Gregory Caldwell Beier
Susarb LLC, Cambridge, Massachusetts
April 2026
version 4.7
From a broader research program by Gregory Caldwell Beier (forthcoming 2026).1
(c) 2026 Gregory Caldwell Beier. Licensed under CC BY-NC-ND 4.0.
Why has the total burden of externalities grown despite two centuries of institutional effort to address them? This paper proposes a structural explanation: technology scaling creates new constraint dimensions (environmental, institutional, systemic) faster than the economy's observation architecture can track them, while the price system's bandwidth on those dimensions remains fixed at zero. The formal foundation is the reverse water-filling result of rate-distortion theory (Cover and Thomas, 2006): a scalar channel concentrates all bandwidth on one dimension and allocates zero to the rest. The paper reconciles Smith and Pigou as descriptions of the same mechanism under adequate versus inadequate observation, positions the argument relative to the green accounting literature (Nordhaus and Tobin, 1972; Hamilton and Clemens, 1999), and proposes a Scaling assessment field with incentive compatibility established within the Hurwicz-Myerson framework. One prediction is testable with existing data: the MiFID II natural experiment (January 2018), where exogenous observation withdrawal should produce operational degradation scaling with coordination-dependence rather than information asymmetry.
Keywords: externalities, technology scaling, information architecture, rate-distortion theory, total factor productivity, green accounting, Smith, Pigou, observation, disclosure, mechanism design
JEL Codes: B12, D62, H23, O33, O44, O47, Q54, Q56
The number of active constraint dimensions on which externalities accumulate has grown since the Industrial Revolution, even as institutional remedies have successfully addressed specific dimensions. Sulfur dioxide emissions in the US have fallen roughly 90% since 1970. Lead exposure has declined to negligible levels. Ozone-depleting substances peaked in the late 1980s and are declining. These are real successes. They are also, in each case, the remediation of a single constraint dimension after decades of damage accumulation. During the decades required for remediation, new technologies created new constraint dimensions - atmospheric carbon, biodiversity loss, microplastic contamination, algorithmic harms to institutional trust, antibiotic resistance - that were not on the policy agenda when the earlier remedies were designed. The question is whether the rate at which new constraint dimensions are created exceeds the rate at which existing ones are remediated. This paper argues the answer is yes, and identifies the structural mechanism.
This paper proposes a structural explanation for the persistence and growth of externalities that the existing literature has not formalized. The explanation has two components.
The first is that externalities correspond to information the price system structurally cannot carry. The price is a scalar signal. By the classical reverse water-filling result of rate-distortion theory (Cover and Thomas, 2006, Chapter 10), a scalar channel observing a multi-dimensional source concentrates all bandwidth on one dimension and allocates zero to the rest when compression is below the source entropy rate. The dimensions receiving zero bandwidth are the dimensions on which costs accumulate unobserved. The result is textbook information theory (Cover and Thomas, 2006, Chapter 10). The contribution is the observation that this result, applied to price formation, identifies the structural source of externalities: they are the costs that accumulate on the dimensions the scalar price cannot see.
The second is that technology scaling is the mechanism that produces new constraint dimensions faster than the observation architecture can absorb them. In 1776, when Smith described the invisible hand, no technology scaled fast enough to produce constraint interactions that outran the community's capacity to observe them. The pin factory's externalities were local, visible, and manageable. Technology scaling since the Industrial Revolution has progressively violated this condition. Each technology wave - coal, petroleum, industrial chemistry, synthetic fertilizers, plastics, telecommunications, social media, artificial intelligence - created new constraint dimensions and new interactions between existing dimensions at rates that exceed the observation architecture's fixed bandwidth of zero on constraint dimensions. The gap between the rate of constraint-dimension production and the rate of constraint-dimension observation is the structural driver of externality growth.
Together these two components explain why externalities persist despite institutional effort: remedies address specific constraint dimensions after the costs are visible, while technology scaling produces new constraint dimensions before any remedy can be designed. The aggregate burden grows because the production rate exceeds the remediation rate.
Arrow (1969) identified externalities as missing markets - incomplete information structures. The present paper identifies the specific mechanism that makes the information structures progressively more incomplete over time. Nordhaus and Tobin (1972) proposed adjusting welfare measures for environmental costs. Hamilton and Clemens (1999) operationalized the adjustment as "genuine savings." The UN System of Environmental-Economic Accounting (SEEA) and the World Bank's Adjusted Net Savings provide ongoing measurement. The green accounting literature has measured the problem for decades. The information-theoretic framing adds a structural explanation for why the adjustment is needed (the scalar channel cannot carry constraint information), why the adjustment is growing (technology scaling produces new constraint dimensions faster than observation absorbs existing ones), and what specific architectural intervention would reduce the need for the adjustment by making constraint information visible at the moment of scaling rather than decades later.
The paper proceeds as follows. Section 2 develops the formal framework connecting rate-distortion theory to externalities. Section 3 identifies technology scaling as the mechanism that produces new constraint dimensions. Section 4 explains why technology interaction at scale produces the most dangerous and least visible externalities. Section 5 reconciles Smith and Pigou. Section 6 engages the green accounting literature and identifies what the information-theoretic framing adds. Section 7 describes the proposed architectural intervention. Section 8 addresses mechanism design. Section 9 presents testable predictions including one testable with existing data. Section 10 states limitations. Section 11 concludes.
The formal framework applies Shannon's (1948) rate-distortion theory to price formation. The application proceeds in four steps.
Step 1: The source. Economic agents possess multi-dimensional assessments of the constraint environment of a transaction. A constraint dimension is any dimension of the economic environment that affects outcomes but is not reflected in the scalar price - water availability, atmospheric loading capacity, supply chain concentration, institutional resilience, ecosystem service provision, labor market stability, and the interactions among them. A farmer selling grain has assessments of soil health, water availability, fertilizer dependency, weather trajectory, pest pressure, market concentration among buyers, policy risk, and the scaling trajectory of each of these under continued production. Formally, the source is a K-dimensional random vector V = (V_1, ..., V_K) representing the constraint environment, with covariance matrix Sigma.
Step 2: The channel. The market mechanism maps the multi-dimensional source to a scalar price P. The price reflects the consensus dimension - the dimension along which supply meets demand. In the notation of rate-distortion theory, the channel has rate R corresponding to one dimension of observation.
