C — and the channel through which the valuation failure of 2008 became a monetary collapse (Section 8.4). Credit intermediation is not abolished — it is relocated to instruments denominated in the unit but explicitly not the unit: maturity-transforming claims that trade at floating prices and cannot be presented at par. The seal thus draws the line where the 2008 failure showed it must be drawn — between money and credit — and enforces the line at the protocol level rather than by supervision.

Seal 3 — Extinction loop (metabolism has a closed sink). The metabolism levy δ on idle balances flows to the Global Public-goods Fund (GPF) or is extinguished; it cannot be re-lent by the collecting authority, recycled into the issuer’s own balance sheet, or credited back to the taxed holders. The extinction loop is what makes the stock identity sustainable at the lower bound of ks: without a closed sink, the levy is a transfer rather than a metabolism, and the stock identity would require ever-finer adjustments of ks to remain satisfied. The loop also supplies the funding base for the measurement commons on which Seal 1 depends — audit capacity, sensor networks, and replication infrastructure are financed from metabolism, which makes integrity maintenance (m(t) in equation (8)) self-funding rather than a discretionary budget line that a captured legislature can starve.

The three seals are complements, not substitutes. Birth-locking without the proliferation ban invites the satellites to do the inflating off-ledger; the ban without birth-locking leaves the ledger itself discretional; either without the extinction loop leaves the stock identity without its balancing term. Section 8 reads four historical episodes as natural experiments in which exactly one or two of the seals were missing.

7.3. Demand Validation Under Ex-Post Issuance

The architecture’s most consequential operational feature is that issuance is ex post: units are minted only after the underlying value event has been measured and ratified. This inverts the sequence of fiat credit money (issue first, validate never) but creates a problem that credit money does not have — the validation lag. If measurement of a negentropy increment takes time τv, then during the window between the value event and ratification the economy contains real value V(t) with no corresponding unit stock: M(t) < ks·V(t) transiently, and the shortfall shows up as a liquidity squeeze concentrated in exactly the sectors generating new value.

The framework’s answer is a demand-validation instrument with three pre-committed features. First, a provisional claim is issued against a filed measurement record — tradable, interest-bearing, and explicitly junior: it is a bond against future units, not a unit. Second, provisional claims are haircut by a schedule h(τ) that increases with the age of the underlying measurement filing, so that delay is priced rather than subsidized; a filing that stalls in ratification sees its claims depreciate, giving the claimant a standing incentive to supply the evidence auditors need. Third, ratification is a terminal event: on ratification, provisional claims convert at par into newly minted units (minted at that moment, against the now-verified increment); on rejection, they convert at the haircut value into GPF obligations, so that the cost of a false filing is borne by the filer and the cost of a true-but-slow filing is shared with the system rather than dumped on the innovator.

Two properties of this mechanism deserve emphasis. It preserves Seal 1 (no units exist before measurement) while removing the liquidity squeeze that Seal 1 would otherwise cause; and it creates a market price — the discount on provisional claims — that continuously reports the system’s confidence in its own measurement pipeline. That price is the integrity stock Q(t) made observable; Section 9’s H4 uses exactly this logic, at country scale, to define its measurement-integrity proxy.

7.4. The Four-Layer Reward for Theoretical Discovery

Because issuance is downstream of measurement, the architecture must answer a question fiat systems never face: what induces agents to produce the measured negentropy in the first place — particularly the theoretical and scientific discovery whose negentropy is real, large, and hardest to meter? The framework’s answer is a four-layer reward structure, ordered by decreasing immediacy:

• Issuance reward. The verified discoverer receives newly minted units against the ratified increment — the direct monetary reward, bounded by the calibration protocol to avoid windfall concentration.
• Provisional-claim liquidity. During the validation lag, the discoverer’s filed claims trade in the market of Section 7.3, providing working capital before ratification.
• GPF dividend. Because metabolism funds the public-goods commons, the discoverer’s contribution raises the system’s measured V(t), which — through the stock identity — expands the unit stock and the GPF base from which all holders benefit; discovery is thus partially socialized by construction, at a rate set by ks and δ rather than by discretionary appropriation.
• Ratification standing. Repeated successful filings lower the filer’s haircut schedule h(τ) — a reputational asset with a direct monetary yield, which converts the integrity of a research program into collateral.

