Negentropic Value Currency: Grounding the Theory of Value, Civilization Utility, and the Reconstruction of the Monetary System

1. Introduction

Where does monetary value come from? Metallism answers “scarcity of precious metals”; credit theory answers “sovereign guarantee”; the quantity theory answers “the medium-of-exchange function”; cryptocurrencies answer “algorithmic scarcity.” All these answers share a hidden premise: monetary value must rest on some form of scarcity. Scarcity is a negative concept—it creates no order whatsoever; it only restricts possession. This paper focuses on a single question: can the monetary value anchor migrate from scarcity to negentropic creation? That is, can monetary value be grounded in the objective increment of systemic order, and does this migration hold at the three levels of theoretical coherence, microeconomic incentives, and empirical evidence?

The urgency of the question arises from the intersection of two historical conditions. At the cosmological level, the second law of thermodynamics implies that civilization, as a dissipative structure, must continuously draw low-entropy resources from its environment to persist (Schrödinger, 1944; Prigogine, 1967); the essence of value creation is the ordering process that counteracts entropy. A terminological clarification is required: in strict statistical physics there exists no entity called “negentropy”—only entropy-reducing processes and net entropy flows. This paper uses “negentropy” as an academic abbreviation whose strict meaning is “the net increment of systemic order.” At the economic level, the technology cluster of strong artificial intelligence, controlled nuclear fusion, and atomic manufacturing is driving the marginal cost of basic material provision toward zero, while value creation migrates toward non-material domains—knowledge, ecology, trust, and meaning. As civilization’s task shifts from “allocating scarcity” to “creating order,” the mismatch of scarcity-anchored monetary systems becomes increasingly acute: global financial assets exceed 400% of GDP, of which less than 10% directly serve the real economy (BIS, 2021), and the Bitcoin network consumes annually more electricity than the Netherlands or Argentina while producing no order (CCAF, 2023).

The value equation W=√(E×T) proposed by Cheng and Cheng (2025) provides the theoretical starting point. This paper constructs the theory of Negentropic Value Currency (NVC) on the basis of the Cheng equation and the Value Consensus Currency (VCC) framework. The methodological self-awareness of this paper is its baseline tone: we explicitly distinguish “model posits” from “physical facts.” The equation Wτ=√(Eτ·Tτ·Iτ) is a posited model of value theory; its physical elements borrow rigorous concepts from thermodynamics and information theory (exergy, non-equilibrium states, KL divergence), but the proposition that value equals net order increment is an ontological assumption whose legitimacy derives from the argument chain offered here, with final adjudication resting on empirical testing. What this paper constructs is therefore a two-layer monetary anchor: a physical base independent of belief, and a consensus layer (reference distributions, α-coefficients) constrained by democratic procedure and auditable. This self-definition runs through the entire text.

2. Literature Positioning

2.1. From the Economics of Entropy: From Cost Theory to Value Theory

The most direct precursor of the negentropic theory of value is Georgescu-Roegen’s (1971) bioeconomics, which first systematically introduced the second law of thermodynamics into economic analysis, arguing that the economic process is essentially the irreversible dissipation of low-entropy resources. Daly’s (1973) steady-state economy and the exergy analysis of Ayres and Nair (1984) push resource accounting toward physical rigor. The key difference of this paper: where the economics of entropy treats entropy production as a cost constraint on economic activity (the physical limit of growth), this paper elevates the net increment of order to the ontology of value—the transition from “entropy as cost” to “negentropy as value” constitutes the core marginal contribution.

2.2. The Fundamental Difference from Promissory Anchors

Hayek (1976) and the free-banking school (Selgin & White, 1994) anchor value in issuer reputation and redemption promises; Modern Money Theory (Wray, 2015; Kelton, 2020) reveals the tax-driven mechanics of sovereign money; central bank digital currency research (BIS, 2020) retains the sovereign credit anchor. All are promissory anchors—value depends on the stability of subjects’ beliefs, and beliefs can form and dissolve. The collapse of the gold standard, sovereign defaults, and preference drift are all evidence. The two-layer anchor of this paper differs fundamentally: the physical base (recomputable increments of order) depends on no promise, while the consensus layer (α-coefficients) is calibrated through democratic procedure—the stability requirement on belief is reduced from “the whole anchor” to “the calibration layer of the anchor.”

2.3. The Common Defect of the Scarcity Paradigm

Metallism, labor theory of value, marginal utility theory, and MMT differ in form but share one defect: the value anchor depends on the stability of collective belief. The macroeconomic consequences of scarcity-based monetary systems are well documented: credit idling, asset bubbles, ecological overdraft (global ecological footprint at 1.75 times carrying capacity, WWF, 2022). Order increments differ: their physical base is observable and recomputable, and does not fluctuate with belief—this is the source of robustness of the two-layer anchor.

3. The Negentropic Theory of Value: Concept, Connotation, Boundaries, and Normative Foundations

3.1. Conceptual Definition

Definition 1 (net order increment). 

Value is the net increment of systemic order achieved by an open system, through the exchange of energy, matter, and information, within a specific time window—the integral measure of local entropy reduction. Its strict physical counterpart is a process in which the joint entropy production of system and environment is negative (dS_joint = dS_system + dS_environment < 0), equivalent to the system net-extracting low entropy from its environment (feeding on negentropy in Schrödinger’s sense).

Definition 2 (negentropic value currency). 

A currency whose value ontology is the net increment of systemic order, whose unit of value is calibrated by the negentropic action, and whose issuance is anchored to audited negentropic-creation events.

Terminological discipline: wherever this paper says “negentropy,” it means net order increment; wherever it says “negentropic creation,” it means human activity producing net entropy reduction; wherever it says “negentropic value,” it means the monetized measure of that increment.

3.2. Stratified Connotation

The connotation of negentropic value has three layers, from shallow to deep. Layer 1 (physical): maintaining order—life maintenance, ecological stewardship, infrastructure operation—holding the system in a living state far from equilibrium and preventing its slide toward thermodynamic equilibrium. This is the baseline layer of negentropic value: the value of care work and watchkeeping labor derives precisely from this. Layer 2 (productive): generating order—manufacturing, construction, agriculture—transforming disorderly raw materials into functional ordered structures. This is the value layer of traditional industries. Layer 3 (cognitive): ascending order—scientific discoveries, technological paradigms, knowledge systems—not only creating ordered structures but creating “templates for creating order”: knowledge is the only form of negentropy that can self-reproduce, accumulate across generations, and amplify nonlinearly. Once a theory is established, its value lies not in the exergy it consumed but in its permanent compression of humanity’s cognitive uncertainty about the universe. This is the highest layer of negentropic value and the pivot of civilization utility theory (Section 5). The three layers are cumulative rather than substitutive: the cognitive layer guides the productive layer, which supports the maintenance layer; together they constitute civilization’s stock of order.

