The Critical Claim Stock: A Thermodynamic Ceiling on Debt Sustainability and an Institutional Design Without Fixed Claims

I developed this paper through an extended dialogue with Claude Opus. Most of the language is the output of generative AI. The arguments, assumptions, and conclusions are wholly mine. The entire transcript is available upon request.

Part I — The problem

1. Credit is a claim, not a substance

Money is not a commodity that circulates. It is an accounting entry recording an obligation, transferable and extinguishable, with nothing underneath it (Innes 1914; Macleod 1856). This is not a heterodox position; it is the operating description of a banking system. A loan does not move existing funds from a saver to a borrower. It creates a deposit and an offsetting obligation at the same instant, and repayment destroys both.

The consequence that matters is this: the token is never the binding constraint on production. Production requires labor, materials, technique and time. None of those vanish in a credit contraction. Plant stands idle, workers stand idle, needs go unmet, and the only absent thing is an entry that costs nothing to create.

Keynes put it as the distinction of an entrepreneur economy: production is undertaken to end with more money than it began with, so the operative constraint is monetary calculation rather than physical capability (Keynes 1933, 1936). Marx made the same observation as M–C–M′ with different politics.

2. The arithmetic shortfall

Credit is created as principal. Repayment is demanded as principal plus interest. At any point in time the sum owed therefore exceeds the sum in existence.

The conventional reply is that this dissolves over time: interest is paid out as income and re-spent, new lending continuously enters, and the stock is never called at once. That reply is correct, and it is conditional. It holds only while growth or credit expansion continues. When either stalls, the shortfall becomes visible in the ordinary way — default, foreclosure, contraction.

Read structurally rather than morally, this means the business cycle is not a malfunction of a debt system. It is the mechanism by which unfundable claims are written off (Minsky 1986). Stability generates the leverage that ends it.

3. The thermodynamic bound

Interest compounds. Compounding is exponential and unbounded. The physical return that must service it is neither.

The Earth is not a closed system — roughly 10^17 watts arrive continuously and the planet radiates at higher entropy than it receives — so surplus is real and net production is possible. But the flux is bounded in rate, and terrestrial low-entropy mineral stock is bounded in total (Georgescu-Roegen 1971). Capital is not accumulation in the physical sense; it is a temporary ordering purchased by a larger disordering elsewhere.

Soddy stated the divergence first and most exactly: real wealth is subject to decay while debt compounds by mathematical law, so the two must diverge, and the divergence is resolved by periodic repudiation (Soddy 1926). He was dismissed for fifty years.

One correction to the strict entropic reading is required, and it changes the design. Real wealth has two components with different behavior. Physical stock decays and requires continuous throughput to maintain. Knowledge does not. It is non-rival, it compounds, and it is the only component of real wealth that genuinely accumulates. It decays only under failure of transmission — Roman concrete, Damascus steel, Saturn V tooling — which makes transmission institutions a real and ongoing throughput cost.

Knowledge raises the ceiling on conversion efficiency. It does not lift the flux bound. Knowing how to build the plant is not the plant.

4. What follows

In a claim-holding society, accumulated knowledge is appropriated privately, because the claim is the instrument of appropriation. Absent claims, cognitive accumulation has no private container and accrues to the whole. Enclosure is not the natural state of knowledge; it requires an instrument.

Four design constraints follow from Part I:

1. No instrument may accrue independently of realized physical return.
2. No instrument may compound.
3. The bound on throughput must be visible in prices rather than enforced administratively.
4. The non-produced endowment, and the cognitive commons, must not be privately appropriable.

Part II — The model

5. The core prohibition

Prohibited: claims contractually owed regardless of realized physical return. Compounding obligations. Any instrument whose service requirement is independent of the throughput it financed.

Permitted and intended: returns to labor and to conversion efficiency.