The four layers replace the patent system’s single, blunt instrument (temporary exclusion) with a gradient of rewards whose slope is set by measurement confidence rather than by legal monopoly. The design deliberately leaves the hardest problem — metering the negentropy of a theoretical result before its applications exist — to the calibration protocol of the first paper and the institutional capacity of the third; what this paper adds is the proof that, whatever the measurement noise at the discovery margin, the seals keep that noise from becoming monetary noise: an over-measured discovery mints traceable units against a specific record, and the clawback is an accounting event, not a crisis.

8. Historical Mappings: Four Episodes as Seal-Failure Case Studies

The episodes below are not econometric tests — the pre-registered test is Appendix E — but consistency checks: if the framework’s taxonomy is right, each canonical monetary disaster should be classifiable as the failure of a specific seal, and each episode’s observed mechanics should match the corresponding failure mode’s signature. They are presented in order of increasing structural subtlety.

8.1. Weimar 1923 and Zimbabwe 2008: Issuance Corruption (Mode C)

Both hyperinflations followed the textbook mechanics of issuance-rule collapse: the issuing authority’s ledger became autonomous from any anchor, the unit’s stock was expanded to finance state expenditure, and the unit’s accounting function (Proposition 0) was destroyed by the speed of the expansion itself. In the framework’s terms, both episodes are pure Seal-1 failures: no birth-lock existed, so issuance was upstream of — indeed, independent of — any measurement. The framework adds two observations to the standard account. First, in both cases the measurement link had not failed: real economic capacity (V in the identity) did not fall by the orders of magnitude the unit’s value did, which is exactly the Mode-C signature — the issuance ledger diverges from an intact reality. Second, both stabilizations (the Rentenmark 1923; dollarization 2009) worked by re-imposing a birth-lock — a binding rule connecting issuance to something outside the issuer’s discretion — not by repairing demand management. The episodes therefore discriminate between the framework and quantity-theory accounts in the framework’s favor on mechanism: what was restored in 1923 and 2009 was not confidence in the quantity path but a constraint on the issuance act itself.

8.2. Wörgl 1932: Metabolism at Small Scale (the δ Instrument)

The Wörgl experiment — a local scrip bearing a 1% monthly holding cost — is the closest historical analog of the metabolism parameter δ, and its documented effects match the framework’s predictions: velocity rose, local employment recovered against the national trend, and the scrip circulated where the official unit was hoarded. Two qualifications matter for design. The experiment operated at municipal scale, where the unit was a complement to rather than a replacement for the national unit; the transition analysis of Section 6.3 explains why that complementarity is precisely the regime in which a holding cost helps rather than hurts (σ near 1 locally, the legacy unit absorbing the store-of-value function). And the experiment’s termination — by central-bank legal action, not by economic failure — is a datum about institutional complementarity: a metabolism instrument requires constitutional protection of the kind Seal 3 provides, because its distributional victims (hoarders and the legacy issuer) are concentrated and well-organized while its beneficiaries are diffuse. The episode is thus evidence both for the δ instrument and for the necessity of embedding it beyond the reach of the legacy issuer’s veto — a point the third paper develops institutionally.

8.3. The 1970s Stagflation: Measurement Failure and its Consensus Misreading (Mode A)

The 1970s are the framework’s hardest case, because the seals that failed were not the obvious ones. The supply shocks were, in this framework’s vocabulary, a measurement-layer failure in the precise sense of Mode A: the accounting systems of the time registered neither the ecological entropy debt of energy extraction nor the changed time-structure of production, so measured value diverged from true value before any policy response was conceived. The policy error then compounded the measurement failure at the consensus layer: demand management treated a real re-pricing as a nominal gap, and the unit’s value absorbed the confusion. The primary lesion is therefore Mode A, with a Mode B overlay in the ratification of the misreading — and the episode is the hardest for this framework precisely because the seals assume the measurement pipeline’s outputs are correctly understood. The episode disciplines the framework in two ways. It motivates the dual-price construction (CCP and MFP) of the first paper, whose divergence is designed to make exactly this interpretive failure visible as a price signal rather than discoverable only ex post; and it motivates the demand-band ±30% corridor, which gives the system a pre-committed non-response region — a rule not to confuse re-pricing with instability — where discretionary consensus failed. The stagflation decade is thus the historical warrant for replacing discretionary interpretation with a banded rule, in the same sense that Weimar is the warrant for the birth-lock.

