PRIORITY FILING - INITIAL DRAFT
A fully revised and formatted version will follow.
Gregory Caldwell Beier
Susarb LLC, Cambridge, Massachusetts
March 19, 2026
From the Prolegomena to the Unification of Economics, Computer Science, Mathematics, and Physics by Gregory Caldwell Beier (forthcoming 2026).
© 2026 Gregory Caldwell Beier. Licensed under CC BY-NC-ND 4.0.
The companion papers in this series analyze constraint domains in isolation: aquifer depletion, atmospheric carbon loading, electrical grid capacity, ecosystem resilience. Each domain has its own Scaling dynamics, its own geometry, its own disclosure ecosystem. But constraint environments interact with each other. Precipitation changes driven by atmospheric dynamics affect aquifer recharge rates. Water-intensive power generation couples the electrical grid to the aquifer. Extreme weather events couple the atmosphere to the grid to infrastructure resilience simultaneously. The most dangerous reality debt accumulates not within any single constraint domain but at the intersections where misallocation in one domain cascades into failure in another. A well-calibrated Scaling assessment of aquifer depletion can be rendered wrong by a climate shift the hydrologist never assessed, because the aquifer's recharge depends on precipitation patterns that are themselves a constraint variable in the atmospheric domain. This paper develops the economics of cross-domain constraint coupling. The companion paper on scaling risk (Beier, 2026ah) proves that interaction effects across agents within a single constraint domain constitute a distinct information type. The factorial coordination paper (Beier, 2026ag) showed that disclosures about the same constraint produce combinatorial information. The present paper extends both results across domain boundaries: constraint domains are coupled through shared physical, biological, and institutional systems, the coupling produces emergent risks invisible within any single domain's analysis, and the disclosure architecture must surface cross-domain interactions that no single-domain Scaling assessment captures.
Keywords: constraint coupling, cross-domain risk, cascading failure, water-energy nexus, systemic risk, information architecture, interaction effects, emergent risk, coupled systems
JEL Codes: D82, Q25, Q54, H23, D85
Consider the coupling between the Ogallala Aquifer and the atmosphere. The Ogallala's recharge rate depends on precipitation over the High Plains, which depends on atmospheric circulation patterns, which are shifting under climate change. A hydrologist producing a well-calibrated Scaling assessment of aquifer depletion under current extraction rates must make assumptions about future recharge - and those assumptions depend on climate dynamics that lie in a different constraint domain from the one the hydrologist is assessing. If the climate shifts reduce precipitation over the recharge zone by 15% over the next two decades, the hydrologist's depletion trajectory is wrong not because the hydrological model was miscalibrated but because a coupled constraint domain shifted in a way the single-domain assessment did not incorporate.
Now extend the coupling one step further. The agricultural economy overlying the Ogallala depends on irrigation from the aquifer. The energy system serving that agricultural economy depends on water for cooling (thermal power plants) and on the grid infrastructure that distributes power to irrigation pumps. A drought driven by the same climate shift that reduces aquifer recharge simultaneously stresses the grid (higher cooling demand, reduced water for thermal generation) and the aquifer (higher irrigation demand, lower recharge). The coupling produces a correlated shock across three constraint domains - water, energy, and agriculture - whose combined effect exceeds the sum of the three individual-domain effects because each domain's stress amplifies the others.
Haldane and May (2011) analyzed an analogous coupling structure in financial networks, showing that interconnections among banks that are individually stabilizing (risk diversification) can be collectively destabilizing (contagion channels that transmit shocks across the system). Helbing (2013) generalized this to globally networked risks, arguing that the increasing coupling of technological, economic, and environmental systems produces emergent fragility invisible to single-system analysis. Rinaldi, Peerenboom, and Kelly (2001) documented the specific infrastructure interdependencies - how failure in one infrastructure system (power) cascades to others (water treatment, communications, transportation) through coupling that system-specific analysis does not capture.
The present paper brings the coupling problem into the compression framework. Single-domain Scaling assessments, however well-calibrated, miss cross-domain coupling because the Scaling field asks "what happens when this activity is replicated at scale within this domain" - not "what happens when this domain shifts because a coupled domain shifted." The cross-domain interaction is a different information type that the current disclosure architecture does not explicitly address.