This is the whole of the restriction. Interest was a claim indifferent to whether anything was produced; that indifference is the defect, and compounding above the flux ceiling is its arithmetic consequence. Yield within physical constraint is the objective of the system, not a tolerated residue. The model is not a zero-yield design.

6. Conversion at onset

All existing debt and equity claims convert to public holding. There is no time-based compensation stream: return accrues to participation, not to waiting.

Stated accurately, this is repudiation executed as a balance-sheet operation rather than as a default. The distinction from crisis-driven repudiation is administration and timing, not kind — the claims were unpayable against bounded throughput either way. The line between who is compensated and who is not is Veblen’s: industry versus business (Veblen 1904). Keynes reached the same terminus from liquidity preference, as the euthanasia of the rentier (Keynes 1936, ch. 24).

Enclosure instruments — patent, copyright, trade secret — are extinguished in the same action. This is not a separate reform. If cognitive stock is the only accumulating real wealth, then intellectual property becomes the sole remaining instrument of private accumulation once financial claims are gone, and a more durable one than debt because it does not decay. Separating the two phases opens a window through which claims flee into method.

Standing objection, recorded. Mansfield found roughly 60% of pharmaceutical innovations would not have been developed absent patent protection, against low double digits across most other industries (Mansfield 1986). Pharmaceuticals are where this provision binds hardest and where public research (§11) carries the greatest burden of proof.

7. Money and prices

Money is medium of exchange and unit of account. It is issued as expenditure, never as loan. The stock is indexed to measured physical throughput. Nobody is in debt for the existence of the medium of exchange.

Prices are retained throughout. Calculation in money persists, so the socialist calculation problem does not arise, and prices continue to aggregate dispersed local knowledge that no central body can hold (Hayek 1945). This is the model’s principal advantage over planned systems and it is deliberate.

Scope of the demand signal. Prices are a valid signal for goods that exist. Demand is not the selector for what gets attempted (§11). These are distinct functions and the model uses one without the other.

Two standing limits on demand as a guide justify the separation. Non-excludable goods are systematically undersupplied by expressed demand regardless of value (Samuelson 1954), and willingness to pay is weighted by ability to pay, so demand measures the distribution of purchasing power at least as much as it measures need. Neither is a reason to discard prices for exchange.

8. The carbon anchor

CO2e is priced upstream at extraction and at import. The efficiency ratio kWh/CO2e is published per process and per firm.

The price is quantity-anchored, not rate-set. It rises as the remaining budget depletes. No authority chooses the number; the physical stock does. Revenue is distributed per capita (Barnes 2006).

This is the structural centerpiece rather than an environmental appendix. It puts the flux bound inside the price system instead of enforcing it through an allocator, which is what allows the model to dispense with administrative ranking of production. Stated plainly: interest was a false scarcity signal, because money is not scarce. Carbon is a true one, because the budget is finite. The design replaces a fabricated constraint with a real one and keeps the mechanism that made the fabricated one function.

Preference remains sovereign and becomes bounded. Wasteful goods are disciplined by price rather than by anyone deciding about them.

Non-produced assets — land, minerals, atmospheric sink — appreciate as knowledge-intensive goods fall. This is intended. They are the genuinely scarce things, and their rents are collected and distributed rather than accruing to title (George 1879).

Scope limit, explicit. kWh/CO2e ranks candidate processes against each other for the same output. It does not rank across uses: ratios are not comparable between different outputs, and an efficient trivial good outranks an inefficient necessary one on the metric alone. That question is answered upstream at §13.1, not by the anchor.

One useful side effect. Because carbon-intensive goods inflate as the budget depletes while knowledge-intensive goods deflate, idle balances do not appreciate against a general basket. The hoarding problem that would otherwise require a carrying cost on money (Gesell 1916) is substantially self-resolving.

9. Provisioning — how a firm obtains means

The question is not how a firm finances capital. It is how a firm obtains it. Financing creates a money claim against future output. Provisioning transfers physical capacity. The machines exist; they are produced under §7 issuance and allocated directly.