Step 3: The distortion. The reverse water-filling solution (Cover and Thomas, 2006, Theorem 10.3.3) characterizes the optimal allocation of observation bandwidth across dimensions for a Gaussian source under mean squared error distortion. The optimal codec allocates bandwidth to each dimension in proportion to max(0, sigma_k^2 - lambda), where lambda is a water level determined by the total rate. When the total rate corresponds to one dimension, the codec allocates all bandwidth to the highest-variance dimension and zero to the rest. The dimensions receiving zero bandwidth accumulate distortion equal to their full variance.
Step 4: The economic interpretation. The price system is not an optimal codec - it concentrates all bandwidth on the consensus dimension regardless of the variance structure, whereas an optimal codec would allocate bandwidth to equalize marginal distortion reduction across dimensions. This means the price system's actual distortion is strictly greater than what the optimal codec would achieve at the same compression rate. The reverse water-filling bound is therefore a conservative lower bound on the price system's distortion: the real information loss is at least as large as the bound, and in practice larger, because the price system does not optimize its bandwidth allocation across dimensions. The excess distortion - the gap between the price system's actual distortion and the information-theoretic minimum - is strictly positive whenever more than one dimension has variance above the water level (Beier, 2026h, applying Cover and Thomas, 2006). This excess is the formally computable lower bound on the information loss that corresponds to the externality: costs accumulate on constraint dimensions because the scalar channel allocates zero bandwidth to them, and the bound tells us the minimum magnitude of the accumulation.
Prices are not entirely silent on constraint dimensions. When a constraint dimension is correlated with the consensus dimension, the price carries some constraint information through the cross-correlation. The price of coastal real estate reflects some flood risk. The price of agricultural land reflects some water availability. The excess distortion formula accounts for this: the externality on dimension k is the variance of dimension k minus the distortion-reducing contribution of any cross-correlation with the priced dimension (Beier, 2026h, Section 4.2). The excess is reduced by partial loading but remains strictly positive unless the constraint dimension is perfectly collinear with the price - a knife-edge condition that cannot hold across all dimensions simultaneously when K > 2. The information prices carry about constraint dimensions is structurally insufficient, and the insufficiency is computable.
The mapping from distortion to welfare requires a further step, developed as a stylized case in Appendix A and in full generality in the companion paper (Beier, 2026h). Appendix A presents a single-agent decision problem in which an investor allocates capital across two assets - one exposed to a constraint dimension the price does not observe. The constraint dimension has a negative expected cost (the externality burden) and additional variance, both invisible to the uninformed investor. The investor overinvests because the asset appears more attractive than it truly is: the expected return looks higher (hidden cost) and the perceived risk looks lower (hidden variance). The welfare loss is proportional to the square of the hidden expected cost and is economically significant when the constraint-dimension cost is material relative to the consensus return. The result extends to multi-agent settings through the standard value-of-information framework (Blackwell, 1953): an agent who observes the price plus the constraint-dimension information makes weakly better decisions than an agent who observes the price alone, with strict improvement whenever the optimal action differs across constraint states.
The full welfare derivation with agent decision problems and equilibrium analysis is developed in the companion paper (Beier, 2026h). This paper uses the distortion as a lower bound on the welfare loss to establish the qualitative result: externalities arise on the dimensions the price does not observe, the number of unobserved dimensions grows with the complexity of the constraint environment, and the welfare loss is bounded below by a computable information-theoretic quantity.
The formal framework explains why any given externality exists. It does not explain why the total burden of externalities has grown for 250 years. The explanation is that technology scaling produces new constraint dimensions faster than the observation architecture absorbs existing ones.
A technology deployed at small scale produces constraint interactions with its local environment. The same technology deployed at system scale produces constraint interactions with every environment it touches, plus the interactions between those environments. Coal burned in one furnace produces local smoke. Coal burned in ten thousand furnaces across a continent produces an atmospheric loading whose consequences - global warming through the greenhouse effect - were invisible to any single observer in the 18th century. Foote (1856) demonstrated that CO2 traps heat and predicted warming from elevated atmospheric concentrations. Tyndall (1861) confirmed the mechanism through more rigorous experiments. But the effect would not be quantitatively modeled - how many degrees of warming result from a given increase in atmospheric CO2 - until Arrhenius (1896).
This is not to claim that externalities did not exist before the Industrial Revolution. They did. Deforestation, soil exhaustion, fishery collapse, urban waste, and the externalities of colonial resource extraction were all operative at scale well before coal. The timber crisis that drove the adoption of coal was itself an externality of pre-industrial economic activity. The claim is not a binary break - "before coal, no externalities; after coal, externalities" - but a claim about rates. Technology scaling since the Industrial Revolution has accelerated the rate at which new constraint dimensions are produced, while the observation architecture (the scalar price) has not changed. The gap between the production rate and the observation rate has widened on a trend basis, even as specific dimensions have been successfully remediated.
The rate at which a technology produces new constraint dimensions is proportional to the speed and breadth of deployment. In 1776, technology scaled at the speed of manual deployment. A pin factory's capacity grew at the rate a factory owner could hire workers and build workspace. In 2026, technology scales at the speed of capital deployment, digital replication, and network effects. A software platform can reach a billion users in five years. An AI model can be deployed across every industry in a decade. The constraint interactions produced by these deployments accumulate at a pace that exceeds any existing observation architecture by orders of magnitude.
The rate at which the observation architecture can track constraint dimensions is fixed at zero for the price system. The scalar price has no bandwidth for constraint dimensions regardless of how fast technology scales. Institutional remedies - regulation, taxation, litigation - address specific constraint dimensions after the costs are visible, with lags measured in decades. Leaded gasoline took from the 1920s to the 1970s-1990s for phase-out. Asbestos was in commercial use by the late 1800s and not banned until the 1970s-2000s. The lag for CFCs ran from the 1930s to the Montreal Protocol in 1987, and social media's mental health effects are still in the early stages of regulatory response more than fifteen years after scaled deployment. Each remedy is designed for a specific constraint dimension after decades of damage accumulation. During the decades of accumulation, new technologies have produced new constraint dimensions that will require their own decades-long remediation cycles.
The structural mechanism is therefore a rate mismatch: the price system's bandwidth on constraint dimensions is fixed at zero while technology scaling produces new constraint dimensions at an accelerating rate, and institutional remedies close specific gaps only after multi-decade lags. The net effect is a growing stock of unobserved constraint-dimension costs, even as specific dimensions are periodically remediated through targeted institutional effort.