Section 2 analyzes why single-domain assessments miss coupling. Section 3 develops the information-theoretic structure of constraint coupling. Section 4 shows how the disclosure architecture can surface it. Section 5 examines three coupled systems. Section 6 addresses implications for epistemic infrastructure. Section 7 states limitations. Section 8 concludes.
The Scaling field (Beier, 2026ah) requires the discloser to assess interaction effects at aggregate scale within the specified constraint domain. A hydrologist assessing the Ogallala estimates how N irrigators drawing simultaneously affect the aquifer over T years. The assessment's boundary is the hydrological system - the aquifer, its recharge zone, its users, and the geological properties governing flow and storage.
The boundary is analytically necessary. No analyst can assess every constraint domain simultaneously, and the tractability of the Scaling assessment depends on specifying a system boundary within which the interaction effects are modeled. But the boundary is also where information is lost. The hydrologist's model treats precipitation as an exogenous input - a boundary condition rather than a variable to be assessed. The climate scientist's model treats water demand as an exogenous input - a boundary condition from the agricultural and energy domains. Each analyst's model is internally well-specified but externally incomplete, because the boundary conditions that each treats as given are actually endogenous variables in coupled constraint domains.
The information loss at domain boundaries is a specific form of the compression the companion papers analyze. Within a domain, the Scaling field preserves interaction structure that the price system compresses away. At domain boundaries, the Scaling field itself compresses - it treats the coupled domain's state as a boundary condition (a scalar input) rather than as a full constraint assessment with its own Scaling dynamics. The compression at the boundary is less severe than the price system's compression (the boundary condition carries more information than a price) but it is compression nonetheless, and the information destroyed at the boundary is the coupling structure that determines how shifts in one domain propagate to another.
The coupling between constraint domains can be characterized through the mutual information between their states. Let theta_A denote the state of constraint domain A (the aquifer) and theta_B denote the state of domain B (the atmosphere). The mutual information I(theta_A; theta_B) measures how much knowing the state of one domain tells you about the state of the other.
When I(theta_A; theta_B) = 0, the domains are independent - a shift in the atmospheric state tells you nothing about the aquifer's state, and single-domain assessments lose nothing by treating the other domain as exogenous. When I(theta_A; theta_B) > 0, the domains are coupled - the atmospheric state carries information about the aquifer's state (through the precipitation-recharge channel), and single-domain assessments that ignore this coupling discard the mutual information.
The mutual information between constraint domains is not a fixed quantity. It depends on the physical coupling strength (how sensitive aquifer recharge is to precipitation changes), the temporal dynamics (how quickly atmospheric shifts propagate to hydrological effects), and the current state of both systems (coupling may be weak under normal conditions and strong near thresholds - an aquifer operating well above its critical level is less sensitive to precipitation variation than one near the threshold where small recharge changes trigger regime shifts).
The state-dependent nature of coupling is particularly dangerous. This phenomenon - threshold coupling amplification - means that risks do not simply add across domains; they multiply as coupled systems approach their breaking points. Two constraint domains that appear weakly coupled under normal conditions can become strongly coupled as one or both approach critical thresholds. The Ogallala-atmosphere coupling is relatively weak when the aquifer is fully charged (recharge variation is buffered by abundant storage) and becomes strong as the aquifer depletes toward thresholds where the saturated zone thins and recharge efficiency changes. The emergent risk is that the coupling strengthens precisely as both systems approach their most vulnerable states - a correlation structure that single-domain analysis, treating the other domain as an exogenous boundary condition, structurally misses.
The disclosure architecture can surface cross-domain coupling through three mechanisms that extend the existing framework without requiring a structurally new design.
The first is cross-domain reading. The factorial coordination paper (Beier, 2026ag) establishes that disclosures about the same constraint domain produce combinatorial information through interaction. The same logic extends across domain boundaries: a hydrologist's aquifer assessment read alongside a climate scientist's precipitation projection produces interaction information about the aquifer-atmosphere coupling that neither disclosure alone contains. The interaction is not automatic - it requires a reader (a fund manager, an AI system, a policy analyst) who processes both disclosures and identifies the coupling implications. But the interaction information is latent in the disclosure pair and realizable by any reader who attends to both.