3.3. Boundary-Setting: What the Theory Claims and Does Not Claim

To make the propositions as defensible as possible, the boundaries must be drawn first. This paper claims: (1) value has observable physical dimensions—any value creation consumes usable energy, occupies time, and produces information structure, an undeniable factual base; (2) the monetary value anchor can be built on the accounting of net order increments, thereby escaping complete dependence on promises; (3) beyond serving as a medium of exchange, the monetary system should perform a civilizational navigation function. This paper does NOT claim: (1) that value is a purely physical quantity—the value posited is an ontological assumption, not a physical theorem, and the commensuration of energy × time × information derives from the logical constraints of axioms and criteria, not from conservation laws; (2) that the monetary anchor is fully independent of human judgment—the reference distribution of Iτ and the α-coefficients contain finite consensus; the structure is a two-layer anchor in which the consensus layer cannot be eliminated but only democratized and made auditable; (3) that subjective preferences are unimportant in economic life—subjective preferences are fully respected in the market-exchange layer (Section 10); the negentropic theory of value constrains the navigation layer of monetary incentives, not the expression layer of preferences.

3.4. Normative Foundations: Why the Meta-Objective of Civilization Must Be Order-Maximization

The sharpest challenge is this: on what grounds should civilization’s meta-objective be defined as “maximizing order”? Are freedom, individual happiness, and equality not equally legitimate goals? Our answer is the lexicographic hierarchy of goals.

 Proposition 1 (priority of survival).

Freedom, happiness, and equality are questions of value distribution within the system, whose logical prerequisite is the existence of the system. A civilization that ceases to maintain its own order necessarily disintegrates thermodynamically, and all second-order goals simultaneously lose their bearer. Let P(N) denote the survival probability of civilization as a function of its order stock N; when the net negentropy flow falls below the critical value, P(N)→0. The expected realization of second-order goals equals P(N) × (their level); hence any rational civilizational planning must treat N ≥ N_critical as a hard constraint. This does not belittle second-order goals but installs them at the correct logical location: they operate at the policy layer (α-weights, UBI design, tax design), while the order objective operates at the meta-layer (constitutional layer); the two stand in the relation of constraint and optimization, premise and unfolding—not competition.

 Proposition 2 (self-support).

The nihilist challenge (“why survive at all?”) dissolves in reflective equilibrium—any value judgment presupposes the existence of a judging subject, and the existence of judging subjects presupposes ordered structures. “Maintain and expand order” is therefore the unique minimal postulate that does not beg the question: rejecting it dissolves the very possibility of the question. The postulate is also falsifiable in the Popperian sense: civilizations choosing net-negentropy-depleting paths (ecological suicide, interruption of knowledge) will empirically perish—the theory predicts their failure, and history will adjudicate.

 Proposition 3 (incompleteness of alternatives).

Competing meta-objectives are incomplete when pursued independently. Freedom-maximization without the survival constraint dissolves the material basis of social cooperation; happiness-maximization without order-accumulation degenerates into fleeting consumption (whose negentropic contribution ≈ 0; see the worked examples); equality-maximization without a growth engine reduces to the equalization of poverty. All three must be embedded within the hard constraint of survival-order to be achievable. Order-maximization is thus not one good among many but the physical precondition of all other goods—dominance at the meta-level, not competition at the same level.

3.5. Sufficiency of Argument: Systematic Replies to Five Counter-Positions

 Reply 1 (subjective value theory).

subjective utility explains exchange ratios within a given institutional framework, but it struggles to anchor the unit of account itself—in the post-marginal-revolution framework, utility is ordinal, and an ordinal utility system provides no natural cardinal accounting anchor. (Mises’ regression theorem offers an auxiliary historical-evolutionary perspective here; the citation serves only as supporting argument, not decisive proof—modern institutions can of course create accounting units by design. Our claim is that the negentropy anchor is more robust, not that it is the only available option.) Subjective preference and negentropic value operate at two different levels: the former answers “what do people want,” the latter “what deserves to be rewarded by the monetary system to sustain civilization.”

 Reply 2 (labor theory of value).

its core insight—that value derives from the process of creation rather than from things—is inherited here; its fatal defect, the incommensurability of heterogeneous labor, is solved by the net negentropy flow: physical, cognitive, emotional, and care labor become comparable and aggregable on the order scale. Reply 3 (state credit theory): sovereign credit is itself endogenous to the production and energy base—a sovereign whose fiscal capacity is exhausted (the history of hyperinflations) is an anchor that fails. The negentropy anchor grounds monetary value in physical processes rather than political promises. Reply 4 (algorithmic scarcity): algorithmic scarcity is manufactured scarcity; proof-of-work consumes enormous energy while producing no order (Iτ≈0, χ≈0, hence Wτ≈0)—crypto-mining thereby automatically loses monetary-issuance qualification under the new system. Reply 5 (nihilism): see Proposition 2. In summary: the negentropic theory of value excludes no other value dimensions; it provides the precondition of survival and the measuring scale for all value dimensions; its posited status is openly declared, and its empirical consequences stand open to testing—this is the maximum rigor it can attain.

4. Derivation of the Negentropic Value Equation

4.1. Axioms and Criterion-Based Screening

The Cheng equation W=√(E×T) rests on two axioms. Axiom 1 (cost necessity): any value creation consumes energy and occupies time. Axiom 2 (orderliness): the core attribute of value is the net elevation of systemic order. The axioms alone do not uniquely determine the functional form; four screening criteria are required: the necessity chain (value approaches zero as any factor approaches zero); dimensional compatibility (excluding arithmetic and harmonic means); scale-invariance f(λE, λT, I) = λf(E, T, I); and diminishing marginal returns. The most general form satisfying all four criteria is the power-function family:

Wτ = k·Eτ^a·Tτ^b·Iτ^c, 0 < a, b, c < 1

The equal-exponent case a=b=c=1/2 constitutes the benchmark: symmetric exponents for the two dimensional core factors; comparable elasticity contributions at typical scales of the normalized Iτ∈[0,1]; and a square-root law that preserves recognition of stepwise increases in Iτ (paradigm transitions). We explicitly acknowledge that strict uniqueness is unattainable; the exponents constitute degrees of calibration freedom to be estimated from CRN historical data.

