Gregory Caldwell Beier
Susarb LLC, Cambridge, Massachusetts
March 2026
version 3.0
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 Mars Test evaluates information architectures by asking whether they would keep a colony alive under extreme constraint pressure: small population, high physical structural drift, zero effective surplus on critical dimensions, no institutional path dependence, and no exit. The test defines one extreme of a continuum; the opposite extreme (the Bermuda Test) is the regime where proprietary information and the Grossman-Stiglitz equilibrium are optimal. The empirical claim is that specific Earth constraint dimensions - atmospheric carbon budget, ecosystem stability, climate-financial coupling - are moving from Bermuda toward Mars, and the information architectures governing them have not moved with them. Formal results: full disclosure is the unique Nash equilibrium under zero effective surplus (Theorem 4.3), with the critical surplus threshold driven downward by rising physical structural drift. The Beier Factorial produces superlinear growth in constraint awareness through combinatorial agency formation. A distortion floor is identified: the price system's information destruction is a necessary condition for the disclosure incentive that maintains the eigenstructure on which the price system operates. The Coupling Advantage Theorem establishes a phase separation interval within which full-disclosure architectures self-stabilize while proprietary architectures self-destabilize from identical initial conditions. Proprietary ESG ratings, regulatory mandates, and open-source databases are evaluated against the test; only the full-disclosure architecture passes.
Keywords: Mars Test, Bermuda-Mars continuum, super-transparency, Beier Factorial, sane superintelligence, distortion floor, flutter suppression, ESG ethics, information architecture, constraint dimensions, track record capital, climate overshoot, rate-distortion theory, dimension-specific surplus, Coupling Advantage Theorem
Consider a test for information architectures. Take the system under evaluation - data flows, incentive structures, compression mechanisms, gatekeeping rules - and transplant it to a colony on Mars. Fifty to five hundred people, a hostile physical environment, no surplus to absorb errors, no exit. Would the architecture keep them alive?
Call this the Mars Test. The test strips away institutional path dependence, legacy market structures, and the luxury of absorbing information losses across billions of people and decades of time. What remains is the relationship between information architecture and survival under constraint pressure.
The continuum is parameterized by five conditions: population size N, physical structural drift sigma_e, effective surplus on the constraint dimension under consideration, institutional path dependence, and exit availability. The Mars Test sits at one extreme. Call the opposite extreme the Bermuda Test: large N, low sigma_e, high surplus, deep institutional path dependence, easy exit. Under Bermuda conditions, proprietary information is optimal - markets function, prices aggregate consensus value efficiently, the constraint dimensions carry low variance, and hoarding private information is individually rational because the surplus buffer absorbs any misallocation. The Grossman-Stiglitz equilibrium is the correct description of information production under Bermuda conditions, and the ESG industry's business model is well-adapted to it.
The empirical claim is that specific constraint dimensions - atmospheric carbon budget, ecosystem stability, climate-financial coupling - are moving from Bermuda toward Mars on the continuum, and that the information architectures governing those dimensions have not moved with them. The rate of movement is measurable through sigma_e estimates. The position on the continuum determines which information architecture is optimal. The contribution is identifying where on the continuum the equilibrium shifts and what drives the shift.
Earth's constraint environment is tightening on specific, measurable dimensions, and the test engages those dimensions directly. The IPCC Sixth Assessment Report established the baseline: cumulative emissions have committed the planet to continued warming regardless of near-term policy changes (IPCC, 2021-2023). Observed warming rates have since tracked above the AR6 central projections, though within the assessed uncertainty range. A March 2026 analysis published in Geophysical Research Letters (Foster and Rahmstorf, 2026) found statistically significant acceleration: the warming rate increased from approximately 0.20 C per decade over the 1970s-2015 period to approximately 0.35 C per decade over the past ten years. Berkeley Earth's chief scientist estimates a figure closer to 0.30 C per decade (Rohde, cited in Witze, 2026), while 0.27 C per decade remains the commonly cited intermediate estimate (Forster et al., 2025). The 2015-2024 decade was 0.31 C warmer than the decade that preceded it (Forster et al., 2025). By any of these estimates, the rate is increasing.
The Climate Overshoot Commission - an independent panel convened by the Paris Peace Forum - released its report in September 2023 with a direct assessment: the likelihood of exceeding the Paris Agreement's 1.5 C goal is "alarmingly high and continues to rise" (Climate Overshoot Commission, 2023). Among the responses the Commission considered is solar radiation modification (SRM) - interventions that would reflect incoming sunlight to mask warming. The Commission recommended a moratorium on large-scale SRM deployment while calling for expanded research and governance dialogue. The underlying concern is clear: SRM introduces massive new constraint dimensions (altered precipitation, ozone chemistry, termination shock, governance of deployment and cessation) whose interaction effects are unknown and potentially catastrophic.
In January 2026, the UK government released a national security assessment on global biodiversity loss and ecosystem collapse, prepared with the involvement of the Joint Intelligence Committee and informed by MI5 and MI6 (HM Government, 2026). The report was withheld from its originally planned publication until a freedom of information request forced its release in abridged form. It identifies six ecosystems of strategic importance to UK security and warns that their decline could drive cascading disruptions to food, water, health, and supply chains. Press reporting on a fuller version of the assessment warns that key earth systems may cross irreversible tipping points within two decades (Columbia CGEP, 2026). The EU's 2023 Joint Communication on climate and security describes climate change as a risk multiplier that can cascade across systems, regions, and societies (European Commission, 2023), and the EEAS's 2025 progress report treats environmental degradation as an "existential threat to Europe and the world" (EEAS, 2025).
The constraint dimensions described here carry variance that is rising now, on timescales measured in years and decades rather than centuries. The information architectures that govern how these dimensions are observed, communicated, and acted upon determine whether the constraints are addressed before they become unmanageable.
The Mars Test identifies a specific failure in existing information architectures: the proprietary gating of constraint information behind paywalls, fragmented across incompatible frameworks, and evaluated against commercial rather than truth-seeking criteria. The formal results concern the information architecture that survives Mars boundary conditions, the Beier Factorial mechanism for combinatorial constraint discovery through transparent human interaction, and the sane superintelligence that emerges when AI agents operate within this architecture under air-gapped scoring and human override. Existing ESG information architectures are evaluated against the test, and the stakes of that evaluation reduce to a single claim: any information architecture that fails the Mars Test is consuming the time horizon within which it could prevent the collapse that makes it worthless.