Individual technologies produce individual constraint dimensions that, while invisible in the price, are eventually identifiable through scientific investigation and regulatory attention. Carbon from fossil fuels, ozone depletion from CFCs, lead poisoning from leaded gasoline - each was eventually identified, characterized, and addressed through targeted intervention.
The more dangerous externalities are the interactions between technologies at scale. Coal and industrial chemistry together produced acid rain - a constraint interaction that neither technology produces alone. Petroleum-based fertilizers and industrial agriculture together produced aquifer depletion and algal blooms - an interaction between the energy system and the food system invisible in the price of either. The internal combustion engine and urban planning together produced a land-use lock-in that now constrains decarbonization options - an interaction between the transportation system and the built environment that accumulated over decades and will take decades to reverse. Social media and algorithmic recommendation together produced institutional trust degradation - an interaction between a communication technology and a content optimization technology whose combined effect on democratic institutions was not predicted from the properties of either technology alone.
These interaction externalities are more dangerous than single-technology externalities. Identifying them requires cross-domain observation that no single expert, agency, or analytical framework provides - the acid rain problem was invisible to anyone studying coal combustion or industrial chemistry in isolation. The accumulation is faster because multiple dimensions degrade simultaneously. And remediation is harder because lock-in effects are multiplicative across the interacting systems: undoing the automobile-urban planning interaction requires restructuring both transportation infrastructure and land use simultaneously.
The number of potential interaction externalities grows combinatorially with the number of technologies operating at scale. If N technologies are deployed at system scale, the number of pairwise interactions is N(N-1)/2. The number of higher-order interactions (three-way, four-way) grows faster still. The observation architecture required to track these interactions must span multiple domains simultaneously - which is precisely what a scalar price, or any single-dimension observation channel, cannot do.
Externalities persist because the observation required to identify interaction effects at scale is multi-dimensional and combinatorial, while the observation architecture is one-dimensional and fixed. The mismatch grows with every technology deployed.
Smith's invisible hand coordinates efficiently under a condition that was satisfied in his world and has been progressively violated since: the observation architecture must be adequate to the coordination complexity. In 1776, it was - the pin factory's externalities were local and recoverable through direct observation. Pigou's externalities arise when this redundancy fails, when technology operates at scales and through mechanisms that exceed the community's observational capacity. Smith and Pigou described the same mechanism under different information conditions. Whether markets work depends on whether the observation architecture is adequate to the coordination the market is asked to perform.
The contribution over Arrow (1969), who located externalities as missing markets, is specificity. Arrow identified the incompleteness but not the mechanism that makes it progressive (technology scaling), the rate at which it grows (proportional to deployment speed), the specific information that is missing (constraint-dimension variance computable from rate-distortion theory), or the specific intervention that produces the missing information (a Scaling assessment scored against outcomes). Greenwald and Stiglitz (1986) proved that imperfect information generates pervasive externalities - a result for which the present framework provides an intuitive structural account: the pervasiveness follows from the scalar channel's zero bandwidth on all constraint dimensions simultaneously, not just on the dimensions where markets happen to be missing.
The specificity generates predictions Arrow's framework cannot. Arrow's missing-markets identification has no mechanism for predicting that operational degradation from observation withdrawal will scale with coordination-dependence, or that technologies spanning more sectors at deployment will take longer to have their externalities recognized, or that a scored Scaling assessment will surface constraint interactions before compounding. These predictions follow from the structural mechanism - technology scaling in a fixed-bandwidth observation architecture - and the rate-distortion bound that quantifies the information loss. The MiFID II test (Section 9) makes the discrimination concrete: Arrow's framework predicts that coverage loss increases the cost of capital through standard information channels; the present framework predicts the additional effect that coverage loss degrades operations in proportion to coordination-dependence. The additional prediction is testable and discriminating.
Ostrom (1990) demonstrated that communities can produce constraint information through polycentric governance. The proposed disclosure mechanism is complementary: it produces constraint-dimension information at scales where community governance cannot reach, which Ostrom-style governance can then act upon locally. Coase's (1960) theorem is explanatory rather than prescriptive, as Williamson (1985) emphasized. The relevant transaction cost for externalities is informational, and the disclosure mechanism reduces it by making constraint reasoning public, structured, and scored. The relationship to Pigouvian taxation is complementary, not competitive: a carbon tax embeds constraint information into the price, but calibrating the tax requires knowing the social cost - which requires the constraint-dimension information the scalar price cannot carry. The disclosure mechanism produces the information that tax calibration requires. Disclosure without taxation leaves the externality unpriced. Taxation without disclosure leaves the tax miscalibrated.
The green accounting literature has addressed the measurement problem the previous sections describe. Nordhaus and Tobin (1972) proposed "Measure of Economic Welfare" that subtracted environmental damages from GNP. Hamilton and Clemens (1999) operationalized the concept as "genuine savings," subtracting resource depletion and pollution damages from national savings and showing that several countries had negative genuine savings despite positive reported savings. The World Bank publishes Adjusted Net Savings annually. The UN System of Environmental-Economic Accounting (SEEA) provides a standardized framework for integrating environmental costs into national accounts.
The information-theoretic framing adds to this body of work in ways the measurement approach alone cannot provide.
The green accounting literature documents that standard measures overstate welfare because they exclude environmental costs but offers no structural explanation for why the overstatement persists despite decades of measurement effort. The information-theoretic answer: the scalar price cannot carry constraint information by construction, and technology scaling produces new constraint dimensions faster than green accounting methodologies can measure existing ones. The measurement gap is structural, not a correctable oversight.
The framing also shifts the intervention from backward-looking to forward-looking. Green accounting adjusts reported figures after the fact by subtracting estimated externality costs. The Scaling assessment produces constraint-dimension information at the moment of the economic decision, before the externality accumulates. A constraint interaction surfaced at the first decision point costs almost nothing to address. The same interaction surfaced after decades of compounding costs orders of magnitude more. Green accounting tells you how much you have already lost. The Scaling assessment tells you what you are about to lose, in time to change the decision.
The excess distortion from the rate-distortion framework provides a formally derived, lower-bounded measure of how much information the price system is structurally unable to carry - a computable bound that is independent of the specific externality being measured and applies to every constraint dimension simultaneously. It complements the externality-by-externality measurement approach of green accounting with a structural bound on the aggregate information loss.
The claim that reported total factor productivity is overstated is therefore not novel in direction - Nordhaus and Tobin identified this in 1972. Total factor productivity - the portion of output growth that Solow (1956, 1957) attributed to "technical change" and that Romer (1990) and Aghion and Howitt (1992) modeled as endogenous - is the dominant growth channel in standard growth theory. The claim is that the overstatement is structural, growing, and addressable through information architecture rather than only through after-the-fact accounting adjustment.