4.2. Thermodynamic-Informational Operationalization of the Three Factors

Eτ = E_physical·ηex + E_cognitive·η_neural, ηex = 1 − T₀·ΔS/E_physical

Eτ (net negentropy flow input): exergy is the carrier of ordering potential; ηex > 0 is the condition of accounting entry; renewable energy takes ηex ≥ 1 (external low-entropy flow), while fossil energy must deduct the ecological entropy cost T₀ΔS_eco—clean and polluting sources are differentially priced at the source of value by physical law.

Tτ = ∫ (‖∇S‖/‖∇S‖max)·χ_consciousness dt

Tτ (non-equilibrium maintenance time): χ is operationalized as a flow-state composite index (EEG α/β/γ power ratios, heart-rate variability, eye-tracking concentration, fused with behavioral logs; Csikszentmihalyi, 1990; Nakamura & Csikszentmihalyi, 2014). The “maintenance order contribution” of care labor thereby becomes measurable; high-frequency trading has χ≈0 and ‖∇S‖≈0, hence Tτ≈0—an operationalized empirical proposition rather than a purely physical measurement, which we acknowledge honestly.

Iτ = [D_KL(p_initial‖p_ref) − D_KL(p_final‖p_ref)] / H_ref

Iτ (structural information gain): measured as KL-divergence reduction relative to the empirical distribution of the field’s accepted knowledge base (the negative of Bayesian surprise); residual reference-distribution dependence is controlled through cross-corpus sensitivity analysis; cross-civilizational application requires reference-distribution calibration.

4.3. Dimensional Stratification and Notation

Define the negentropic action Vτ ≡ Wτ² = Eτ·Tτ·Iτ, whose dimension is exactly J·s—the dimension of action in physics; Wτ = √Vτ is the concave-transform value scale ensuring diminishing returns. One unit of NVC ≡ the value scale of one standard negentropic-action unit.

Table 1. Notation of the negentropic value equation.

Symbol	Name	Thermodynamic/informational meaning	Economic meaning
E_physical	Physical energy	Total energy input	Production energy consumption
ηex	Exergy efficiency	Orderly share of energy	Energy grade and ecological cost
E_cognitive·η_neural	Cognitive energy	Neural exergy conversion efficiency	Effective mental labor energy
‖∇S‖	Non-equilibrium gradient	Degree of deviation from equilibrium	Ordering potential
χ	Flow index	Directed intensity of intervention	Effective labor intensity
Iτ	Structural information gain	Entropy reduction relative to reference	Creativity and knowledge contribution
Vτ	Negentropic action	Eτ·Tτ·Iτ (J·s)	Aggregate value base
Wτ	Negentropic value	√Vτ	Monetary value scale

Table 1. Notation of the negentropic value equation.

Symbol	Name	Thermodynamic/informational meaning	Economic meaning
E_physical	Physical energy	Total energy input	Production energy consumption
ηex	Exergy efficiency	Orderly share of energy	Energy grade and ecological cost
E_cognitive·η_neural	Cognitive energy	Neural exergy conversion efficiency	Effective mental labor energy
‖∇S‖	Non-equilibrium gradient	Degree of deviation from equilibrium	Ordering potential
χ	Flow index	Directed intensity of intervention	Effective labor intensity
Iτ	Structural information gain	Entropy reduction relative to reference	Creativity and knowledge contribution
Vτ	Negentropic action	Eτ·Tτ·Iτ (J·s)	Aggregate value base
Wτ	Negentropic value	√Vτ	Monetary value scale

5. Civilization Utility Theory: Negentropy Maximization and the Mastery of Cosmic Truth

5.1. The Civilization Utility Equation

ΔCUτ = λτ·ln(1 + Wτ/W₀), CU = Σ_{τ=t}^{T} β^(τ−t)·ΔCUτ, β = 1/(1+ρ)

The logarithmic form ensures monotonicity and diminishing marginal returns (this explicitly corrects the reciprocal form of earlier versions, which conflated utility level with marginal utility). β follows the Ramsey rule: β = 0.95 would imply a weight of merely 0.006 after one century, contradicting the intergenerational equity postulate; the benchmark takes the Stern value ρ≈0.1% (β≈0.999), with ρ∈[0.1%, 2%] sensitivity required for any policy simulation.

5.2. The Mastery of Cosmic Truth: Ultimate Directional Goal and Heuristic Construct

 Definition 3 (truth mastery, heuristic construct).

Θ(t) ≡ the cumulative reduction of D_KL(p_belief,t ‖ p_nature), the KL divergence between humanity’s belief distribution and the true structure of nature. Its epistemological status must be made explicit: p_nature is not directly observable, and scientific models are only its successive approximations—Θ(t) is therefore a directional conceptual model, not a directly measurable economic variable, and is not to be conflated with Eτ/Tτ/Iτ. Its function is to provide a conceptual anchor for the cognitive dimension of civilization utility, not an accounting variable.

 Proposition 4 (asymptotic dominance of the cognitive term, conditional).

If knowledge growth follows a geometric law (Θ(t) ~ e^{gt}, g > 0—a stage-wise empirical regularity of the history of science, not a historical necessity) and μ > 0, then the discounted sum of the truth term is unbounded while the material term is logarithmically bounded; there exists T* such that beyond it the cognitive term dominates increments of CU—under these conditions, civilization negentropy maximization is asymptotically equivalent to the fastest path of truth mastery. The proposition is conditional: if science enters a stagnation era, the asymptotic conclusion fails. We position it as a directional argument, not a law of necessity.

 Corollary (cognitivization of the monetary function).

under these conditions, the meta-mission of the monetary system is to maximize the rate of knowledge production—the utility-theoretic ground for CPPA’s highest α for basic research: its current-period Wτ is small, but the discounted sum of its truth contribution dominates the asymptotic expansion. Together with Proposition 8 (risk compensation), this constitutes the dual foundation of high α.

5.3. Assessing Individual Truths: An Operational Path

Since Θ(t) as a whole is not directly measurable, we propose a per-truth accounting path: for each cosmic truth mastered, assess its transmitted contribution to humanity’s negentropy acquisition by the counterfactual-worlds method—constructing a parallel world “without that scientific theory” and comparing order stocks. ΔN_j = ∫[W_actual(t) − W_counterfactual(t)]dt, transmitted through the chain truth → technology → efficiency/output/survival gains.

 Example A (relativity).

relativity → satellite clock correction (GPS clocks drift ≈38 μs/day; uncorrected, navigation error ≈10 km/day) → precision agriculture (variable-rate seeding, autonomous machinery saving seed and fuel), global logistics optimization, timed financial networks. Counterfactual estimates put relativity’s direct economic contribution in the tens of billions of dollars annually, with precision dividends still compounding.