Three companion papers provide the formal apparatus. The price system introduces excess distortion Delta > 0 by compressing high-dimensional judgment into scalar signals, a result robust to partial constraint loading (Proposition 1') and multiple prices (Proposition 3), with supplementary disclosure channels producing strictly higher marginal distortion reduction than further price improvement (Proposition 2; all in Beier, 2026h). A self-reinforcing feedback loop emerges: the price system's inability to carry constraint information justifies agents' rational inattention to those dimensions, which ensures constraint information does not enter subsequent prices. The Grossman-Stiglitz paradox is resolved through track record capital - a return to information production independent of trading profit whose key decomposition (Beier, 2026d, Proposition 7) separates the principal's willingness to pay into a consensus premium that vanishes as markets become efficient and a constraint premium W_constraint(q) > 0 that is permanently bounded above zero and independent of price efficiency. Incentive compatibility follows within the Hurwicz-Myerson framework: under the Brier scoring rule with coverage weight alpha < 2/3, honest comprehensive disclosure strictly dominates strategic selection for all agents regardless of calibration quality (Proposition 14). The stability condition S = LD / sigma(LD), with its reflexive coupling and phase transition at S = 1, is derived in Beier (2026e) from the distinction between Beierspace quantities (whose statistical properties are constituted by human decisions) and eigenspace quantities (whose statistical properties arise from physical law); the same paper establishes an informational impossibility theorem: a system in the collapse trap cannot determine from its own data whether its collapse is permanent or recoverable. The present paper integrates these results, extends them to the Mars boundary conditions, and applies them to the concrete problem of Earth's ESG information architecture.
The Mars colony operates under five conditions that jointly determine its information architecture requirements.
Small N. The colony has between 50 and 500 agents, reflecting the near-term realities of interplanetary colonization. The population is too small for market mechanisms to aggregate information through price competition in the way terrestrial markets do. With fewer participants, each agent's private judgment constitutes a larger fraction of the total information available to the colony. Losing any single agent's contribution through hoarding, miscommunication, or incentive misalignment has a measurable effect on the colony's information environment.
High sigma_e. Mars is physically hostile in ways that produce rapid, high-variance structural change. Radiation exposure, dust storms, equipment degradation, atmospheric processing failures, water recycling breakdowns, and crop failures all generate physical structural drift - changes in the constraint environment that originate in physics and chemistry rather than human decisions. In the notation of Beier (2026e), sigma_e is large. The eigenstructure of the colony's constraint environment rotates frequently, as physical processes impose new coupling patterns between subsystems (a dust storm simultaneously affects solar power, thermal management, water recycling, and food production through distinct physical mechanisms).
Zero surplus. The colony has no slack to absorb information losses. On Earth, the price system's excess distortion (Beier, 2026h, Proposition 1) generates misallocation on constraint dimensions, but the misallocation is distributed across billions of people and manifests on timescales long enough for partial correction. On Mars, misallocation on a constraint dimension can be lethal within a single operational cycle. If the water recycling system's interaction with the power grid is not tracked, and the interaction produces a failure, people die before the error can be corrected. There is no accumulated wealth, no insurance market, no backup system redundant enough to compensate for missed constraint interactions.
Surplus is dimension-specific, not aggregate, and the distinction matters for the Earth application. Define the effective surplus on constraint dimension k as the gap between the current state on dimension k and the irreversible threshold on that dimension. A nation can have high aggregate economic surplus ($25 trillion GDP) and zero effective surplus on its atmospheric carbon budget (the remaining carbon budget consistent with 1.5 C is approximately 340 Gt CO2 at current emission rates, or roughly eight years of global emissions; IPCC, 2021-2023, adjusted for post-2020 emissions). The same gap opens in finance: ample capital reserves coexist with zero effective surplus on an information architecture's ability to track aquifer depletion, because the depletion threshold is physical and the capital cannot substitute for the missing information. When the effective surplus on a constraint dimension reaches zero, the Mars conditions hold on that dimension regardless of the economy's aggregate surplus. Theorem 4.3's zero-surplus condition should be read as applying dimension by dimension: the theorem's conclusions hold on each constraint dimension where effective surplus approaches zero, while the Grossman-Stiglitz equilibrium continues to function on dimensions where effective surplus remains large.
The irreversible threshold on a constraint dimension is rarely known with precision. The IPCC gives a range for the remaining carbon budget (approximately 500 Gt CO2 from January 2020 for a 50% probability of limiting warming to 1.5 C, with estimates ranging from 400 Gt at 67% probability to 900 Gt at 17%; IPCC, 2021-2023; after approximately 160 Gt of subsequent emissions through 2024, the central estimate is roughly 340 Gt remaining, and Forster et al. (2025) give an updated central estimate of approximately 130 Gt from January 2025). Ecosystem tipping points are even less precisely characterized - the thresholds for Amazon dieback, AMOC slowdown, or West Antarctic ice sheet collapse are estimated with wide uncertainty bands. The dimension-specific surplus concept operates on ranges, reflecting the threshold uncertainty inherent in every constraint dimension: the effective surplus is itself a range. When the upper bound of the effective surplus range approaches zero - when even the most optimistic threshold estimate leaves little room - the Mars conditions hold on that dimension under any reasonable parameterization. The dimension-specific surplus concept localizes the uncertainty to specific dimensions and makes the empirical challenge visible, which is what allows the formal results in Section 4 to operate dimension by dimension rather than requiring a global claim about aggregate surplus.
No institutional path dependence. The colony has no legacy price system, no pre-existing regulatory apparatus, no financial data vendors, and no proprietary information industry. The information architecture is designed from scratch, which removes the objection that "we can't change the existing system." Mars has no existing system. Whatever architecture emerges must earn its place from first principles.