The proposed intervention adds a specific field to economic disclosure: the Scaling assessment. An agent producing a structured disclosure about a constraint dimension is required to state, with calibrated probability, what happens when the technology, practice, or condition they have assessed operates at system scale.
The Scaling assessment addresses the root cause identified in this paper: the gap between the rate at which technology creates constraint interactions at scale and the rate at which those interactions are observed. Individual constraint dimensions - the water stress at a specific facility, the supply chain concentration of a specific input - are assessable by individual analysts. The Scaling dimension - what happens when every facility in the region draws from the same aquifer, or when every manufacturer depends on the same supply chain node - requires the analyst to look beyond their specific assessment and consider the aggregate consequences.
The Scaling assessment is scored against outcomes through the Brier scoring rule (Brier, 1950; Gneiting and Raftery, 2007). The analyst who states "this technology is safe at scale" and is wrong has the error permanently recorded in their scored track record. The analyst who identifies a scaling risk nobody else sees, and is proved right, has that insight permanently recorded. The scoring mechanism makes honest assessment of scaling risk incentive-compatible for the same reason it makes honest assessment of any constraint dimension incentive-compatible: the proper scoring rule rewards calibrated probability reporting over strategic misrepresentation.
The Scaling field does not require analysts to predict the future perfectly. It requires them to state, with explicit probability and explicit reasoning, what they believe happens at scale - and to be scored against what actually happens. For long-horizon constraint dimensions (climate trajectories, aquifer depletion, institutional erosion), scoring resolves against intermediate observable milestones rather than end-state verification: five-year aquifer depletion rates, decade-scale emissions trajectories, measurable precursors to the predicted interaction. The analyst need not wait fifty years for the final outcome. The trajectory toward or away from the predicted state is observable on shorter timescales, and the Brier score updates as intermediate evidence accumulates. The accumulation of scored Scaling assessments across thousands of analysts, scored against outcomes over years, produces a body of evidence about which technologies and practices produce scaling problems and which do not. The body of evidence is public, attributed, and combinable across analysts through the interaction-discovery process.
The stitch-in-time argument: a negative externality caught at the first decision point - before capital is committed, before infrastructure is built, before communities are dependent on the technology - costs almost nothing to address. The same externality caught after decades of compounding costs orders of magnitude more. The historical record is consistent: leaded gasoline took roughly fifty years from commercial deployment to phase-out, asbestos roughly eighty years from industrial-scale use to regulatory bans, and CFCs roughly fifty-five years from introduction to the Montreal Protocol. In each case, the constraint interaction was identifiable in principle at the moment of deployment but was not assessed because the information architecture had no place for the assessment and no mechanism for scoring it against outcomes.
The disclosure mechanism is not cheap talk in the sense of Crawford and Sobel (1982). Cheap talk is unverifiable communication between agents whose interests may diverge. The sender can misrepresent without consequence. Crawford and Sobel showed that the degree of information transmission depends on the alignment between sender and receiver preferences, and that misalignment produces strategic distortion.
The Scaling assessment is verified communication. The sender's assessment is scored against realized outcomes through a proper scoring rule, and the score is permanently visible. The divergence between cheap talk and scored disclosure is the divergence between a world where agents can misrepresent without consequence and a world where misrepresentation is permanently costly in the agent's track record.
The incentive compatibility result has two layers, established within the Hurwicz (1972) and Myerson (1981) mechanism design framework (developed fully in Beier, 2026r). The first layer is dominant-strategy: truth-telling is the expected-score-maximizing strategy for report content under any strictly proper scoring rule (Savage, 1971; Gneiting and Raftery, 2007). This result holds regardless of what other agents do or report. The second layer is Bayesian: the choice of which constraint dimensions to cover (the commitment domain) is incentive-compatible for agents whose calibration quality exceeds a computable threshold. Agents below the threshold may not participate. This is a real limitation: the agents with the most to hide (those producing the largest hidden externalities) may be precisely those below the threshold. The mechanism makes honest disclosure the dominant strategy for report content among participating agents and makes participation incentive-compatible for agents above the calibration threshold. Coverage of the agents below the threshold depends on the cascade dynamics that follow from initial adoption.
The bootstrapping problem - that track record capital (Beier, 2026d) is valuable only if someone pays for calibrated judgment - is resolved by the structure of the principal's delegation problem. Institutional investors delegate capital allocation decisions to managers. The delegation creates a demand for demonstrated calibration quality that is independent of price informativeness: the principal pays for calibrated judgment because it reduces the expected cost of delegated decisions under constraint uncertainty, not because it enables trading profit. This demand exists whenever delegation exists under uncertainty, which describes the institutional investment industry by construction. The demand does not require that markets already value constraint information broadly. It requires that specific principals (pension funds, sovereign wealth funds, endowments) value calibrated judgment about the constraint dimensions that affect their beneficiaries' 30-to-70-year outcomes. The mechanism creates the infrastructure (format, scoring, track record system) through which this existing demand can be expressed.
The free-rider objection - that externality costs fall on the public, not the fund, so the fund has no financial incentive to pay for constraint-dimension information - dissolves at pension timescales. A pension fund with 50-year liabilities is not externally positioned relative to climate risk, water scarcity, or institutional erosion. These constraint dimensions produce portfolio losses on the fund's own timescale. Atmospheric carbon is not a public good problem for a pension fund investing in coastal real estate, agricultural land, and energy infrastructure through 2075 - it is a direct portfolio risk. The fiduciary duty to beneficiaries is the financial incentive. Paying for constraint-dimension information is not philanthropy. It is risk management on the timescale the fund's liabilities require.