The second is coupled Scaling assessments. The Scaling field could be extended to include an explicit cross-domain coupling section: "This assessment assumes the following boundary conditions from coupled constraint domains: [precipitation from atmospheric domain, energy prices from grid domain, crop demand from agricultural domain]. The assessment's sensitivity to changes in these boundary conditions is: [specified]." The explicit coupling section would not require the hydrologist to become a climate scientist. It would require the hydrologist to identify which boundary conditions matter most, to state what the assessment assumes about them, and to indicate how sensitive the conclusion is to deviations from those assumptions. The sensitivity specification is the information that enables cross-domain reading to identify where the coupling risk is concentrated.
The third is cross-domain scoring. When a Scaling assessment's boundary conditions turn out to be wrong because a coupled domain shifted, the scoring mechanism should distinguish between calibration failure within the assessed domain (the hydrologist's model was wrong about the hydrology) and boundary condition failure across domains (the hydrologist's model was right about the hydrology but the precipitation assumption was wrong because the atmosphere shifted). The distinction matters for the track record: a hydrologist whose within-domain calibration is excellent but whose cross-domain boundary assumptions are frequently wrong is providing useful hydrological analysis that needs to be paired with better climate inputs. The track record should reflect both dimensions rather than conflating them into a single calibration score.
Water, energy, and food production are coupled through physical and economic channels that produce correlated constraint stress. Water is required for energy generation (cooling, hydropower, biofuel irrigation) and for food production (irrigation, livestock). Energy is required for water treatment and distribution (pumping, desalination) and for food production (machinery, fertilizer production, processing). Food production consumes both water and energy while occupying land that could provide ecosystem services.
A drought simultaneously reduces water availability (stressing the aquifer), reduces hydroelectric generation (stressing the grid), increases irrigation demand (stressing the aquifer further), and increases cooling demand (stressing the grid further through thermal generation's water requirements). The correlated stress produces an aggregate shock whose magnitude exceeds what any single-domain analysis would predict, because each domain's stress amplifies the others through the coupling channels. The single-domain Scaling assessment for water does not capture the energy system's increased demand for water during drought. The single-domain assessment for energy does not capture the aquifer's reduced capacity to supply cooling water. The cross-domain coupling is where the emergent risk resides.
Atmospheric warming couples to infrastructure through extreme weather (flooding, heat stress, storm intensity) and through sea-level rise. Infrastructure damage couples to the financial system through insurance losses, municipal bond defaults, and the devaluation of real assets in exposed geographies. Financial stress couples back to infrastructure through reduced investment in maintenance and adaptation, creating a feedback loop in which climate-driven infrastructure damage degrades the financial capacity to prevent further damage.
The cascade structure means that a climate Scaling assessment that ignores the infrastructure and financial coupling understates the total risk. The infrastructure assessment that ignores the climate trajectory overestimates the remaining useful life of exposed assets. The financial assessment that ignores both understates the probability of correlated losses across portfolios with geographic concentration in climate-exposed regions. Haldane and May's (2011) financial network fragility analysis applies with particular force to this coupling: individually rational portfolio diversification across infrastructure assets in different geographies provides no diversification if those geographies share a common climate exposure that the individual-domain assessments treat as a boundary condition rather than a correlated driver.
Agricultural land use affects biodiversity through habitat conversion and fragmentation. Biodiversity loss affects agriculture through the degradation of pollination services, pest control, and soil health that functioning ecosystems provide. The coupling is bidirectional and nonlinear - agricultural expansion into natural habitats produces immediate yield gains but long-term productivity losses as the ecosystem services the expansion destroyed are no longer available to support the agriculture that replaced them.
The single-domain Scaling assessment for agricultural productivity does not capture the biodiversity feedback (the pollination decline that reduces yields in surrounding fields, the pest population increase that follows the removal of natural predator habitat). The biodiversity assessment does not capture the agricultural expansion trajectory that drives the habitat loss. The coupling produces a reality debt that neither domain's analysis detects in isolation: the accumulated cost of agricultural expansion into habitats whose ecosystem services were not priced because the price system carried no information about the coupling.