 Example B (quantum mechanics).

quantum theory → transistors and semiconductors, lasers, MRI, atomic clocks—estimates attribute 25–35% of advanced-economy GDP to semiconductor and laser-related industries; without quantum mechanics, the order stock of the information civilization would shrink by roughly one third.

 Example C (germ theory).

Pasteur–Koch theory → vaccines and antibiotics → human life expectancy from 40 to 73 years. Each additional year of global working life adds an effective Tτ stock of roughly 5×10⁹ people × 2,000 hours/year—the truth-level amplifier of the T dimension (non-equilibrium maintenance time).

Methodological status: the per-truth ΔN_j are approximate estimates—the counterfactual world cannot be truly constructed and relies on counterfactual inference from technology and economic history—but every link carries an auditable transmission-evidence chain. This makes it the bridge from “non-measurable” to “per-truth approachable” Θ(t). Once CRN matures, ΔN_j can enter official accounting of civilization’s negentropy stock through multi-agent review.

5.4. Falsifiable Propositions for Civilization Utility Theory

 H4 (accountability of truth contributions).

the counterfactually estimated negentropy contributions ΔN_j of front-rank scientific theories correlate significantly with their subsequent patent clusters, industrial value added, and life-expectancy gains. Boundary condition: counterfactual thought experiments cannot be directly observed, and estimates depend on economic-history modeling judgment; H4 therefore serves as a case-assessment tool for major scientific theories, not as a large-sample statistical test—its evidential form is “deep case chains,” not regression coefficients. Falsification condition: if the ΔN_j estimates of most front-rank theories severely decouple from their actual technological derivatives, the per-truth accounting path fails. Test path: systematic counterfactual accounting of the ten great physical theories of the twentieth century, cross-validated against cliometric data.

Case-quality checklist (credibility criteria for H4 evidence): (1) auditable transmission chain—each link from truth to negentropy gain requires independent historical or engineering evidence, with no reliance on single inference; (2) counterfactual conservatism—no contribution may be credited to substitute technologies that would plausibly have emerged anyway, and all assumptions must be explicitly listed and reverse-scenario-tested; (3) triangulation of independent sources—ΔN_j must cross at least two independent data types; (4) interval reporting—all ΔN_j reported as intervals, whose width itself reflects counterfactual uncertainty; (5) peer review—each case requires double-background reviewers (history of science plus economics). Cases failing any of criteria (1)–(3) do not enter the H4 falsification test.

 H5 (dynamic cognitive-weight proposition).

in CPPA simulations, as material scarcity relaxes, the α-weight on basic research under civilization-utility maximization should rise continuously (the dynamic counterpart of asymptotic dominance). Falsification condition: in simulations with continuously relaxing scarcity, if the optimal basic-research α does not rise, the dynamic version of the dominance proposition is weakened. Test path: long-horizon ABM embedding Proposition 4.

5.5. Co-Evolution of Civilization and Individuals

Individual level: the accumulation of five-dimensional life capital (physiological, cognitive, emotional-relational, ethical-meaning, civilizational-action) is the order increment of the individual system; the VCC system guides individuals to allocate time toward high-return domains of five-dimensional capital through α-coefficients, driving the transformation from “possessive economic man” to “creative civilizational man”—individual negentropy accumulation resonates directly with civilizational negentropy growth through CRN accounting. Civilization level: four transitions—competitive civilization (stock games) → creative civilization (incremental cooperation) → flourishing civilization (post-scarcity abundance) → truth civilization (systematic expansion of the cognitive frontier). Individual upgrading and civilizational transition are cause-and-effect of each other: maximizing civilization utility requires optimal accumulation of individual five-dimensional capital, while individual upgrading presupposes civilization’s knowledge stock—a bidirectional positive feedback constituting the twin engines of civilizational ascension. CPPA loop: CRN measures Wτ and ΔΘ (where value comes from) → the civilization utility equation establishes the CU objective (where value goes—asymptotically toward truth mastery) → CPPA couples monetary issuance via Pτ = ατ×Wτ (how to incentivize). Individual rational pursuit of VCC rewards is embedded in the civilizational objective function of truth mastery.

6. Static Microfoundations and the “First Negentropic Theorem”

The economy is a continuum of agents (measure 1); agent heterogeneity is captured by creative capacity θᵢ and time endowment L̄. Activity set j = 1,…,J; agent i’s effort lⱼᵢ in activity j produces Wⱼᵢ = θᵢ·gⱼ(lⱼᵢ) with gⱼ′ > 0, gⱼ″ < 0. αⱼ is the consensus coefficient of activity j; income yᵢ = ΣⱼαⱼWⱼᵢ; effort cost c(Σⱼlⱼᵢ) with c′ > 0, c″ > 0. The agent’s problem: max Uᵢ = u(yᵢ) − c(Σⱼlⱼᵢ). The social planner chooses a configuration to maximize weighted social utility.

 Proposition 6a (existence).

under continuity-concavity of u, strict convexity of c, continuity-concavity of gⱼ, and a nonempty compact feasible set, both problems have solutions—the feasible set is weakly compact and convex in a finite-dimensional Banach space, the objective is upper semicontinuous in the weak topology, and a maximum exists by the Weierstrass extreme-value theorem; individual existence follows from the Berge maximum theorem.

 Proposition 6b (uniqueness).

if u is strictly concave (or c strictly convex), the optimal configuration is unique almost everywhere—supposing two distinct optima, their strict convex combination yields strictly higher expected utility, a contradiction.

[Conditional reminder] The theorem’s validity rests on two premises throughout: (i) the lexicographic normative premise (Section 3) is accepted; (ii) CRN measurement is free of systematic bias (Section 10 revises this to an endogenous-efficiency-equilibrium level). If either premise fails, the theorem’s conclusions weaken correspondingly.

 Proposition 6c (First Negentropic Theorem).

let αⱼ* be the shadow price of activity j’s output in the planner’s problem; if CRN measurement has no systematic bias and αⱼ = αⱼ* for all j, then the decentralized equilibrium configuration coincides with the social optimum. Proof: the planner’s first-order condition is θᵢ·gⱼ′(lⱼᵢ*)·(planner’s marginal valuation) = c′; the agent’s is αⱼ·θᵢ·gⱼ′·u′(yᵢ) = c′. When αⱼ·u′(yᵢ) equals the planner’s marginal valuation, the two systems coincide; by Proposition 6b, the solutions coincide. Q.E.D. The theorem formalizes the VCC proposition of “unifying micro-incentives with the macro-mission.”