A second free-rider objection targets the information rather than the risk: if scored assessments are public, why would any fund pay to produce them when competitors can consume them for free? The answer operates through mandate competition, accountability, and infrastructure advantage. The fund does not commission constraint-dimension research as a standalone public good. It adds a clause to investment management agreements requiring its managers to produce scored Scaling assessments. The manager produces the assessment to win and retain mandates, exactly as sell-side analysts today produce research to compete for trading flow. The information is a byproduct of competition for mandates, not a charitable contribution to the commons. Separately, a pension fund must demonstrate to its trustees, beneficiaries, and oversight bodies that it is managing long-horizon constraint risk. Pointing to research someone else paid for is not a fiduciary defense. The scored assessments commissioned under the fund's own mandates, covering the fund's own portfolio exposures, are the evidence of diligence. And the public availability of scored track records benefits the commissioning fund directly: the fund uses the full body of publicly scored assessments to evaluate which managers have demonstrated calibrated judgment and which have not. The fund that commissions assessments first builds the infrastructure through which it can evaluate all subsequent managers. Free-riding on others' assessments is possible for passive consumption, but the fund that builds the mandate infrastructure attracts the best-calibrated managers because it offers the venue where their judgment is rewarded. The cost asymmetry reinforces the logic: commissioning scored Scaling assessments across a portfolio costs basis points; the constraint-dimension losses from uninformed allocation on a 50-year horizon can cost percentage points of total portfolio value. A fund that economizes on constraint-dimension observation to save basis points is accepting percentage-point exposure to save pennies. The assessment capability must be in-house because it is inseparable from the fund's ability to evaluate its own managers. A fund that cannot assess constraint-dimension reasoning cannot distinguish a manager with genuine calibration from one who is lucky or evasive. The assessment infrastructure is not a research expense. It is the core of the delegation relationship. An apparent contradiction: if Brier scores are public and objective, why can't a competing fund simply read the public scores and hire the best-scored managers without paying for any assessment infrastructure? Because the Brier score tells you whether a manager is calibrated. It does not tell you whether the constraint dimensions that manager has covered are the ones your portfolio is exposed to. The public good is the score - the measure of calibration quality. The private good is the coverage map: which constraint dimensions, which asset exposures, which interaction effects are assessed for your specific portfolio's holdings and liability structure. CalPERS needs managers assessing water risk on CalPERS's agricultural land holdings and carbon transition risk on CalPERS's energy exposures, scored against outcomes on CalPERS's timescale. CalSTRS's assessments cover CalSTRS's different portfolio. The score is transferable. The coverage is not.
Beyond self-interest, the pension fund that commissions and publishes scored Scaling assessments provides a public function that no other institution is positioned to deliver: information ballast for the price system. The scored assessments, accumulating across thousands of managers and constraint dimensions, produce pricing gravity on the dimensions the scalar price cannot reach. The pension fund becomes an anchor institution - not through regulation or taxation, but through the weight of calibrated, scored, publicly attributed constraint-dimension observation feeding into every capital allocation decision the market makes.
An institutional prerequisite: the mechanism requires that the humans executing fiduciary duty - CIOs, investment committees, external managers - are compensated on timescales aligned with the fund's liability horizon. If CIO performance is benchmarked against relative returns over one-to-three year windows, a CIO who acts on a 50-year Scaling assessment by reducing exposure to a profitable but constraint-exposed asset will underperform the benchmark today and face termination before the constraint binds. Updating compensation benchmarks to reflect long-term fiduciary duty is a necessary condition for the mechanism's adoption. The information architecture can produce the right signal, but the principal-agent structure within the fund must allow the signal to be acted upon.
The mechanism has multiple equilibria, including a low-adoption equilibrium in which nobody discloses. The selection mechanism is contractual: an institutional investor adds a clause to investment management agreements requiring managers to produce scored Scaling assessments. This is a unilateral action that does not require market-wide coordination. The first mover creates the infrastructure. Network effects - the combinatorial growth in discoverable constraint interactions as more managers disclose - lower the adoption threshold for subsequent movers. The transition dynamics are developed in the companion paper on cascade economics (Beier, 2026ak).
Prediction 1 (Testable with existing data: observation withdrawal degrades coordination-dependent operations). The MiFID II regulation (effective January 2018) exogenously reduced analyst coverage for European firms by requiring asset managers to pay separately for research. Prior literature documents real effects of exogenous coverage loss: Derrien and Kecskes (2013) find reduced capital expenditure and R&D spending following broker closures and mergers; Kelly and Ljungqvist (2012) use exogenous coverage terminations - unrelated to firm fundamentals - to show that information asymmetry is priced, with prices and uninformed demand falling as asymmetry increases.
The information-theoretic framework generates a prediction that discriminates it from the standard information economics view. The standard view treats analyst coverage as reducing information asymmetry between managers and investors. Under this view, coverage loss increases the cost of capital, which reduces investment. The degradation should scale with information asymmetry proxies: firms with wider bid-ask spreads, higher analyst forecast disagreement, and lower institutional ownership should suffer more from coverage loss, because these firms had the most information asymmetry to begin with.
The information-theoretic framework treats analyst coverage as observation bandwidth that maintains coordination-dependent value (Beier, 2026i). The underlying principle - that observation of a coordination-dependent structure is inseparable from the maintenance of that structure, so that withdrawing observation causes the structure itself to degrade, not merely our knowledge of it - predicts that coverage loss produces real operational degradation, not just noisier estimates of an unchanged firm.
This claim has empirical grounding in the analyst discipline literature. Analysts do not merely estimate firm value from the outside. They impose accountability on managerial decisions through continuous external scrutiny. The agency cost framework (Jensen and Meckling, 1976) predicts that unobserved managers extract private benefits at shareholders' expense - and the prediction holds specifically for analyst coverage: firms followed by more analysts manage their earnings less (Yu, 2008), a result robust to instrumental variable strategies addressing the endogeneity of coverage. When coverage is exogenously reduced through brokerage mergers, the effect reverses: financial reporting quality deteriorates and entrenched managers adopt less informative disclosure policies (Irani and Oesch, 2013). The governance consequences extend beyond reporting to real decisions - exogenous coverage loss leads to higher excess CEO compensation and more value-destroying acquisitions (Chen, Harford, and Lin, 2015). Across these studies, the analyst's observation changes the firm's behavior, not just the market's estimate of the firm's value. The observation maintains the coordination quality of the firm's decisions. Withdrawing it allows the coordination to decay through reduced accountability, weaker governance discipline, and degraded decision quality. The degradation is real and operational, consistent with the observation-maintenance principle. The cited literature establishes that analyst observation maintains firm decision quality on average. The agency cost framework predicts this operational effect in general terms: less monitoring produces more agency problems, and the cited empirical results confirm it across multiple governance and reporting dimensions. The present framework's additional prediction is more specific: the operational degradation scales with coordination-dependence as proxied by intangible asset intensity. The agency cost literature predicts that coverage loss hurts all firms through reduced monitoring; the rate-distortion framework predicts that it hurts coordination-dependent firms disproportionately, because a larger fraction of their value depends on maintained observation. This dimensional specificity - which firms are hit hardest and through which structural channel - is novel and constitutes the discriminating test. The degradation should scale with the firm's coordination-dependence - the fraction of the firm's value that depends on maintained coordination rather than physical assets. Intangible asset intensity (intangible assets as a fraction of total assets) is the available proxy: a firm whose value is 90% intangible (software, brand, organizational capital, network effects) depends on maintained coordination for 90% of its value, while a firm whose value is 90% tangible (mines, pipelines, real estate) depends on coordination for only 10%.