9.1 Channels

Worker subscription against members’ own labor claims. Mondragon operates this at roughly 80,000 people; note that Caja Laboral was a bank, and that component does not port.

Capital goods lease from the public stock. The primary channel. Terms denominated in throughput and carbon, terminable on non-performance.

Direct public procurement for lumpy, long-horizon assets that have no other route.

9.2 Why the lease is not a fixed claim

It resembles one and is not, because the remedy is repossession rather than a compounding money judgment. The claim cannot exceed the asset. There is no accrual, no deficiency balance, no negative equity.

9.3 Loss allocation

On failure the asset returns to the public stock. The loss is the throughput consumed in operation and nothing more — bounded, definite, and allocated without seniority tranches. This is the provision that makes a contingent-return system solvable at all: under participation claims alone there is no rule for destroyed real resources.

10. Participation shares

Definition. A share of the residual after operating costs, held by virtue of working in the operation. Paid when residual exists; nothing accrues when it does not.

Not ranked by contribution. There is no founder premium and no idea claim. Ideas are decommodified at §6; applying the same logic internally, the generative insight confers no permanent oversized claim on everything downstream. Knowledge enters the commons; labor draws on the residual.

Not equity. No liquidation claim exists, because productive assets are leased from the public stock. There is nothing underneath to claim.

Not alienable. It cannot be sold, pledged or bequeathed, because its basis is participation and participation does not transfer.

Decay is automatic. The divisor is current participants. A person who leaves stops drawing. No sunset schedule is required, no horizon has to be set, and no interested party sets it.

Realization is near-term. Residual is distributed and spent in near real time rather than held as a stock. This removes the accrual-judgment burden that contingent claims would otherwise impose, and it is why the gains-to-holders objection is inert: hoarding is not the alternative to spending.

Taken together these properties close, without administered rules, what would otherwise be four separate problems: sunset, transferability, inheritance, and most of the verification cost.

11. Innovation and firm formation

Provisioning answers where means come from. It does not answer who gets them.

11.1 Demand is not the selector

The conventional chain — idea, friends and family, private equity, open market — is a sequence of bets at increasing stake against decreasing uncertainty, screened by financiers exposed to total loss. Removing the fixed claim removes the thing risked, and with it the screening incentive. The model does not attempt to replace that screen with a demand estimate, for two evidenced reasons.

1. Judged single-shot selection performs poorly. Judges’ scores, expert panels and machine learning were all near-useless at predicting survival and growth in the Nigerian YouWiN! competition (McKenzie & Sansone 2019). Expert evaluators could assess technical quality but not commercial viability; the two came apart (Scott, Shu & Lubynsky 2020).
2. The venture chain does not work by selecting well. Returns are fat-tailed and ex ante selection is weak; what the system does is fund many cheap parallel experiments and terminate fast (Kerr, Nanda & Rhodes-Kropf 2014). The information is generated by staged capital against milestones, not by the initial judgment (Gompers 1995).

Business plan competitions are therefore rejected as the primary mechanism. A single-shot judged event replaces a high-variance portfolio with a committee’s point estimate and selects on pitch articulation.

11.2 Public research as source

Publicly funded research is a principal source of new technical possibility, and it is the channel consistent with holding ideas as commons (§6).

Calibration, recorded honestly. Roughly 11% of new products and 9% of new processes could not have been developed absent recent academic research — concentrated in pharmaceuticals, medical devices and information processing, and small in machinery, metals, process industries and consumer goods (Mansfield 1991, 1998). The linear science-to-product picture is not supported (Kline & Rosenberg 1986), and a substantial share of innovation originates with users and operators rather than with universities or corporate laboratories (von Hippel 1988).