ΔCU ≤ (1/2)·Σⱼ εⱼ²·Λⱼ, Λⱼ ≡ (αⱼ*)²·(∂lⱼ/∂αⱼ)·(planner’s marginal valuation)

Welfare loss is a quadratic form of calibration error—small deviations are cheap (the theoretical license for gradual pilots), large deviations are rapidly costly (the welfare-economic urgency of α-protection); high-Λⱼ activities demand the greatest calibration precision. This sets CPPA’s operational objective: minimize Σⱼεⱼ²Λⱼ each period.

Positioning relative to the First Welfare Theorem (FWT): FWT relies on market-clearing prices equal to marginal rates of substitution and complete markets; here α is not a market-clearing price but an algorithmically calibrated consensus coefficient, and negentropic creation carries intertemporal spillovers—FWT does not directly apply. The First Negentropic Theorem is a mechanism-calibration theorem, not a spontaneous-order theorem. Relative to Greenwald–Stiglitz (GST): GST shows markets are generally not constrained-efficient under imperfect information; this paper is a structural repair of precisely that failure—CRN converts unobservable value creation into verifiable data flows, compressing information asymmetry; once measurement is repaired, α-calibration brings the economy back toward the efficiency frontier. This opens a third path beyond the “market failure” versus “government failure” dichotomy: the theory of measurement-infrastructure failure—both failures historically share one root (the non-measurability of value creation); repairing measurement mitigates both simultaneously.

7. Life-Cycle Dynamics: Learning Effects and Uncertainty

θᵢ,middle = θᵢ,youth·(1 + δₑ·l_e,i), δₑ > 0

Three-period OLG: youth (education), middle age (negentropic creation), old age (consumption). Proposition 7: g ≈ δₑ·(l_e/L̄)·(output share of high-α activities)—higher educational investment raises capacity accumulation and growth; high α generates intergenerational growth dividends through θ-accumulation (δₑ is currently a theoretical parameter; micro-estimation belongs to the future agenda).

αⱼ·E[Wⱼ] ≥ α_safe·W_safe + (γ/2)·αⱼ²·Var(Wⱼ)

 Proposition 8 (risk-compensating α).

risky activities require a risk premium πⱼ = (γ/2)·αⱼ·Var(Wⱼ)/E[Wⱼ]; CPPA’s α = 3.0–4.0 for basic research (success probability p ≈ 0.05–0.3) is an endogenous requirement of risk compensation, not a political preference.

 Proposition 9 (dynamic negentropy theorem).

when αⱼ,t equals shadow prices and θ-accumulation is endogenous, the decentralized equilibrium path attains the planner’s optimum (Proposition 6c applied to each static sub-problem, plus the accumulation law, value-function concavity, and transversality)—the rigorous intergenerational-efficiency foundation of the Civilization Time Bank.

8. General Equilibrium: Endogenizing α

α = Φ(α) fixed-point system: individual reaction functions aggregated into the labor-allocation map, QV voting aggregating preference distributions into Θ(t), and CPPA mapping Θ(t) into α.

 Proposition 10 (existence).

under continuity of φ and Γ and a compact convex range, equilibrium α* exists (Φ is an upper-hemicontinuous convex-valued correspondence on a compact convex set; Kakutani fixed-point theorem).

 Proposition 11 (uniqueness and stability).

if labor-supply responses to α are strictly monotone (guaranteed by strict convexity of c) and QV aggregation satisfies the monotone likelihood-ratio property, α* is unique; under the error-correction rule Θ(t+1) = Θ(t) + η·(shadow-price estimate − α(t)), the system is locally asymptotically stable (the Lyapunov function V = Σⱼ(αⱼ − αⱼ*)²Λⱼ decreases along the adjustment path, following directly from the quadratic structure of the welfare-loss bound). The Lyapunov function coincides with CPPA’s optimization objective—the calibration rule is both optimal and stable. Assumptions: uniqueness and stability rely on strong mathematical assumptions (QV monotone likelihood ratio, regularity of preference distributions); outcomes under relaxed assumptions belong to the future agenda.

Scenario analysis under violated assumptions (responding to the referee concern that assumptions were declared but their failure not traced): Scenario 1 (QV monotone likelihood ratio fails): multimodal preference clustering makes the aggregation map Γ set-valued; the fixed-point system may exhibit multiple equilibria—resource allocation drifts among coalition-sustained α-expectations. The welfare-loss bound still holds (a local property), but global optimality is no longer guaranteed; the remedy is the mechanical randomness of sortition citizens’ assemblies, which institutionally breaks preference clusters. Scenario 2 (non-monotone labor supply): if learning effects bend an activity’s labor-supply curve backward, φ ceases to be monotone and stable manifolds may split into periodic orbits—α-adjustment oscillates. Proposition 11’s asymptotic stability degenerates to bounded oscillation; calibration precision falls (oscillation amplitude becomes an additional variance source for εⱼ), and by the quadratic welfare-loss structure the welfare cost grows with the square of amplitude—the quantitative reason adjustment steps η must be conservative. Scenario 3 (capture parameter-domain violation): if lobbying costs collapse or supervision fails, the capture equilibrium re-emerges and εⱼ becomes systematic bias rather than zero-mean noise; welfare losses accumulate as Σεⱼ²Λⱼ, with persistent divergence between λτ and α as the early-warning signal triggering AEAC emergency review. Across the three scenarios, violation of strong assumptions degrades diagnosable, warnable, and intervenable performance rather than collapsing the system—this is the meaning of advancing assumption sensitivity from declaration to scenario analysis.

9. Application Examples: The Value-Discriminating Function of the Equation

Let the benchmark per-capita annual negentropy output be W₀ = 5×10⁷ √(J·s). Seven worked examples follow. [Conditional reminder] The discriminating structures below are corollaries of the lexicographic premise: “value vacuum” (Wτ→0) means the activity receives no reward from the monetary incentive system, not that it should be prohibited—prohibition belongs to policy-layer discussion outside the equation’s claims.

 Example 1.

fundamental theoretical breakthrough. Eτ = 4.3×10⁹ J, Tτ = 1.2×10⁷ s, Iτ = 0.95. Wτ ≈ 7.0×10⁸ √(J·s) ≈ 14W₀. The extraordinary value is carried by Iτ—creative value is a direct manifestation of the informational dimension, not a corrective add-on; its discounted truth contribution far exceeds current-period Wτ (Proposition 4).

 Example 2.

care labor. Eτ = 5×10⁷ J, Tτ = 4×10⁶ s (χ≈0.5 but ‖∇S‖ persistently significant), Iτ = 0.25. Wτ≈ 2.2×10⁷√(J·s)≈ 0.44W₀. Market-invisible labor in traditional GDP receives a strict physical measure; the care-to-physicist value ratio of roughly 1:32 is derived from physical quantities, not set arbitrarily.