The discriminating test: regress post-MiFID II changes in capital expenditure, R&D spending, and operating margins on (a) intangible asset intensity and (b) standard information asymmetry proxies (bid-ask spread, analyst forecast dispersion, institutional ownership concentration), controlling for firm size, sector, country, and pre-MiFID coverage level. The information-theoretic framework predicts the coefficient on intangible asset intensity is negative and significant after controlling for information asymmetry proxies. The standard view predicts the information asymmetry proxies are sufficient and intangible asset intensity adds no explanatory power after controlling for them. The test is feasible with Compustat Global, I/B/E/S, and MiFID II implementation data available as of 2026.
An identification concern: intangible asset intensity is not randomly assigned. High-intangible firms are systematically younger, faster-growing, concentrated in different sectors, and may have had different analyst following patterns pre-MiFID II. Research unbundling affected small-cap coverage more than large-cap, and intangible intensity correlates with firm size and sector. The regression controls for size, sector, and country, but these may not be sufficient. A more robust design would pair high- and low-intangible firms within the same sector and size decile using propensity score matching on pre-MiFID characteristics, then estimate the differential effect of coverage loss within matched pairs. Alternatively, using the variation in MiFID II implementation intensity across European jurisdictions as an instrument for coverage loss would address the concern that coverage changes are endogenous to firm characteristics. The prediction is that the coordination-dependence channel (intangible intensity) explains variation in operational outcomes beyond what the financing channel (cost-of-capital proxies) captures, and this prediction should hold across identification strategies. A note on scope: this test validates the observation-maintenance mechanism at the firm level - that withdrawing observation degrades coordination-dependent value. The extension from firm-level observation-maintenance to system-level externality production (technology scaling creating unobserved constraint dimensions) is the paper's theoretical claim, not the direct object of this empirical test.
Prediction 2 (Testable with existing data: technology complexity predicts recognition lag). The time between a technology's commercial deployment and the first regulatory or scientific recognition of a major externality provides a historical measure of the observation gap. Historical cases span a wide range: leaded gasoline (~50 years), asbestos (~80 years), CFCs (~55 years), neonicotinoids (~20 years), social media mental health effects (~10 years). The declining trend may reflect increasing scientific capacity and communication speed. The framework generates an additional prediction beyond faster science: technologies that interact with more sectors at deployment (measured ex ante by the number of distinct SIC/NAICS codes in the technology's supply chain and customer base at the time of commercial introduction) should have longer recognition lags, controlling for the decade of deployment, because multi-sector technologies produce interaction externalities that require cross-domain observation to identify. This is testable by regressing recognition lag on the technology's supply-chain breadth at deployment, with decade fixed effects to control for scientific capacity.
Prediction 3 (Requires disclosure adoption: Scaling assessment accuracy). In sectors where the Scaling assessment is adopted, the rate of unanticipated externality events (regulatory enforcement actions triggered by previously unknown constraint interactions) should decline relative to non-adopting sectors. Identification: difference-in-differences comparison across adopting and non-adopting sectors, controlling for regulatory intensity and sector risk.
Prediction 4 (Requires disclosure adoption: real versus reported productivity). Sectors operating under the disclosure regime should exhibit lower reported productivity growth (because constraint-dimension costs are no longer hidden) but higher long-run realized productivity (because capital allocation is directed toward technologies with net-positive productivity after constraint-dimension accounting). Identification: panel comparison of reported versus externality-adjusted productivity across sectors over a multi-decade horizon.
The formal framework is developed for Gaussian sources under MSE distortion. The Gaussian model yields a lower bound on excess distortion for non-Gaussian sources, and the MSE measure yields a lower bound on economically relevant distortion under downside-dominant loss functions. The qualitative results hold under these extensions. The quantitative bounds tighten.
The mapping from rate-distortion distortion to welfare loss is sketched for a stylized case in Appendix A and developed fully in the companion paper (Beier, 2026h). The stylized case shows the bound bites when constraint-dimension shocks are large enough to change optimal allocations. The full welfare derivation with heterogeneous agents and equilibrium analysis is in the companion paper, available on Zenodo with a DOI.
The historical narrative in Sections 3-4 is illustrative, not quantitative. The claim that technology scaling has accelerated the rate of constraint-dimension production is supported by the historical examples but is not derived from a formal model of technology deployment and constraint-dimension generation. The rate-distortion framework is static: it characterizes the distortion for a given K-dimensional source at a given compression rate. The paper's most interesting claim - that K itself is growing because technology creates new dimensions - is outside the static framework. A dynamic rate-distortion model in which source dimensionality grows at one rate (technology scaling) and observation capacity grows at another (institutional response) would formalize the technology-observation gap and characterize the trajectory of externality accumulation. This dynamic formalization is the paper's central open question and is a direction for future work. The static framework provides the lower bound at any given K; the dynamic question is how K evolves over time.
The claim about TFP overstatement is directional, not precisely quantified. The magnitude depends on contested externality cost estimates (the social cost of carbon ranges from $51 per ton in the U.S. federal interim estimate (EPA, 2021) to $185 per ton in Rennert et al. (2022)) and on attribution (what fraction of externality costs should be charged against TFP rather than against other economic categories). The green accounting literature cited in Section 6 provides specific methodologies for these calculations. This paper's contribution is the structural explanation for why the adjustment is needed and growing, not the magnitude of the adjustment.
The discount rate disagreement that affects externality cost estimates (Nordhaus's total social discount rate of roughly 4.5% versus Stern's total social discount rate of roughly 1.4%)2 reflects incommensurable value judgments about intergenerational equity.
The mechanism's coverage is limited to agents above the calibration threshold who choose to participate. The agents with the most to lose from disclosure may choose not to participate. Participating agents disclose honestly, and the body of honest disclosure, combined with network effects, produces a cascade of adoption among agents for whom the benefits of track record capital exceed the costs of honest reporting.