No exit. The colonists hold one-way tickets. There is no option to sell the colony's assets and relocate to a better-informed jurisdiction. The only hedge against information failure is collective competence - the colony's aggregate capacity to observe, model, communicate, and act on constraint information. This transforms information architecture from an economic optimization problem (maximizing returns subject to costs) into a survival problem (maintaining S > 1 on all critical constraint dimensions simultaneously).
A sixth condition follows from the physical realities of interplanetary distance:
Local repairability. All equipment must be repairable with locally available materials and locally held knowledge. There is no internet connection to Earth capable of supporting real-time software updates, patches, or remote diagnostics. Round-trip communication delays of 6 to 44 minutes (depending on orbital position) make interactive troubleshooting infeasible for any time-critical system. All critical software must therefore be open source as an operational necessity, because closed-source systems whose maintainers are on another planet cannot be fixed when they break. Hardware must be documented at the component level. Data formats must be open and parseable by any system the colony can build or repair.
From these conditions, four claims follow, each of which the subsequent sections formalize.
The price system is the wrong codec under Mars boundary conditions. The scalar compression that produces excess distortion Delta > 0 on Earth (Beier, 2026h) becomes potentially lethal on Mars, because the uncompressed constraint dimensions carry variance that translates directly to mortality risk. Partial constraint loading does not rescue the codec: excess distortion remains at 84% of the eigenbasis value even when 40% of the price's information capacity loads on constraint dimensions (Beier, 2026h, Proposition 1'). Nor does the existence of multiple prices: derivative instruments span redundant consensus risks rather than independent physical constraints, leaving the effective rank on the constraint subspace far below K-1 (Beier, 2026h, Proposition 3). On Mars, where every constraint dimension carries lethal variance, the price system's structural inability to reach those dimensions is a design flaw that no improvement to market microstructure can fix. The colony cannot afford to compress K constraint dimensions into one scalar and then spend reconstruction resources recovering the lost information (the $44.3 billion annual reconstruction expenditure that terrestrial markets absorb; Burton-Taylor, 2025). It must track multiple dimensions simultaneously. Furthermore, the rational inattention feedback loop identified in Beier (2026h, Proposition 2, Remark) - in which the price system's inability to carry constraint information justifies agents' inattention to those dimensions, which ensures constraint information does not enter subsequent prices - would be lethal on Mars, where "rational inattention" to a constraint dimension means no one is watching the system that fails.
Full disclosure follows as individually rational under zero surplus. When survival probability is a function of collective S = LD / sigma(LD), and S is strictly decreasing in any reduction of the disclosure rate D, each agent's expected payoff from disclosure exceeds the expected payoff from hoarding for any discount rate, because the probability of surviving to collect the hoarding payoff is itself degraded by the hoarding. Track record capital then emerges as the unique stable compensation mechanism: when the binding constraint is collective survival rather than individual wealth accumulation, the only return to information production is influence over resource allocation decisions, allocated to agents whose predictions have been validated against outcomes (Beier, 2026d).
The binding individual constraint is cognitive suppleness - the capacity to absorb large model revisions without degraded learning, formalized in Beier (2026e, Theorem 8.1). Agents who cannot update their models fast enough when the physical environment shifts make decisions that endanger the colony. The suppleness multiplier is a survival prerequisite in this regime, where model lag translates directly to mortality risk.
The architecture that emerges from the Mars boundary conditions is a distributed multi-dimensional codec, fundamentally unlike a price system.
The state vector. The colony maintains a shared, continuously updated representation of its full state vector V = (V_1, V_2, ..., V_K), where K is the number of constraint dimensions the colony can currently track. Each V_k represents a distinct aspect of the colony's operational and environmental state: power generation capacity, water recycling efficiency, atmospheric composition, radiation exposure, crop health, equipment degradation, social cohesion, supply reserves, and the interactions among these. The dimensionality K is not fixed; it grows as the colony discovers new constraint interactions (a process formalized in Section 4).
Sensor nodes. Every agent is a sensor node. Each agent observes some subset of the state vector through their work, their training, and their physical location within the habitat. The water recycling engineer has high-resolution observations of V_water but noisy observations of V_agriculture. The agricultural specialist has the reverse. The information architecture's job is to combine these heterogeneous, partial observations into a colony-wide estimate of V that is as accurate as possible given the colony's total information capacity LD.
Multi-dimensional compression. Compression still occurs - agents have finite attention, and not all K dimensions can be tracked at full resolution. But the compression is optimized via reverse water-filling across dimensions (the same mathematical structure as the rate-distortion optimum in Beier, 2026h, Proposition 1), rather than concentrated on a single consensus dimension as the price system does. High-variance constraint dimensions receive more attention; low-variance dimensions receive less. The allocation adjusts as the environment changes - when a dust storm shifts variance from dimension 3 to dimension 7, the colony's attention allocation shifts accordingly.
Track record capital as currency. The colony allocates decision weight to agents in proportion to their track record on the dimensions they report on. An agent whose predictions about water system performance have been consistently validated against outcomes receives more influence over water-related resource allocation decisions; poor predictions reduce that influence correspondingly.
The formal foundation for this mechanism is established in Beier (2026d), which resolves the Grossman-Stiglitz paradox by introducing track record capital as a return to information production independent of trading profit. The independence is not assumed but derived: the principal's willingness to pay for calibrated judgment decomposes into a consensus premium W_consensus(q, tau_p) that vanishes as price efficiency increases and a constraint premium W_constraint(q) that is permanently bounded above zero (Beier, 2026d, Proposition 7). The constraint premium is positive because constraint dimensions V_2 through V_K carry variance that the price system structurally cannot compress, and the physical environment continuously generates new constraint variance on these dimensions (Beier, 2026d, Claim 9). On Mars, where all dimensions are constraint dimensions (there is no "consensus value" that a price system aggregates), the entire return to information production flows through the constraint premium. Track record capital is the only compensation mechanism whose return does not depend on a functioning price system, which makes it the unique stable currency under Mars boundary conditions where the price system is the wrong codec.