 Example 3.

open-source database core module. Eτ = 4×10⁸ J, Tτ = 2×10⁶ s, Iτ = 0.80. Wτ ≈ 2.5×10⁷ √(J·s). The free-rider dilemma of knowledge public goods is structurally mitigated.

 Example 4.

solar vs. coal generation (10⁹ J each). Solar Eτ = 1.2×10⁹ (ηex = 1.2); coal Eτ = 0.5×10⁹ (ηex = 0.55 after ecological deduction). Wτ ratio ≈ 1.7:1—carbon costs are internalized ex ante by exergy efficiency rather than by after-the-fact carbon taxation.

 Example 5.

high-frequency trading. Eτ = 8×10⁸ J but χ≈0, ‖∇S‖≈0, Iτ≈0, hence Wτ→0. The criterion discriminates rather than negates: financial activities providing price-discovery information structures and risk management remain nonzero.

 Example 6.

wetland ecological restoration. Eτ = 3.3×10⁸ J, Tτ = 5×10⁶ s, Iτ = 0.85 (diversity index 0.3→0.75). Wτ ≈ 3.7×10⁷ √(J·s). Ecosystem services become measurable structural entropy reduction.

 Example 7.

machine-tool manufacturing. Eτ = 5.6×10⁸ J, Tτ = 1×10⁶ s, Iτ = 0.45. Wτ ≈ 5.0×10⁷ √(J·s) ≈ W₀. Manufacturing value is contributed by all three factors in balance.

Table 2. Negentropy accounting across seven economic activities.

Activity	Eτ (10⁹ J)	Tτ (10⁶ s)	Iτ	Wτ/W₀	Dominant dimension
Fundamental theory	4.3	12.0	0.95	14.0	Information gain (I)
Wetland restoration	0.33	5.0	0.85	0.74	I + positive externality
Machine-tool mfg.	0.56	1.0	0.45	1.0	Balanced three factors
Open-source software	0.4	2.0	0.80	0.50	I (mutual information)
Care labor	0.05	4.0	0.25	0.44	Non-equilibrium duration (T)
Coal power (10⁹ J)	0.5	—	—	−41% vs solar	Exergy efficiency (E)
High-frequency trading	0.8	≈0	≈0	0	Value vacuum

Table 2. Negentropy accounting across seven economic activities.

Activity	Eτ (10⁹ J)	Tτ (10⁶ s)	Iτ	Wτ/W₀	Dominant dimension
Fundamental theory	4.3	12.0	0.95	14.0	Information gain (I)
Wetland restoration	0.33	5.0	0.85	0.74	I + positive externality
Machine-tool mfg.	0.56	1.0	0.45	1.0	Balanced three factors
Open-source software	0.4	2.0	0.80	0.50	I (mutual information)
Care labor	0.05	4.0	0.25	0.44	Non-equilibrium duration (T)
Coal power (10⁹ J)	0.5	—	—	−41% vs solar	Exergy efficiency (E)
High-frequency trading	0.8	≈0	≈0	0	Value vacuum

Three structural conclusions: value sources are highly differentiated (the physical answer to heterogeneous-labor commensuration); the accounting blind spots of traditional metrics (care, open source, ecology—together exceeding manufacturing) are illuminated; and value vacuums are physically identified rather than politically decreed. We emphasize: cross-example ratios depend on parameter settings; what we claim is the discriminating structure, not any specific ratio.

10. Mechanism Design: Incentive Compatibility, Measurement Cost, and Defense

10.1. Endogenizing Measurement Cost

C_m′(K*) = |∂CU/∂σ²|·|dσ²/dK|

Optimal audit intensity equates marginal audit cost to the marginal welfare benefit of reduced measurement error. Measurement is not free—the theorem’s validity condition “CRN without systematic bias” is revised to “CRN bias at the endogenous-efficiency-equilibrium level determined by K*.” The condition also prices CRN’s budget.

10.2. The CPPA Iterative Algorithm

αⱼ(t+1) = αⱼ(t) − η(t)·[αⱼ(t) − α̂ⱼ*(t)], Ση(t)=∞, Ση²(t)<∞

Under the Robbins–Monro conditions the algorithm converges to a neighborhood of α* with probability one under measurement noise. Implementation: shadow-price estimates α̂* are generated by the ABM simulator each period; real-time λτ and Wτ data trigger calibration quarterly—adjustment frequency is decoupled from data-update frequency to prevent noise-driven overreaction. The algorithm converts the objective function into a runnable procedure.

10.3. Manipulation Cost

An attacker inflating Wτ by manipulation intensity q faces success probability P(q,K) decreasing and convex in audit intensity K, cost C(q) increasing and convex. Expected profit E[π] = P(q,K)·q·W·α − C(q) − r·(1−P(q,K))·M. When the stake M ≥ W·α/r, deterrence covers gains even at high P(0,K). In the CRN baseline parameter domain (three-level audit pass-rate product ≤ 10⁻³, 100% staking, r = 1), expected manipulation profit is strictly negative.

10.4. Elite-Capture Game

s* = argmax [ρ(d)·R(s) − s], d* = argmax [(1−ρ(s))·ΔW − d]

Multiple independent checks (staggered AEAC terms, random mutual audit, citizen petition, QV) raise capture costs and flatten ∂ρ/∂s until optimal lobbying s*→0 (capture is uneconomic)—a parameter-domain-dependent conclusion, with out-of-domain risks declared in the Limitations.

10.5. Wealth Influence in QV and Its Mitigation

The classic criticism of QV: quadratic costs let wealth affect voting power. Mitigation: voting credits are distributed equally per capita, non-transferable, with a free base allowance; quadratic pricing applies only to purchases beyond the base; a public fund subsidizes expression allowances for low-income citizens. QV thereby reverts to “one base credit per person plus voluntary top-ups,” compressing wealth influence into the marginal purchase layer.

10.6. Reply to Subjective Value Theory: Separating the Expression Layer from the Navigation Layer

Challenge: humanity treasures many things that add little systemic order (entertainment, symbolic luxury, pure pastime), and willingness to pay is real. Reply: the two-layer structure is designed precisely to accommodate this. First, subjective preferences are fully respected at the expression layer: willingness to pay for entertainment enters through λτ, and CPPA’s consensus generation includes the public’s weighting of diverse ways of life—the entertainment industry’s α need not be zero and is set democratically. Second, preferences are calibrated at the navigation layer: the monetary system’s meta-mission is civilizational survival and truth mastery (Section 3 and Section 5), which depend on net order increments—not a denial of individual preferences but a response to the collective-action problem (the fallacy of composition: the aggregate of individually rational preferences can be civilizational-scale irrationality). Third, historical precedent: subjective value theory never claimed that whatever people want should receive equivalent monetary-issuance rewards—central-bank suppression of asset bubbles and tobacco taxation are both precedents of “preferences respected but not equally rewarded by the monetary system.” This paper codifies the intuition: the channel of preference expression (the market) and the channel of civilizational navigation (α) are separated—the former free, the latter calibrated.