11.3 The mission-agency structure

The functional approximate is mission-agency provisioning with program managers and termination authority — the DARPA and NIH structure (Mazzucato 2013), not university competitions. The operating conditions that make it work are specific (Azoulay, Fuchs, Goldstein & Kearney 2019):

1. A defined problem with identifiable technical approaches.
2. Program managers holding real budget and termination authority.
3. Term limits forcing turnover.
4. No in-house laboratories.
5. A transition path to an adopter.

Termination tolerance rather than selection quality is the variable that produced results: HHMI’s tolerance for early failure yielded more breakthroughs than NIH’s grant structure (Azoulay, Graff Zivin & Manso 2011).

Heilmeier’s catechism is the usable selection instrument and makes no reference to market demand. Recorded honestly: its “who cares” question asks who benefits without asking who pays, which is a beneficiary criterion in different clothes.

11.4 Plurality is load-bearing

Several independently budgeted provisioning bodies, each judged on realized throughput of what it backed, with mandatory continuation review rather than one-shot award. This reproduces staging without credit and without a single committee’s taste.

A singular allocator is the failure mode that historically kills systems lacking credit markets — not that capital is unavailable, but that one body’s view of what is promising becomes the only view (Scott 1998).

11.5 The transition path

ARPA-E produced strong technical results with weak transition: good technology, no adopter. DARPA’s transition path is defense procurement and NIH’s is clinical practice; both have an external criterion standing in for demand.

The public capital stock (§9) serves as the procuring adopter. Provisioning bodies fund development, the stock procures what results as means of production, and the carbon anchor supplies the procurement criterion, since kWh/CO2e ranks candidate processes for the same output. This closes the transition gap without a demand signal and without an assessor of need — the criterion is physical rather than preferential. It works for means of production only.

11.6 Household staking is rejected

Allowing households to wager commons dividends into unproven ventures is rejected. It incentivizes gambling with subsistence means, and the screening benefit does not offset the welfare cost.

12. Commons distribution

Per-capita shares of carbon revenue, land and mineral rents, and collective fund distributions (Barnes 2006; George 1879). Every living person holds a share of the non-produced endowment.

Decreasing per-capita returns per household are required, to negate a natalist incentive to acquire shares.

There is no equal-outcome objective. Participation shares differ by operation and by residual. The commons distribution is a floor, not a leveling. Governance of the commons itself is a substantial literature (Ostrom 1990) and is not addressed here.

13. Provision, surplus, and concentration

13.1 Basic provision off the top

Necessary goods — subsistence, shelter, health, insulin and its class — together with education and public health, are provisioned directly under §7 issuance. They are not subject to the ranking question, because they are not competing for allocation.

What remains after basic provision is discretionary by definition and therefore a near-zero factor in the allocation problem. The apparent dilemma of necessary goods versus trivial ones arises only for goods that have not been provisioned; provision the first category and the comparison does not occur. The utilitarian question underneath has a long settled literature and is not re-derived here.

Unlabeled parameter, recorded. The model does not state which sufficiency threshold it adopts or on whose account. That is a live choice with distributive consequences, and leaving it implicit hides a judgment rather than removing one. It should be named in any operational version.

13.2 Surplus and concentration

Residual accrues to participants (§10) and to a collective fund, taxed in significant portion and returned as public expenditure.

Concentration is largely self-limiting: participation shares are non-alienable, non-heritable, and cease on departure. What remains is stock accumulated from distributed residual, which must be spent near-term to be realized.

Exposure. If state expenditure comes to depend on collective fund returns, the state acquires the creditor’s interest and will defend the return requirement. Norway is the live case. Fund distributions should therefore be per-capita rather than budget-substituting, which keeps the state’s interest out of the return.

14. Transition sequence

PhaseAction
0Simultaneous announcement and execution. Any lead time is arbitraged into hard assets and foreign claims.
1Conversion of all claims to public holding and extinguishment of enclosure instruments — one action, not two (§6).
2Upstream carbon price stood up; per-capita distribution begins (§8).
3Public capital stock constituted from converted assets; lease channel opens (§9).
4Provisioning bodies chartered with independent budgets and termination authority (§11).
5Banking reduced to payments and custody.