Incentive compatibility is established within the Hurwicz-Myerson mechanism design framework (Beier, 2026d, Propositions 11-14). Under the Brier scoring rule with coverage weight alpha < 2/3, honest comprehensive disclosure strictly dominates strategic selection for every agent regardless of calibration quality (Beier, 2026d, Proposition 14). The calibration threshold is zero: no agent, no matter how poorly calibrated, benefits from selectively disclosing only favorable assessments. This result is essential for the Mars architecture because it means the full-disclosure equilibrium does not require screening out low-quality agents - the scoring mechanism handles incentive alignment automatically.
Track record capital cannot be hoarded, inherited, or transferred - only accumulated through validated disclosure, and only lost when predictions fail.
Binding constraints. The binding individual constraint is cognitive suppleness s - how quickly an agent can update their model of the colony's constraint environment when the environment changes. The binding collective constraint is LD - the colony's total information throughput, the product of aggregate learning capacity and aggregate disclosure rate.
This architecture is the eigenspace extension theorem (Beier, 2026e, Theorem 8.1) operating in real time. The number of usable dimensions K* is determined by the colony's aggregate information capacity LD, amplified by cognitive suppleness s, and bounded above by the constraint dimensions whose drift rate does not exceed the colony's capacity to track them. The theorem's ceiling - K*_max = |{k : sigma_k < LD}|, the set of dimensions whose drift rate falls within the attention budget - is the hard boundary of what the colony can see.
Theorem 4.3 (full disclosure as unique Nash equilibrium under Mars conditions) is derived in Section 4 after the Beier Factorial mechanism is introduced, because the Nash equilibrium result depends on the combinatorial structure of information production under full disclosure.
The reflexive coupling emerges from three results that no single companion paper derives alone: excess distortion Delta > 0 in the price system (Beier, 2026h), a constraint premium W_constraint(q) > 0 sustaining disclosure independently of price efficiency (Beier, 2026d), and the stability condition S = LD / sigma(LD) (Beier, 2026e).
Proposition 3.1 (The distortion floor). Consider an economy with the following structure: (i) the price system operates with excess distortion Delta = D_price - D*(R_price) on K - 1 constraint dimensions (Beier, 2026h, Proposition 1); (ii) disclosure is sustained by the constraint premium W_constraint(q), which is strictly increasing in the variance of the uncompressed constraint dimensions sum_{k=2}^{K} lambda_k (Beier, 2026d, Proposition 7); (iii) the eigenstructure's stability requires S = LD / sigma(LD) > 1 (Beier, 2026e, Theorem 5.2); and (iv) the disclosure rate D is sustained only when the constraint premium exceeds the cost of disclosure: W_constraint(q) > c_D for a positive measure of agents. Then there exists Delta_min > 0 such that for Delta < Delta_min, the disclosure channel collapses and S falls below 1.
Proof. The chain of implications is: Delta -> 0 implies sum_{k=2}^{K} lambda_k -> 0 (the constraint dimensions carry vanishing variance, since Delta converges to sum_{k=2}^{K} lambda_k as SNR_1 -> infinity; Beier, 2026h, Proposition 1, part v). By Beier (2026d, Proposition 7), W_constraint(q) = sum_{k=2}^{K} (1/2gamma) ln((tau_{Vk} + tau_{DVk}(q)) / tau_{Vk}). As lambda_k -> 0, the prior precision tau_{Vk} = 1/lambda_k -> infinity, so the fractional precision improvement tau_{DVk}(q)/tau_{Vk} -> 0 and W_constraint(q) -> 0. When W_constraint(q) < c_D for all agents, no agent finds disclosure profitable: lambda_D* = 0. With D = 0, x = LD = 0 and S = 0 < 1. The eigenstructure destabilizes (Beier, 2026e, Theorem 5.2: below S = 1, self-destabilizing dynamics drive x toward 0).
The distortion floor is Delta_min = inf{Delta : there exists q such that W_constraint(q, Delta) >= c_D}. It is strictly positive because W_constraint(q, 0) = 0 < c_D and W_constraint is continuous in Delta. QED.
Remark on the condition Delta -> 0 implies sum lambda_k -> 0. This is the strongest version: the constraint dimensions carry vanishing variance. A weaker version holds when Delta -> 0 through increasing price precision on V_1 (SNR_1 -> infinity) with lambda_k fixed: in this case Delta -> sum lambda_k > 0, and the distortion floor does not bind because the constraint premium remains positive. The distortion floor binds when Delta approaches zero because the constraint dimensions themselves carry less variance - a regime in which the economy's constraint environment is low-dimensional and the price system is adequate. The floor's economic content is therefore: in any economy where the constraint dimensions carry substantial variance (the empirically relevant case), reducing Delta by improving the price system does not threaten the disclosure incentive, but if the constraint variance were to vanish, the disclosure incentive would vanish with it and the eigenstructure would lose its support. The reflexive coupling is between the existence of constraint-dimension variance and the sustainability of the information architecture that tracks it.
The distortion floor differs from the standard public goods framing. Standard externality theory says environmental information is undersupplied because agents cannot capture the social benefit. The distortion floor says the information destruction is structurally coupled to the information production incentive: the constraint premium that sustains disclosure is grounded in the same uncompressed variance that constitutes the excess distortion. It is a reflexive coupling between the price system's failure mode and the information architecture's survival condition. The Observation-Maintenance Identity (Beier, 2026i) provides the deeper grounding: for coordination-dependent structures, observation through an information channel and maintenance of dimensional coherence are the same act. The price system's compression withdraws maintenance from constraint dimensions, and excess distortion is excess dissipation. The distortion floor follows: reducing distortion toward zero withdraws the maintenance deficit that creates the incentive for supplementary disclosure.
On Mars, the distortion floor does not exist because the price system does not operate. The colony's information architecture does not depend on excess distortion to motivate disclosure - it depends on survival. On Earth, the distortion floor defines the regime in which the price system and the disclosure system are reflexively coupled - each depending on the other's operation for its own sustainability. The Mars architecture eliminates the distortion floor by eliminating the dependence on the price system for constraint-dimension coordination.
Structured disclosure improves the discloser's judgment quality over time through the same feedback loops that the cognitive science literature identifies as prerequisites for expert performance.