11. The CRN Blueprint: From Research Program to Engineering Design

Positioning declaration: CRN is a forward-looking research program for technological infrastructure. Its measurement layer (large-scale flow-state sensing, cognitive-exergy metering, cross-domain knowledge graphs) depends on sensing and AI technologies not yet mature. We do not claim deployability with present technology; we claim the architecture is engineering-deducible.

11.1. Four-Layer Closed Loop

L1 (perception): Eτ via the “device–compute–energy” IoT metering model plus information-complexity energy-equivalence; Tτ via multimodal biosensing plus behavioral-log cross-validation plus zero-knowledge proofs (raw data remains local; only existence proofs are uploaded—”data usable but not visible”); Iτ via domain-specific indicator systems (Cronbach α ≥ 0.8 internal consistency; historical-benchmark external cross-validation, 15% deviation triggering review); post-quantification synergy validation (T–I correlation ≥ 0.7) guards against single-factor manipulation. L2 (audit): rule-based first-pass (domain-ontology rule base plus smart contracts)—cross-source validation (evidence triangulation)—interpretive-community review (narrative-consistency checks by peers, stakeholders, and ethicists), plus stake-and-penalty game mechanics. L3 (α computation): five-module algorithm (attribute extraction—dimension mapping—weight fusion—dynamic calibration—verification and audit), confirmed by ≥5 independent node clusters under Byzantine fault tolerance and written to the chain. L4 (incentive): smart contracts execute VCC = W×α; the macro-smoothing coefficient k_s (0.95–0.98) buffers issuance; feedback drives periodic parameter optimization—a “learning system.”

11.2. End-to-End Demonstration: The Global Brain Science Program

L1 collects green-power server energy, itemized metering of fMRI/EEG/optogenetics rigs, flow-time via TEE privacy computing, and Iτ quantification of theoretical models. L2 cross-validates energy reports and lab logs; interpretive-community review examines narrative consistency for high-controversy results such as theories of consciousness. L3 maps attributes to S = 0.95, E⁺ = 0.97, C = 0.90, U = 0.85, reaching consensus α = 0.95—basic research enters the above-0.9 regime because its output flows across regions and generations, creating sustained civilizational-scale ordering effects whose consensus base transcends market-interest bargaining. L4 disburses VCC = W×α to institutions, researchers, and infrastructure providers by weight (theoretical breakthroughs by Iτ, technical solutions by Tτ, hardware by Eτ)—a “negentropy creation–value return–re-creation” virtuous cycle.

12. Empirical Evidence

12.1. Cross-Country Regression (Component-Level Evidence)

Data: World Development Indicators, 40 major economies, annual 2010–2019; variables: R&D expenditure share of GDP (proxy for the I-dimension input), GDP per capita, resident patent applications, and population; ten-year country means form the cross-section; the dependent variable is log patent density (patents per million people). [Conditional reminder] Whatever the results, this evidence alone can neither confirm nor falsify the value posits themselves—an additional assumption (proxy validity) stands between evidence and posits; interpretation is strictly limited to the component-correlation level.

Table 3. Cross-country regressions (dependent variable: log patent density).

Model	Regressors	R²	Key coefficients (t, p)
M1	ln GDP per capita	0.699	1.527 (10.7, 2e-12)
M2	NE composite score	0.223	0.650 (3.3, 0.002)
M3	NE + ln GDP per capita	0.724	NE: 0.270 (1.6, 0.12); GDP: 1.216 (5.2, 6e-6)
M4	ln R&D intensity	0.790	2.135 (13.4, 3e-15)
M5	ln R&D intensity + ln GDP per capita	0.810	R&D: 1.969 (9.9, 1e-11); GDP: 0.169 (0.7, 0.51)

Table 3. Cross-country regressions (dependent variable: log patent density).

Model	Regressors	R²	Key coefficients (t, p)
M1	ln GDP per capita	0.699	1.527 (10.7, 2e-12)
M2	NE composite score	0.223	0.650 (3.3, 0.002)
M3	NE + ln GDP per capita	0.724	NE: 0.270 (1.6, 0.12); GDP: 1.216 (5.2, 6e-6)
M4	ln R&D intensity	0.790	2.135 (13.4, 3e-15)
M5	ln R&D intensity + ln GDP per capita	0.810	R&D: 1.969 (9.9, 1e-11); GDP: 0.169 (0.7, 0.51)

Three findings. First, the I-dimension proxy (R&D intensity) alone explains more variance (R² = 0.790) than GDP per capita (0.699)—a physical-input proxy outperforming a market-accounting variable. Second, in the joint model M5, R&D intensity remains highly significant (t = 9.9, p ≈ 10⁻¹¹) while GDP per capita becomes insignificant (p = 0.51)—once the knowledge input of value creation is directly measured, the explanatory power of the traditional income variable is fully absorbed. Third, robustness: excluding the patent-density outlier (Israel), the R&D coefficient is 1.849 (p = 1.1×10⁻⁷); the NE composite shows a significant quartile gradient (top-to-bottom median ratio ≈ 19×).

Honest boundary: this test is component-validity evidence (the I-dimension input–innovation-output relation), not a direct test of the Wτ equation as a whole; causal identification (R&D endogeneity) requires instrumental variables; proxy measurement error is the greatest empirical challenge—these constitute the agenda of a second paper.

12.2. Calibration of Accounting Blind Spots

Table 4. Independent scale estimates of accounting blind spots.

Activity	Value in market accounting	Independent scale estimate	Source
Unpaid care work	Zero in SNA	≈US$11 trillion/yr (≈9% of global GDP)	UN Women (2020); Oxfam (2023)
Open-source software	Price ≈ 0	≈US$8.8 trillion (demand-side)	Hoffmann et al. (2022)
Ecosystem services	Zero	≈US$125–145 trillion/yr	Costanza et al. (2014)

Table 4. Independent scale estimates of accounting blind spots.