8.4. 2008: Captured Valuation and Boundary Proliferation (Mode B)

The 2008 crisis has two layers in this taxonomy, and both must be named. At the valuation layer it is the form consensus distortion (Mode B) takes within a scarcity-anchor system: a vast range of activities in the chain of structured derivatives was assigned high prices and high returns in the prevailing accounts while corresponding to no net order creation — the market-pricing system itself functioned as a captured α. At the monetary layer the distortion propagated through boundary proliferation: the satellites — asset-backed commercial paper, repo liabilities, structured tranches — issued money-like claims that traded at par until they did not, and whose aggregate stock had quietly become a multiple of the anchored base. In the stock identity’s terms, the effective M had drifted far above any ks·V while the measured M — the statistic supervisors watched — had not; the crisis was the violent re-convergence of the two. The framework’s reading again discriminates between mechanisms: what failed was not underwriting standards or leverage ratios, which are symptoms, but the boundary between the anchored ledger and its unanchored satellites — the absence of a proliferation ban enforced at the protocol level. Post-2008 reforms moved the boundary (central clearing, liquidity rules) but left it supervisory rather than structural; the framework’s claim is that a boundary policed by supervisors drifts, as 2008 showed it drifts, toward the regulated sector’s preferred perimeter, whereas a boundary enforced by the unit’s construction — the impossibility of par-valued satellite claims in the unit — does not. Section 9’s H6 and H5 test the band and extinction instruments under simulated replicas of exactly this shock structure.

9. Hypotheses and the Evidential Division of Labor

The paper’s empirical content is organized as six pre-registered hypotheses, and the division of labor among them is itself a methodological claim. Five of the six are executable in silico, because they are claims about the behavior of a specified mechanism; the sixth — H4 — is a claim about the world, which this paper executes only at the pre-registered baseline depth. The reason for that restraint is discipline, not omission: H4 requires a cross-country archival design whose variable construction, identification strategy, and decision rules must be fixed before the data are examined, and whose baseline execution this paper carries out (Appendix F), with the full estimator suite reserved for the follow-up empirical paper. Appendix E therefore contains H4’s complete pre-analysis plan, registered in the text here, so that the hypothesis enters the literature with its falsification conditions attached rather than as a rhetorical gesture.

H1 (unit convergence under shocks and attacks). Under simulated shocks to measured value V(t) — trend breaks, measurement noise, and adversarial falsification episodes — the accounting unit converges to the pre-registered tolerance band whenever platform coverage holds the viability condition; peak deviation responds to the falsified share with the near-unit slope predicted by the monotonicity proposition; and the stochastic audit layer restores band compliance after attack detection, all without discretionary issuer action. Status: executed; Appendix C.

H2 (the ks buffering bound). A permanent technological leap of magnitude g is absorbed by adjusting ks within its institutional band [0.95, 0.98] over the procedural lag whenever g does not exceed a critical value g∗, and every shock above g∗ leaves a residual deviation that grows monotonically — the signature of an exhausted buffer; the predicted critical interval is [2%, 5.3%]. Status: executed; Appendix D.

H3 (stabilizer decomposition). Under the standard falsification shock, ablating each of the four embedded stabilizers of Section 6.2 one at a time raises the cumulative unit deviation relative to the full system — every marginal contribution is positive — with the objectivity anchor carrying the largest contribution, as the pre-registered priority ordering predicts. Status: executed; Appendix D.

H4 (measurement integrity and monetary stability, cross-country). Across countries and over time, the integrity of a monetary system’s measurement-and-ratification chain — proxied by national statistical capacity and by institutional safeguards against ledger and consensus capture — predicts the stability of the unit’s accounting function (proxied by inflation volatility), conditional on standard monetary determinants. Status: executed in Appendix F against the complete pre-analysis plan registered as Appendix E (data sources, variable construction, identification strategy, and falsification rules). Formal verdict under the pre-registered decision rules: not confirmed — both integrity coefficients carry the predicted sign and pass the magnitude screen, but neither reaches significance in the available 2017–2024 panel, a null we report as underpowered rather than precise.

H5 (stock identity and the necessity of extinction). With the extinction layer active, the deviation of the money–value stock ratio from ks converges to the fixed point predicted by Proposition 0a within the pre-registered tolerance; with the layer deactivated, the deviation grows monotonically — a difference-in-mechanism test of the extinction layer’s necessity. Status: executed; Appendix D.

H6 (band and composition). Under alignment between creation shares and demand shares, the market premium remains inside the dual-price band; under concentrated misalignment, the share of goods congested above the pre-registered threshold respects the composition bound of Section 4.7. Status: executed; Appendix D, where criterion (ii) is partially falsified and the bound repaired, the repair reported rather than suppressed and folded back into the main text (Remark, Section 4.7).