Beier (2026d, Section 3.4) develops the mechanism from the cognitive science of expert performance. Feedback improves judgment reliably only in high-validity environments where the relationship between observable cues and eventual outcomes is regular enough for learning (Kahneman and Klein, 2009). The structured disclosure format - with explicit confidence levels, timestamped predictions, and proper scoring against outcomes - engineers a high-validity feedback environment in domains where the natural environment lacks one. Experimental work on calibration training confirms that explicit feedback produces measurable improvement (Lichtenstein and Fischhoff, 1980), and the conditions identified in the deliberate practice literature - structured task, unambiguous feedback, sufficient iteration (Ericsson, Krampe, and Tesch-Romer, 1993) - map directly onto the five-field disclosure format, proper scoring, and rolling disclosure cadence.
On Mars, this means the colony's aggregate learning capacity L is not a fixed parameter. It increases over time as colonists practice structured disclosure, receive outcome feedback, and become better calibrated. The stability condition S = LD / sigma(LD) improves through both channels: D stays high (full disclosure is the Nash equilibrium) and L rises (the disclosure discipline trains better judgment). The proprietary architecture cannot access this improvement because proprietary analysts do not receive the structured outcome feedback that drives calibration improvement - their feedback is filtered through institutional hierarchies, delayed by reporting cycles, and compressed into performance metrics that measure trading profit rather than prediction accuracy.
The Mars architecture's disclosure rate responds to environmental conditions in a way that current financial markets do not.
In aerospace engineering, flutter suppression systems increase control surface activity in proportion to turbulence intensity - the wing that locks its ailerons is the one that breaks. The Mars architecture's analog: when sigma_e spikes (a dust storm, an equipment failure, an unexpected atmospheric event), the architecture responds by increasing disclosure, not decreasing it.
Current financial markets do the opposite under stress. When volatility spikes, proprietary models go dark. Firms reduce disclosure to protect competitive positions. Information flow decreases at precisely the moment it is most needed. The rational inattention feedback loop (Beier, 2026h, Proposition 2, Remark) accelerates during stress: prices become less informative, agents become less attentive to constraint dimensions, and the next period's information environment degrades further.
Define the flutter suppression property: an information architecture exhibits flutter suppression if dD/d(sigma_e) > 0 - the disclosure rate increases when physical structural drift increases.
Conjecture (Flutter suppression under Mars conditions). The Mars architecture satisfies the flutter suppression property. The argument: rising sigma_e steepens pi(S), which increases the marginal survival benefit of disclosure dpi/dS * dS/dD * (1/N), which increases each agent's optimal d_i. Under zero surplus (the Mars case), d_i = 1 regardless of sigma_e, so the property holds trivially (D = 1 is already maximal; it cannot increase further, but it does not decrease). The non-trivial conjecture is for positive surplus: that the interior equilibrium D*(sigma_e) is increasing in sigma_e. Proving this requires solving the N-agent game for the equilibrium disclosure rate at positive surplus and differentiating with respect to sigma_e - a computation the paper does not perform. The comparative statics on Theorem 4.3 support the direction (higher sigma_e steepens pi, which shifts each agent's best response toward higher d_i), and the Mars limiting case confirms the endpoint (at zero surplus, D = 1 for all sigma_e). The full derivation at positive surplus is deferred.
Flutter suppression, if it holds, produces a testable prediction: markets or organizations with volatility-responsive disclosure (disclosure rate increasing during stress events) will exhibit smaller Frobenius norm changes in their covariance estimates during crises than markets or organizations with constant or decreasing disclosure rates, controlling for shock magnitude. This prediction is specific to the framework and does not follow from standard information economics. The prediction is testable independently of the conjecture's proof status.
The Beier Factorial is the combinatorial process by which autonomous agents form agencies through transparent interaction. The formal results establish superlinear growth (Proposition 4.1: O(N^alpha) for alpha > 1 on Mars) and increasing marginal returns (Proposition 4.2: the marginal contribution of the (N+1)th agent is strictly increasing in N on Earth). Whether the growth rate achieves factorial scaling (N!) depends on the depth of the recursive agency-of-agencies structure and the constraint interaction density at each level of recursion, which is an empirical question the formal results do not resolve. The proven rates are polynomial (at minimum quadratic under dense pairwise coupling) and potentially exponential (under deep recursive structure), with the binding constraint being the attention budget LD rather than the combinatorial space itself.
Minsky (1986) described intelligence as emerging from the interaction of simple agents organized into agencies - composite structures whose capabilities exceed those of their constituents. In Minsky's framework, the agents are computational subprocesses within a single mind, and the agencies are functional groupings that arise from their interaction. The Society of Mind was a theory of individual cognition, not of collective information production.
The Beier Factorial extends the agent/agency structure to a population of autonomous humans interacting in a real-time, high-disclosure economy. The extension changes the object in three ways that matter for the formal results.
An agent in the Beier Factorial is a human sensor node - a person who observes, models, and reports on some subset of the system's state vector V. The agents are heterogeneous autonomous individuals with different training, different physical observation access, different cognitive styles, and different models of how the world works. This heterogeneity is the source of the combinatorial richness that produces the mechanism's growth.
An agency is a composite inference structure that emerges from the interaction of multiple agents through disclosure. The agency is not reducible to the union of its agents' individual observations. It produces joint inferences - conclusions about constraint interactions that no constituent agent could reach alone, because the interaction lives in the space between their respective observation sets.
The departure from Minsky has several dimensions. Agency formation is voluntary and driven by disclosure rather than hardwired into computational architecture. Agencies persist, grow, or dissolve based on track record validation against outcomes, accumulating attention capital when productive and losing it when not. And the combinatorics extend beyond agent-agent interaction to agency-agency composition: agencies can form higher-order agencies, producing a recursive structure whose combinatorial explosion is kept productive by the same track record mechanism that prunes unproductive agencies at every level.
Three colonists work in different habitat subsystems: water recycling, power generation, and food production. Over breakfast, they share observations from the previous cycle. Colonist A reports that the water recycler's efficiency dropped 3%. Colonist B reports that the solar array's output shifted timing by 20 minutes. Colonist C reports a growth anomaly in crop section 4.