The coupling problem has a specific implication for the epistemic infrastructure paper (Beier, 2026aq): constraint domain ontologies must define cross-domain linkages, not only within-domain variables. An aquifer ontology that specifies depletion rates, recharge rates, and extraction patterns but does not specify the precipitation dependence that links the aquifer to the atmospheric domain is incomplete in a way that enables the coupling blind spot this paper identifies.
The ontology design should include, for each constraint domain, a coupling map: a specification of which other constraint domains the domain is physically, biologically, or economically coupled to, through what channels, and with what sensitivity. The coupling map does not require the ontology to model the coupled domain - that is the coupled domain's ontology's job. It requires the ontology to identify the coupling and to specify the boundary conditions whose sensitivity the coupled Scaling assessment should report. The coupling map turns the domain boundary from a place where information is silently compressed into a place where the information loss is explicitly identified and flagged for cross-domain reading.
The paper argues for the importance of cross-domain constraint coupling but does not model the coupling formally. A formal model would specify the joint dynamics of coupled constraint states, the information loss at domain boundaries when assessments treat coupled states as boundary conditions, and the information gain when cross-domain disclosures are read jointly. The joint dynamics are domain-specific (the water-energy coupling has different mathematical structure from the climate-infrastructure coupling), and a general model of coupled constraint dynamics is beyond this paper's scope.
The coupled Scaling assessment proposed in Section 4 adds complexity to an already demanding disclosure format. The five-field structure is tractable because each field addresses a specific dimension of the analyst's own domain. Adding a cross-domain coupling section requires the analyst to identify relevant couplings to domains outside their expertise and to specify sensitivity to boundary conditions they may not be qualified to assess. The trade-off between information richness and disclosure burden, analyzed in the companion paper on incentive architecture (Beier, 2026ap), applies with particular force to the coupling extension.
The three coupled systems in Section 5 are illustrative. Many other coupling structures are economically important - the coupling between public health constraints and economic productivity (as the COVID-19 pandemic demonstrated), the coupling between geopolitical constraints and supply chain resilience, the coupling between demographic constraints and fiscal sustainability. The scope is limited to catalog all relevant couplings but to establish the general principle that cross-domain coupling produces emergent risks that single-domain analysis misses.
The state-dependent nature of coupling (Section 3) means that coupling strength is hardest to estimate precisely when it matters most - near thresholds where the coupling is strongest and the consequences of misestimation are largest. The paper identifies this as the core difficulty of coupling assessment but does not propose a solution beyond the cross-domain reading and sensitivity specification mechanisms in Section 4.
Constraint domains do not exist in isolation. Aquifers couple to the atmosphere through precipitation. Grids couple to aquifers through cooling water. Agriculture couples to both through irrigation and energy demand. The coupling means that a well-calibrated Scaling assessment within one domain can be wrong because a coupled domain shifted - and the information architecture that surfaces within-domain interaction effects does not automatically surface between-domain coupling.
The most dangerous reality debt accumulates at the intersections. A fund manager whose allocation decisions are informed by excellent single-domain assessments of the Ogallala, the atmospheric trajectory, and the grid's capacity - each well-calibrated within its domain - may still be allocating capital into a correlated exposure that no single assessment detected, because the correlation operates through coupling channels that domain boundaries compress away. Surfacing the coupling does not require every analyst to become a polymath. It requires the disclosure architecture to identify domain boundaries as places where information is lost, to specify the boundary conditions whose sensitivity matters, and to support the cross-domain reading through which the coupling information that single-domain assessments compress is recovered from the interaction of disclosures that individually do not contain it.
This paper presents results from the Prolegomena to the Unification of Economics, Computer Science, Mathematics, and Physics (Beier, forthcoming 2026). Constraint coupling economics extends the within-domain Scaling analysis (Beier, 2026ah) and the factorial coordination framework (Beier, 2026ag) across domain boundaries, showing that the most consequential information failures occur at the intersections where constraint domains interact. The author invites engagement from the systems engineering, systemic risk, and coupled human-natural systems communities.