Smith's framework was adequate to a world where technology and observation moved at comparable speeds. The framework's implicit condition - that the observation architecture is adequate to the coordination complexity - was satisfied in 1776 and has been progressively violated for 250 years as technology scaling has outpaced observation. The externalities that have accumulated - atmospheric carbon, aquifer depletion, biodiversity loss, soil degradation, institutional erosion - are the compounded costs of operating a scalar observation architecture in a multi-dimensional constraint environment of growing complexity.
The externality problem has been diagnosed from multiple angles - as a market failure requiring taxation (Pigou), as information incompleteness requiring new markets (Arrow), as a measurement gap requiring adjusted accounting (the green accounting literature), and as a governance challenge addressable through polycentric institutions (Ostrom). Each diagnosis is correct within its scope. What has been missing is the structural mechanism that makes the incompleteness progressive: technology scaling in a fixed-bandwidth observation architecture. The interaction effects between technologies at scale are the most dangerous and least visible externalities because they require cross-dimensional observation that no scalar channel can provide.
The Scaling assessment completes the observation architecture by forcing the assessment of constraint interactions at the moment of scaling, scored against outcomes, with incentive compatibility established within the mechanism design tradition. The price system continues to clear markets. The Scaling assessment supplements it with a multi-dimensional observation layer that carries the constraint information the scalar channel compresses away. Smith's coordination mechanism operates on richer information. The observation architecture becomes adequate to the complexity it is asked to coordinate.
Two directions follow immediately. The first is empirical: the MiFID II natural experiment provides a test of the framework's discriminating prediction using existing data. The author invites collaboration from empirical finance researchers with access to the required firm-level panel data. The second is theoretical: the dynamic formalization of the technology-observation gap - a model in which source dimensionality grows at one rate and observation capacity grows at another, characterizing the trajectory of externality accumulation - is the paper's central open question and the natural next step for the research program.
This paper presents results from the Prolegomena to the Unification of Economics, Computer Science, Mathematics, and Physics. The present paper is self-contained.
The total social discount rate combines a pure rate of time preference (the ethical parameter) with a term reflecting diminishing marginal utility of consumption as society grows richer. Stern uses a pure rate of time preference of 0.1% with an elasticity of marginal utility of 1, yielding roughly 1.4% total. Nordhaus uses a pure rate of time preference of roughly 1.5% with an elasticity of roughly 2, yielding roughly 4.5% total. The divergence is driven primarily by the pure rate of time preference - the degree to which future welfare is discounted simply for occurring in the future. The disclosure mechanism cannot resolve this disagreement. It can make the disagreement visible and attributable: each analyst's Scaling assessment specifies the discount rate assumed, and the track record scores the assessment against outcomes over time.
A natural question: if the farmer knows the aquifer is declining, why doesn't this information enter the price of agricultural land through standard transaction channels? It does, partially - the cross-correlation qualification in Section 2 accounts for this. But the farmer's local information is about their aquifer, not about the aggregate interaction of aquifer depletion with regional climate change with supply chain dependencies with regulatory trajectory. The individual transaction price carries some local constraint information, consistent with the partial-loading result. What it cannot carry is the system-level interaction effects, which require cross-domain aggregation that no individual transaction can perform.
This appendix derives the welfare loss from unobserved constraint-dimension variance in a stylized setting. The full derivation with heterogeneous agents and general equilibrium is in Beier (2026h).
Setup. An investor allocates wealth W between two assets. Asset 1 has return r_1 = mu_1 + epsilon_1, where mu_1 is known. Asset 2 has return r_2 = mu_2 - c + eta + epsilon_2, where mu_2 is the consensus return (carried by the price), c > 0 is the expected constraint-dimension cost to the investor on their investment timescale, eta is a mean-zero constraint-dimension shock with variance sigma_eta^2, and epsilon_2 is idiosyncratic noise with variance sigma_epsilon^2. The price of Asset 2 reflects mu_2 but not c or eta, because the constraint dimension is invisible to the scalar channel.
The definition of c requires precision. In a static, one-period model, a Pigouvian externality does not reduce the investor's private return - the polluting factory profits while the downstream fishery bears the cost. If c were a pure social cost borne entirely by third parties, the investor would have no private reason to adjust their allocation even if informed. The model would describe a social planner's problem, not an investor's problem.
On the timescales relevant to pension funds and sovereign wealth funds (30 to 70 years), the separation between private return and social cost breaks down. Externalized costs enter the investor's return through four channels that operate on long horizons. Regulatory internalization prices the externality before the investment matures - carbon costs externalized in 2025 will face carbon pricing well before 2075. Litigation transfers externality costs to producers - tobacco, asbestos, and PFAS established the pattern. Physical damage to other portfolio holdings creates cross-asset exposure - a diversified pension fund that owns coastal real estate, agricultural land, and carbon emitters simultaneously suffers portfolio losses when the externality from one holding damages the others. Systemic risk from accumulated constraint-dimension failures increases portfolio-wide tail risk. The term c therefore represents the expected present value of constraint-dimension costs that will be internalized into the investor's return through these channels over the investment horizon. On a two-year hedge fund horizon, c is approximately zero - none of the internalization channels have time to operate. On a fifty-year pension horizon, c is large and material. The model applies to long-horizon investors whose liability timescales are long enough for externality internalization to affect their returns.
The distinction between c and eta matters. The expected cost c represents the systematic constraint-dimension burden - the average cost from regulatory, litigation, physical, and systemic channels that the asset will face on the investor's timescale. The shock eta represents the uncertainty around that average. Both are invisible to the uninformed investor.
The investor's problem. The investor chooses portfolio weight alpha on Asset 2 to maximize expected utility. Under mean-variance preferences: max_alpha [alpha * E[r_2] + (1-alpha) * mu_1 - (gamma/2) * alpha^2 * Var(r_2)].
Case 1: Constraint dimension observed. The investor knows both c and the distribution of eta. The expected return on Asset 2 is mu_2 - c. The variance is sigma_epsilon^2 + sigma_eta^2. The optimal weight is alpha* = (mu_2 - c - mu_1) / (gamma * (sigma_epsilon^2 + sigma_eta^2)). The investor reduces exposure because the true expected return is lower than the consensus return and the true variance is higher.
Case 2: Constraint dimension invisible (the price system). The investor does not know the constraint dimension exists. The price carries mu_2. The investor perceives expected return mu_2 and variance sigma_epsilon^2 only. The optimal weight is alpha_blind = (mu_2 - mu_1) / (gamma * sigma_epsilon^2). The investor overinvests for two reasons: the expected return appears higher than it truly is (by c), and the perceived variance is lower than the true variance (by sigma_eta^2).