No individual colonist can identify the cause. Colonist A's model of water recycling does not include solar array timing. Colonist B's model of power generation does not include crop biology. Colonist C's model of food production does not include water recycler thermodynamics. The three observations, taken individually, are three unrelated anomalies requiring three separate investigations.
The three-person agency - the joint inference produced by combining all three observations in a single conversation - identifies a dust storm pattern that is simultaneously coating solar panels (shifting power timing), changing thermal cycling in the water system (reducing efficiency through altered heat exchange), and reducing photosynthetic light in the greenhouse (producing the crop anomaly). The constraint interaction lives in the joint space. No pair of the three observations is sufficient to identify it; all three are required, and the identification requires a model that spans water, power, and agriculture simultaneously.
On Mars, surfacing this joint inference is obviously rational. The dust storm interaction is a threat to colony survival; knowing about it allows preventive action (cleaning solar panels, adjusting water system parameters, supplementing greenhouse lighting). Keeping any of the three observations private - treating the anomaly as proprietary information to be exploited for personal advantage - is indistinguishable from sabotage at zero surplus.
The breakfast problem illustrates the general mechanism. The constraint interaction was invisible to each agent individually and to any pair. It became visible only when three heterogeneous observation sets were combined through disclosure and conversation. The number of such interactions that can be discovered grows with the number of agents and with the density of constraint coupling in the environment.
Formalize the mechanism. Let N be the number of disclosing human sensor nodes. Each node i observes a subset O_i of the state vector V with node-specific noise characteristics. An agency A_S, formed by a subset S of nodes, produces a joint inference by combining the observations {O_i : i in S}. Define V(A_S) as the set of constraint dimensions visible to agency A_S but not visible to any proper sub-agency - the novel inferences that require the full subset S.
Let K*(N) denote the total number of constraint dimensions visible to at least one agency formed from N sensor nodes:
K*(N) = |union_{S subset {1,...,N}, S nonempty} V(A_S)|
The theoretical maximum number of agencies is 2^N - 1 (every non-empty subset). Most of these potential agencies produce no novel inference - the vast majority of random subsets of sensor nodes share no relevant constraint interaction in their joint observation space. The productive agencies are a small fraction of the combinatorial total.
The growth rate of K*(N) depends on the constraint interaction density of the environment - the fraction of pairs, triples, and higher-order subsets of state vector dimensions that exhibit non-trivial interactions. Define the interaction density at order m as:
rho_m = (number of m-tuples of dimensions with non-trivial interaction) / C(K, m)
where C(K, m) is the number of m-element subsets of the K-dimensional state vector.
On Mars, the constraint interaction density is high. Every habitat subsystem is coupled to every other through shared resources (power, water, atmosphere, thermal management). A change in any one subsystem propagates to others through physical mechanisms. The interaction graph is dense, not sparse.
Proposition 4.1 (Superlinear growth on Mars). Let N sensor nodes observe a K-dimensional state vector with constraint interaction density rho_m at order m. Under full disclosure, K*(N) grows as O(N^alpha) for alpha > 1, where alpha depends on the interaction density profile {rho_m : m = 2, 3, ...} and on the distribution of observation subsets across nodes.
Proof sketch. The (N+1)th sensor node, upon joining the disclosure network, forms potential agencies with every existing subset of nodes. The number of new agencies containing the (N+1)th node is 2^N - 1. The fraction of these that produce novel inferences is determined by the interaction density and the overlap between the new node's observation set O_{N+1} and the observation sets of existing agencies. When rho_m is bounded below by a constant for some m >= 2 (dense coupling), the expected number of productive new agencies grows at least linearly in the number of existing nodes, because each existing node's observation set has non-trivial probability of interacting with the new node's observations. The cumulative K*(N) therefore satisfies K*(N+1) - K*(N) >= c * N for some constant c > 0 depending on rho, which yields K*(N) >= (c/2) N^2 for large N. More generally, if productive interactions exist at order m, K*(N) grows as O(N^m) in the regime where N is large enough to populate m-element agencies but small enough that K*(N) has not exhausted the available dimensions.
On Mars, N is small (50-500), so the growth is superlinear but bounded by both the population and the colony's aggregate attention budget LD. The practical ceiling is the set of dimensions whose drift rate falls within the attention budget (Beier, 2026e, Theorem 8.1, Part B). The superlinear growth describes how fast the colony approaches that ceiling as it adds disclosing agents, not a claim about unbounded dimensional discovery.
Earth has 8 billion potential sensor nodes. The constraint environment is orders of magnitude more complex than Mars: climate-financial interactions, ecological-agricultural feedback, epidemiological-economic coupling, technology-geopolitical linkages, all operating across scales from local to planetary. The number of constraint dimensions K is, for practical purposes, unbounded relative to current observational capacity - the economy's K* is a negligible fraction of the actual dimensionality of the problems it faces.
Under a super-transparent economy, the Beier Factorial operates at a scale that produces factorial growth in discoverable constraint dimensions, exceeding the polynomial rates proved for Mars. The distinction from Mars rests on three differences in the boundary conditions. On Mars, K*(N) is bounded above by the habitat's finite constraint dimensionality - eventually the colony discovers all interactions its environment contains and K* saturates. On Earth, the constraint dimensionality so vastly exceeds current K* that the binding constraint is the number of disclosing agents and the rate at which they form productive agencies. There are always more dimensions to find.
The recursive agency-of-agencies structure compounds this advantage by operating at much greater depth on Earth. A team of three that discovered a dust storm interaction on Mars is close to the maximum useful agency depth for a 200-person colony. On Earth, agencies of agencies of agencies - hierarchical inference structures combining the insights of thousands of sub-agencies into progressively higher-order constraint maps - can reach depths whose combinatorics exceed exponential scaling (the recursive agency-of-agencies count is related to Bell numbers and hierarchical compositions that grow faster than 2^N). The number of distinct hierarchical agency structures constructible from N agents grows faster than the number of flat subsets (which is already 2^N - 1), because the hierarchical structures include all possible compositions, not just all possible subsets.