Two features of this structure are load-bearing. First, the in-silico hypotheses are stated with corridor definitions and shock magnitudes fixed before simulation (Appendices C and D report the pre-set values alongside the results), so the simulations function as tests of the mechanism’s sufficiency, not as illustrations of it. Second, H4’s separation is the paper’s answer to the standard objection that formal monetary architectures are validated by their own simulations: the only hypothesis whose truth is independent of the framework’s assumptions is the one this paper refuses to self-certify.

10. Limitations

Five limitations bound the paper’s claims.

First, real-data estimation enters this paper only at baseline depth. H4 — the only hypothesis about the world rather than about the mechanism — is executed in Appendix F as the pre-registered two-way fixed-effects baseline, with the full robustness suite (system GMM, extended windows) reserved for the follow-up empirical paper. The historical mappings of Section 8 are consistency checks, not tests, and are presented as such.

Second, behavioral parameters in the simulations are author-set where the literature offers no anchor. Appendix C’s Table C.1 now labels every parameter’s provenance — anchored to an external estimate, derived within the framework, or set by the authors for the design target — so that readers can identify exactly which claims are robust to parameter choice (the corridor-compliance results, which were stress-tested across the full parameter bands) and which inherit the authors’ calibration judgment.

Third, the model is single-system. Spillovers between an NVC-issuing system and neighboring fiat systems — exchange-rate dynamics between the unit and legacy currencies, competitive devaluation incentives, and the game theory of parallel units — are identified in Section 6.3’s transition analysis but not modeled; they belong to the international-extension paper the series leaves open.

Fourth, institutional capacity is assumed, not designed. The seals presuppose a ratification authority with the competence and independence to run the measurement pipeline; the third paper of the series supplies that institutional design, and this paper’s claims are conditional on it. Where this paper needed institutional elements at a point of use, they are restated inline rather than assumed silently, but the defense of those elements is the third paper’s burden.

Fifth, measurement engineering is out of scope. The CRN is treated as an abstract measurement apparatus; its sensor, survey, and audit implementation — and its cost — are engineering questions the framework poses but does not answer. The demand-validation instrument of Section 7.3 is designed to be robust to realistic measurement lag and noise, but “realistic” is a simulation assumption, not a measured fact.

11. Conclusion

This paper set out to answer the question the first paper’s value equation posed but could not itself answer: given a unit of account defined by measured negentropy, what keeps its stock anchored, its ledger honest, and its circulation stable across shocks, transitions, and adversarial pressure? The answer has three layers. An accounting layer — the stock identity M(t) ≡ ks·V(t) with ks held in [0.95, 0.98] — replaces discretionary supply management with a constitutive rule, and the constancy propositions (0a, 0, 0b) establish that the rule preserves the unit’s accounting function by construction rather than by policy. A structural layer — the three seals of birth-locking, proliferation ban, and extinction loop, with the metabolism parameter δ in its 0.5%–1% band and a closed sink — converts the four failure modes (measurement falsification, ledger autonomy, satellite proliferation, consensus capture) from crises into accounting events with traceable clawbacks. And a dynamic layer — the cycle analysis, the four stabilizers, and the transition tipping result — shows the architecture to be stable not only in steady state but along the path to it, with a computable critical coverage and pre-committed transition policy.

The evidential posture has been deliberately asymmetric. What can be tested inside the model has been tested: five of six pre-registered hypotheses are executed in Appendices C and D, including one (H6) whose partial falsification and repair are reported rather than suppressed. What could not be tested inside the model — the cross-country claim that measurement-chain integrity predicts monetary stability — has been separated out as H4, given a complete pre-analysis plan in Appendix E, and executed at baseline depth in Appendix F, where the pre-registered rules return a verdict of not confirmed: correct signs, economically large point estimates, insufficient precision. The hypothesis enters the literature with its falsification conditions attached and its first verdict reported unsoftened.

The limits are correspondingly explicit. This paper does not re-derive the value equation, does not defend the normative premise, and does not design the institutions; those burdens belong to the first and third papers, and every inherited element has been restated at the point of use so that this paper can be read, and judged, on its own. What remains — the institutional design of the ratification authority, the audit commons, and the three constitutional firewalls — has been taken up in the companion paper on governance (Cheng and Cheng, 2026c). The immediate agenda is empirical: complete the H4 program of Appendix E as more years of annual measurement-integrity data accumulate (the baseline execution of Appendix F fixes the design and the verdict discipline), and pilot the architecture’s settlement and metabolism instruments at small scale, under the seal structure, where the Wörgl precedent says they work and the transition analysis says they are safe to test.