Phases 1 and 2 are one action. Separating them produces a window in which claims flee into intellectual property.

Part III — Assessment

15. Failure modes

15.1 External boundary — dominant. The model is closed; the world is not. Carbon pricing requires border adjustment on embodied emissions, and holders exit into foreign claims and hard assets ahead of conversion. There is no internal solution — only capital controls, autarky, or simultaneous multi-jurisdiction adoption, none of which are plausible in isolation.

15.2 Program manager scale. DARPA runs roughly $4B across about a hundred program managers in a single mission domain. Economy-wide firm formation is orders of magnitude larger, and the model depends on recruiting exceptional individuals who then rotate out. Nothing in the literature suggests the structure scales; its record is generally attributed to being small and unusual.

15.3 Diffusion of user innovation. The locus of innovation is contested. Von Hippel’s own sample splits — scientific instruments and process equipment show high user-origination, polymers and additives show manufacturer-origination (von Hippel 1988) — and the predictive variable is sticky information: users innovate where need information is costly to transfer to the producer, producers innovate where solution information is costly to transfer to the user (von Hippel 1994).

The gap is therefore sector-specific rather than economy-wide. Where need information is sticky, the innovating operator is a participant and the improvement raises the residual they draw on (§10), so the reward channel exists and is direct. The genuine remainder is diffusion: an operator whose improvement benefits other firms captures nothing from it. That is a spillover problem, and the model deliberately maximized spillover at §6 by putting knowledge in the commons.

The opposing account puts innovation in the managerial hierarchy and the in-house laboratory (Chandler 1977, 1990), with the shift away from that model documented by Chesbrough (2003). Teece’s position bites both ways: the innovator frequently fails to capture value while holders of complementary assets do (Teece 1986), so observed user innovation does not by itself demonstrate that an incentive existed. Neither branch rescues the model — if users innovate, the diffusion gap stands; if firms innovate through appropriable in-house research, §6 abolishes the appropriation.

15.4 Scope-3 attribution. The kWh/CO2e ratio is the central administered price in the economy. Measurement capture will concentrate on boundary definition and indirect-emissions attribution. This is where the lobbying goes, and the model relocates rather than removes the problem of who computes the number.

15.5 Provisioning failures are large and slow. Market failures are numerous, small and fast; provisioning failures are few, large and slow, and fail characteristically for want of local feedback (Scott 1998). Under a bounded flux, a decade of throughput into the wrong thing costs more than a thousand cheap terminations. Plurality (§11.4) is the mitigation and it is partial.

15.6 Informal credit. Promises between parties cannot be prohibited. Trade credit, deferred settlement and receivables discounting reconstitute a shadow term structure, as every historical interest prohibition eventually produced. The absence of an issuance franchise bounds it; nothing eliminates it. The design question is whether the shadow layer is registered and visible or driven somewhere unmeasurable.

16. Standing assessment

Structural claim. The model does not require growth. It does not require a measured physical return rate as an input. It does not require an allocator for means of production. It contains no instrument that compounds. Prices allocate what exists; the carbon budget bounds throughput; shares are participatory and decay on departure; the non-produced endowment and the cognitive commons are held in common.

Resolved. The distributional freeze that afflicts any fixed-issuance reform; debt-deflation under a falling price level; the aggregate interest shortfall; lender-of-last-resort dependency; loss allocation on failure; the calculation problem; the legitimacy load of administrative allocation; claim sunset; transferability and inheritance; verification and audit cost; the tension between deflation gains and per-capita distribution.

Open. External boundary; program manager scale; diffusion of user innovation across firms; scope-3 measurement capture; the magnitude profile of provisioning failure.

Open as parameter rather than mechanism. The sufficiency threshold defining basic provision (§13.1).

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