The urgency reinforces the growth requirement. Earth's problems require growth rates exceeding polynomial because the time budget is unknown and shrinking. The warming rate is accelerating. Tipping points may be crossed within decades. The information architecture must discover and act on constraint dimensions fast enough to prevent irreversible state changes in physical systems. Superlinear growth might be sufficient for a 200-person colony maintaining a habitat with known physics; it is insufficient for a planet facing an unknown number of interacting tipping points on an unknown timeline.
Proposition 4.2 (Increasing marginal returns to disclosure on Earth). Under full disclosure and dense constraint coupling, the marginal contribution to K* of the (N+1)th disclosing human sensor node is strictly increasing in N whenever the constraint interaction density rho_m exceeds a computable threshold for some m >= 2 and all existing nodes disclose fully.
Proof. The (N+1)th node forms potential new agencies with every existing subset. The number of subsets is 2^N - 1, which is strictly increasing in N. The expected number of productive new agencies is at least rho * 2^N for some effective interaction density rho > 0 (this follows from the same argument as Proposition 4.1, extended to account for the growing base of existing nodes). Since the number of potential productive agencies grows exponentially in N while K*(N) grows at most exponentially (bounded by the total constraint dimensionality of the environment), the marginal contribution K*(N+1) - K*(N) is strictly increasing in N in the regime where K*(N) has not yet saturated the environment's constraint dimensionality - which, on Earth, is the regime we occupy.
Under hoarding (partial disclosure), the marginal contribution of the (N+1)th node is bounded above by the node's individual observation capacity |O_{N+1}|, because the hoarding nodes do not form agencies with the new entrant. The ratio of marginal K* under full disclosure to marginal K* under hoarding therefore grows as at least (rho * 2^N) / |O_{N+1}|, which is unbounded in N. The more agents are already disclosing, the greater the advantage of disclosure over hoarding for the next agent.
The increasing-returns information externality operates here in full. Each disclosing human creates new agency possibilities with every existing discloser. The more people disclose, the more valuable each additional disclosure becomes. The externality is specific to the Beier Factorial structure - it does not arise in standard information economics, where the value of information production is determined by the information's scarcity (which decreases as more agents produce it) rather than by the combinatorial richness of the agency space (which increases).
The Beier Factorial departs from Minsky's Society of Mind in kind, not scale. Minsky conceived of agents as computational subprocesses interacting through fixed architecture within a single cognitive system, with agencies identified by the theorist analyzing the resulting functional groupings. The Beier Factorial's agents are autonomous humans whose agency formation is voluntary, dynamic, and driven by disclosure rather than hardwired architecture. Agencies self-organize and are validated or pruned by outcome scoring - a quality mechanism Minsky's framework has no counterpart for, since the Society of Mind theorizes how intelligence works without addressing how it improves. Track record validation is what makes the combinatorial growth productive rather than noisy: agencies that produce validated predictions grow, and those that do not dissolve.
The computational difference compounds the structural one. Where Minsky's framework operates within a single mind's budget, the Beier Factorial distributes the search across all participating agents, with the combinatorial space growing factorially while each individual's cost grows at most linearly. The burden of searching for productive agencies is distributed, and - as Section 5 develops - can be augmented by AI agents operating under air-gapped scoring.
With the Beier Factorial mechanism established, the Nash equilibrium result can be stated precisely.
Theorem 4.3 (Full disclosure as unique Nash equilibrium under Mars conditions). Consider N agents in a Mars colony with zero surplus and sigma_e > sigma_e_crit (high physical structural drift). Each agent i chooses a disclosure rate d_i in [0, 1]. The colony's aggregate disclosure rate is D = (1/N) sum_i d_i, and its stability ratio is S = LD / sigma(LD), where sigma(LD) = sigma_e + sigma_b(LD) with sigma_b strictly decreasing in LD (Beier, 2026e, Proposition 4.1). Each agent's survival probability is pi(S), a strictly increasing function of S with pi(S) = 0 for S <= 0.
The agent's payoff is:
U_i(d_i, d_{-i}) = pi(S(d_i, d_{-i})) * [W_i(d_i) + R_i(d_i, d_{-i})]
where W_i(d_i) is any private benefit from hoarding (trading profit, reputational advantage from information asymmetry) and R_i(d_i, d_{-i}) is the agent's Beier Factorial return - the agency-derived constraint knowledge that reduces the agent's operational risk. R_i is grounded in the constraint premium W_constraint(q) from Beier (2026d, Proposition 7): because the constraint premium is permanently bounded above zero and independent of price efficiency, R_i > 0 for any agent with positive calibration quality q > 0, even in the absence of a functioning price system. On Mars, where the price system does not operate, R_i reduces to the constraint premium itself plus the operational survival value of the agency-derived knowledge - both strictly positive under the stated conditions.
Under zero surplus, pi(S) is steep: small reductions in S produce large increases in mortality probability. Specifically, the zero-surplus condition implies that partial derivative of pi with respect to S at S = 1 is large relative to any W_i. The key parameter is:
(d pi / dS) * (dS / dD) * (1/N) vs. (dW_i / dd_i)
The left side is the survival benefit of the agent's marginal disclosure. The right side is the private benefit of marginal hoarding. Under zero surplus, dpi/dS is large at all S values near the operating point (because there is no buffer between S and catastrophe), and dS/dD > 0 by the stability condition. The private hoarding benefit W_i is bounded above by the total economic surplus of the colony, which is approximately zero by assumption.
For any discount rate delta > 0, the present value of hoarding is:
PV_hoard = sum_{t=0}^{infinity} delta^t * pi(S_hoard)^t * W_i
The present value of disclosure is:
PV_disclose = sum_{t=0}^{infinity} delta^t * pi(S_disclose)^t * R_i
Since pi(S_disclose) > pi(S_hoard) (disclosure raises S, which raises survival probability), and R_i >= 0 while W_i is bounded by the near-zero surplus, PV_disclose > PV_hoard for all delta in (0, 1). The inequality holds regardless of the discount rate because the survival probability pi enters multiplicatively - even an agent who heavily discounts the future prefers to be alive in the next period.