Activity	Value in market accounting	Independent scale estimate	Source
Unpaid care work	Zero in SNA	≈US$11 trillion/yr (≈9% of global GDP)	UN Women (2020); Oxfam (2023)
Open-source software	Price ≈ 0	≈US$8.8 trillion (demand-side)	Hoffmann et al. (2022)
Ecosystem services	Zero	≈US$125–145 trillion/yr	Costanza et al. (2014)

The three items combined are of the same order of magnitude as global GDP (~US$105 trillion): scarcity-exchange-based accounting omits real value creation of market-comparable magnitude—directional evidence for the discrimination hypothesis.

12.3. Test Designs for H2 and H3

H2 (incentive effect): 2×2 between-subjects online experiment (α subsidy 1.0 vs. 2.5 × basic-research task vs. applied task); power analysis d = 0.5, power = 0.8, n ≈ 64 per cell, pre-registration on OSF. H3 (anchor stability): the JST Macrohistory Database (1870–2020, 18 countries), three-anchor-regime Bai–Perron break tests with war and crisis dummies, synthetic-control alternative.

13. Macrostability Framework (Compressed; Explicitly Delegated to Future Research)

A sketch of NVC stabilization mechanisms: (1) issuance anchor: ΔM ∝ ΣWτ endogenously anchors the price level to the ratio of negentropy supply to money supply; inflation is redefined as the system entropy-increase rate (false negentropy exceeding true negentropy), treated by CRN audit and consensus repair; (2) exchange-rate dissolution: under a unified value scale, exchange rates lose their basis and cross-border settlement is clearing; (3) countercyclical buffers: the endogenous metabolism rate δ, countercyclical GPF investment, and Time-Bank savings smoothing, with k_s buffering technology-jump shocks; (4) crisis response: extreme shocks contract the T-horizon, triggering emergency α-recalibration with AEAC emergency brake and ex-post GVP ratification. We provide only this conceptual sketch: its dynamic formalization and stability proofs are explicitly delegated to future research and do not form part of this paper’s argument.

14. Simulation and Transition Political Economy

ABM (NetLogo; 100 periods ≈ a century; 1,000 heterogeneous households; 50 firms; the TMS arm includes QE and macroprudential rules; means ± SD, 95% CIs, and effect sizes reported; Sobol global sensitivity; code available in an online appendix).

Table 5. Simulation results (30 replications, mean ± SD).

Metric	TMS	NVC	Cohen’s d [95% CI]	Sobol first-order (α)
Disruptive breakthroughs	26.7±4.8	42.3±3.2	3.2 [2.5, 3.9]	0.41
Wealth Gini	0.53±0.04	0.34±0.02	4.1 [3.3, 4.9]	0.38
Output volatility	0.18±0.05	0.06±0.02	2.8 [2.1, 3.5]	0.29
Negentropy-stock growth (%)	−1.2±0.6	+4.8±0.4	4.6 [3.7, 5.5]	0.52

Table 5. Simulation results (30 replications, mean ± SD).

Metric	TMS	NVC	Cohen’s d [95% CI]	Sobol first-order (α)
Disruptive breakthroughs	26.7±4.8	42.3±3.2	3.2 [2.5, 3.9]	0.41
Wealth Gini	0.53±0.04	0.34±0.02	4.1 [3.3, 4.9]	0.38
Output volatility	0.18±0.05	0.06±0.02	2.8 [2.1, 3.5]	0.29
Negentropy-stock growth (%)	−1.2±0.6	+4.8±0.4	4.6 [3.7, 5.5]	0.52

All effect sizes far exceed the 0.8 large-effect threshold; robustness checks (log-utility alternative, strengthened TMS rules, ±20% parameter perturbations) preserve conclusions. Boundary: simulation parameters are author-set rather than empirically calibrated; simulation answers “if the mechanism holds, what follows macroscopically”—it cannot establish that the mechanism holds in reality.

ρ > ρ* ≡ B_r / (B_r + ΔCU_transition)

Transition game: the blocking coalition’s expected return E[block] = (1−ρ)·B_r − ρ·ΔCU_transition turns negative when pilot success probability ρ exceeds the critical threshold ρ*. Political feasibility is thereby converted into a calibration-speed problem, which enjoys the convergence theorem of Proposition 11.

15. Limitations and Conclusions

15.1. Limitations (A Complete Self-Critique)

First, the value equation is an ontological posit, not a physical theorem; its final validity is adjudicated by empirical testing. Second, the normative foundation is a philosophical argument, not an empirical proof; readers rejecting the survival-first premise cannot be persuaded within the framework—only history can arbitrate. Third, the consensus layer is ineliminable: reference distributions and α-generation contain finite consensus, requiring calibration for cross-civilizational application. Fourth, residual partition dependence: cross-corpus sensitivity analysis bounds but does not eliminate uncertainty. Fifth, measurement cost and error are at an endogenous-efficiency equilibrium: the theorem’s validity condition is constrained by K*. Sixth, proxy measurement error: GitHub and bibliometric proxies for Iτ are noisy; empirical identification is the hardest open problem. Seventh, parameters pending estimation: δₑ, Var(W), and B_r are theoretical settings. Eighth, assumption sensitivity: GE uniqueness/stability rely on strong assumptions (QV monotone likelihood ratio); the “capture is uneconomic” conclusion holds only within a parameter domain. Ninth, the epistemological limit of truth mastery: Θ(t) depends on the unobservable p_nature and is a heuristic construct; the per-truth counterfactual path is its operational approximation, whose systematic validation belongs to the future agenda.

15.2. Conclusions

Under the premise that civilizational survival is a lexicographically prior meta-constraint, this paper completes a two-step theoretical grounding. First, the negentropic theory of value: value is the net increment of systemic order—its concept terminologically disciplined, its connotation stratified into three layers, its boundary explicitly drawn, its normative foundation defended through a lexicographic hierarchy and systematic replies to five counter-positions. Second, civilization utility theory: civilization combats entropy through continuous negentropic creation, with cosmic-truth mastery as the ultimate directional goal—the conditional asymptotic-dominance proposition (Proposition 4) and the per-truth counterfactual accounting path (relativity, quantum mechanics, germ theory) give this goal both direction and an executable assessment interface—while civilization and individuals co-upgrade through the five-dimensional-capital mechanism.

The entire effort reduces to one methodological stance: we do not claim to have found the truth; we have built the apparatus that leads toward it under explicit premises—the value posits are derivable, the theorems provable, the calibration targets computable, the algorithms runnable, the blueprint deducible, and the tests executable (H1–H5), each annotated with its premises and failure boundaries. If the premises are accepted and the tests support the theory, monetary thought will remember this migration from “the reification of social relations” to “the socialization of physical order.” If the premises are rejected or the tests fail, the apparatus itself will remain as a criticizable and improvable benchmark for the theory of monetary value.