A clarification on the variance assumption: the blind investor perceives variance sigma_epsilon^2 because c and eta represent constraint costs that have not yet materialized in historical returns. Coal's return series in 1960 did not contain the variance of carbon regulation that would arrive decades later. Aquifer depletion rates in 2000 had not yet produced the water-cost shocks that will affect agricultural land values through 2050. The constraint dimension is invisible precisely because the scaling interaction has not yet produced observable financial consequences - it is a forward-looking cost that the scalar price, reflecting historical and current conditions, cannot carry.
A clarification on the informed/uninformed comparison: the two cases are counterfactual, not simultaneous. The model does not assume that informed investors coexist with uninformed investors and somehow fail to trade the price to its informed level. If informed investors existed in sufficient numbers, they would trade, the price would adjust, and the scalar channel would carry c through standard price discovery. The "informed" case represents the world after the disclosure mechanism creates the information. The "uninformed" case represents the current world. The welfare loss is the cost of the information's absence, not a violation of market efficiency - it is the gap the disclosure mechanism is designed to close.
The information problem has two layers, and the rate-distortion framework addresses the first. Individual agents possess local constraint-dimension information: the farmer observes the aquifer declining, the supply chain manager observes the single-source dependency, the atmospheric scientist measures the CO2 trajectory. These fragments of constraint-dimension knowledge exist.3 The scalar price compresses them away because it has zero bandwidth on constraint dimensions - this is the rate-distortion result, and it applies to information that agents already possess. The second layer is that the aggregate picture - the expected cost c, which reflects the interaction of aquifer depletion with supply chain fragility with regulatory trajectory with climate physics - has not been assembled because no mechanism aggregates the fragments into a composite assessment scored against outcomes. The disclosure mechanism addresses both layers: it prevents the scalar channel from compressing away local constraint information (by providing a structured, multi-dimensional format that carries what the price cannot), and it aggregates the fragments into the interaction picture that no individual possessed. Rate-distortion theory explains why existing local information is lost. The disclosure mechanism recovers it and assembles what did not previously exist.
The overinvestment. The gap between the uninformed and informed allocations is:
alpha_blind - alpha* = c / (gamma * (sigma_epsilon^2 + sigma_eta^2)) + (mu_2 - mu_1) * sigma_eta^2 / (gamma * sigma_epsilon^2 * (sigma_epsilon^2 + sigma_eta^2))
The first term is the overinvestment from the hidden expected cost (the investor allocates as if the return is mu_2 when the true return is mu_2 - c). The second term is the overinvestment from the hidden variance (the investor allocates more because they perceive less risk). Both terms are strictly positive. The uninformed investor overinvests in the externality-producing asset.
The welfare loss. The expected utility difference between the informed and uninformed investor, evaluated under the true return distribution, is:
Delta_EU = (gamma/2) * (sigma_epsilon^2 + sigma_eta^2) * (alpha_blind - alpha*)^2
The dominant term, when the hidden expected cost c is the primary driver, is approximately:
Delta_EU ≈ c^2 / (2 * gamma * (sigma_epsilon^2 + sigma_eta^2))
The welfare loss is proportional to the square of the hidden expected externality cost and is economically significant when c is material relative to the consensus return.
When the bound bites. The welfare loss is economically significant when c is material. For assets exposed to unpriced carbon costs (c estimated at $51-185 per ton of emissions, applied to the asset's carbon intensity), unpriced water depletion costs (the present value of aquifer degradation attributable to the asset's water draw), or unpriced supply chain fragility (the expected cost of disruption weighted by concentration), the hidden expected cost c can be a substantial fraction of the consensus return mu_2. The overinvestment is proportional to c and the welfare loss proportional to c^2.
When the bound is vacuous. When c is negligible - when the asset produces no material externality cost - the overinvestment approaches zero and the welfare loss vanishes. Assets with small constraint-dimension footprints are approximately correctly priced by the scalar channel.
A note on risk aversion. The welfare loss is inversely proportional to risk aversion gamma. Less risk-averse agents take larger positions and therefore lose more from unobserved constraint costs. The absolute welfare loss at institutional scale, however, is driven by the magnitude of assets under management: a pension fund with $500 billion in assets exposed to hidden constraint costs has a larger absolute welfare loss than a $5 billion hedge fund despite higher risk aversion, because the total exposure dominates the per-unit sensitivity.
Connection to third-party costs. The welfare loss derived above accrues to the long-horizon investor through the eventual internalization of constraint-dimension costs. The externality in the Pigouvian sense accrues to third parties through the physical consequences of the overinvestment - atmospheric loading, aquifer depletion, institutional erosion. The two losses are produced by the same overinvestment: the blind investor's excess allocation means more capital deployed to the externality-producing technology, more of the physical externality produced, and eventually (through regulatory, litigation, physical, and systemic channels) more cost internalized back to the investor. Reducing the investor's blindness (by making c and sigma_eta^2 visible through constraint-dimension disclosure) reduces the overinvestment, which reduces both the third-party damage and the investor's eventual internalized cost. The mechanism aligns private and social incentives on long timescales precisely because the internalization channels ensure the investor eventually shares the cost.
The effect is not uniformly directional. If constraint-dimension information reveals that a technology's externality cost c is lower than the market's vague prior (if the market was overpricing risk in the absence of data), disclosure could increase investment. The net effect is more efficient allocation - capital directed toward technologies whose constraint profiles warrant it and away from technologies whose profiles do not.
The result extends to K constraint dimensions, N agents, and general equilibrium (Beier, 2026h). In the general case, the aggregate welfare loss is the sum across all unobserved constraint dimensions of the cost-weighted decision errors, and the interaction effects between dimensions (Section 4 of this paper) produce additional welfare losses that grow combinatorially.
This paper identifies the structural mechanism that produces externalities and explains why the total burden has grown on a trend basis despite targeted remediation: technology scaling creates constraint dimensions faster than the observation architecture tracks them, while the price system's bandwidth on constraint dimensions remains fixed at zero. The interaction effects between technologies at scale are the most dangerous and least visible category. The Scaling assessment forces the observation of constraint interactions at the moment of scaling, scored against outcomes. The information-theoretic framing adds a structural explanation to the existing green accounting literature's measurement framework. The author invites engagement from the growth economics, environmental economics, mechanism design, economic history, and science and technology studies communities.