The Nash equilibrium is d_i = 1 for all i (full disclosure). Any unilateral deviation d_i < 1 reduces D, reduces S, reduces pi, and the survival cost exceeds the hoarding benefit at zero surplus. The equilibrium is unique because the payoff function U_i is strictly increasing in d_i at d_i = 1 for any profile d_{-i} in which d_j = 1 for all j != i - no agent has an incentive to deviate from full disclosure when all others disclose.
Remark. The result depends critically on zero surplus. As surplus increases, the survival function pi(S) flattens (the colony can absorb information losses without immediate mortality), and the private hoarding benefit W_i may exceed the marginal survival benefit of disclosure. Mars boundary conditions produce this equilibrium uniquely; the claim for Earth is that the constraint environment is converging toward the conditions under which it holds.
Remark (Illusion of surplus). The Nash equilibrium depends on agents possessing an accurate assessment of effective surplus on the constraint dimension. The rational inattention feedback loop (Beier, 2026h, Proposition 2, Remark) creates a specific failure mode: when the price system carries zero information about a constraint dimension, agents whose attention is optimized through prices perceive the effective surplus on that dimension as unchanged even as the physical surplus approaches zero. They behave as if they are in the Bermuda regime on a dimension where the physical reality is approaching Mars. The theorem's equilibrium shift requires that agents perceive the tightening, which requires an information channel capable of carrying constraint-dimension signals - the channel whose absence is the problem the theorem identifies. The transition dynamics from hoarding to disclosure therefore depend on an exogenous shock to attention (a constraint event that manifests in prices) or on an exogenous disclosure channel (structured constraint reporting that bypasses the price system). The Mars architecture provides the latter.
Following the proof discovery protocol (Section 11 of Beier, 2026e):
(a) Timescale separation: the disclosure decision (fast) is separated from the track record accumulation (slow) and the physical structural drift (variable). The Nash equilibrium analysis operates on the disclosure timescale.
(b) Fixed points: d_i = 1 for all i is the unique Nash equilibrium under the stated conditions. d_i = 0 for all i is not a Nash equilibrium because at D = 0, S = 0, pi = 0, and any agent can improve their payoff by disclosing (which raises S above zero and thus pi above zero).
(c) The "phase portrait" in strategy space: the basin of attraction of full disclosure is the entire strategy space under zero surplus, because any configuration with D > 0 has the property that each agent's best response is d_i = 1.
(d) Parameter sweep: the critical parameter is surplus. As surplus increases from zero, the survival function pi flattens, and at a computable surplus threshold s_crit, the Nash equilibrium shifts from full disclosure to an interior equilibrium where some hoarding is individually rational. s_crit depends on sigma_e, N, and the eigenvalue spectrum {lambda_k}.
(e) Counterexample outside conditions: at surplus s > s_crit, full disclosure is not a Nash equilibrium. The counterexample: with sufficient surplus, an agent can hoard information about a constraint dimension, wait for the constraint to manifest, and profit from being the only agent who anticipated it. The profit exceeds the marginal survival cost because the surplus buffer absorbs the information loss. This is precisely the Grossman-Stiglitz equilibrium (Grossman and Stiglitz, 1980) - it requires surplus to function.
(f) Unrequested finding: the threshold s_crit is a function of N, sigma_e, and the eigenvalue spectrum {lambda_k}. At fixed sigma_e, s_crit increases with N because each agent's marginal contribution to D is 1/N - in a population of 8 billion, any single agent's hoarding has negligible effect on aggregate D. This explains the current equilibrium: proprietary information is individually rational on Earth today because the marginal survival cost of one agent's hoarding is diluted across the population.
But s_crit is not monotone in sigma_e. When sigma_e rises on a global constraint dimension - climate, atmospheric carbon budget, ecosystem stability - the survival function pi(S) steepens for all N agents simultaneously, because the constraint affects everyone regardless of population size. The steepening of pi increases dpi/dS, which increases the left side of the inequality (dpi/dS) * (dS/dD) * (1/N) vs. (dW_i/dd_i), partially offsetting the 1/N dilution. On dimensions where sigma_e is rising fast enough, the offset dominates: there exists a sigma_e threshold sigma_e_crit(N) above which the full-disclosure equilibrium becomes individually rational even at large N, because the survival cost of aggregate hoarding exceeds the aggregate hoarding benefit even though each individual agent's marginal contribution to the problem remains negligible.
The tragedy of the commons takes a specific form in the framework's language: each agent's hoarding is individually negligible and collectively lethal. Ostrom (1990) spent a career demonstrating that commons dilemmas are solved not through privatization or centralized regulation but through institutional designs that combine competitive and cooperative incentives - monitoring, graduated sanctions, conflict-resolution mechanisms, and nested governance structures. The full-disclosure architecture is, in Ostrom's terms, a proposed governance institution for an information commons: the track record mechanism provides monitoring (every disclosure is scored), the coverage-adjusted scoring provides graduated sanctions (withholding assessments reduces the agent's composite score), and the recursive agency structure provides nested governance (agencies that produce validated predictions govern attention allocation on their dimensions). What the framework adds to Ostrom's analysis is the dynamic instability: the information commons governed by the price system alone is self-destabilizing below S = 1, because the feedback loop between rational inattention and structural compression erodes the commons' information base over time. The stability condition identifies the information-theoretic threshold below which no institutional design can sustain the commons without a supplementary channel - a quantitative boundary that Ostrom's empirical principles instantiate without formalizing.
The climate finance literature has documented partial pricing of constraint dimensions consistent with the framework's predictions. Carbon emissions appear in the cross-section of stock returns (Bolton and Kacperczyk, 2021), and climate risk hedging portfolios can be constructed from asset prices, implying partial constraint loading at epsilon > 0 in the notation of Beier (2026h, Proposition 1') (Engle, Giglio, Kelly, Lee, and Stroebel, 2020). Drought trends are underpriced in food company stocks across 31 countries (Hong, Li, and Xu, 2019) - precisely the pattern the framework predicts when constraint dimensions carry variance that the price system transmits only partially and with delay - and sea-level-rise risk shows up partially in coastal real estate valuations (Giglio, Maggiori, Rao, Stroebel, and Weber, 2021). These findings collectively document partial loading on constraint dimensions while leaving excess distortion large: Delta remains at 84% or more of the eigenbasis value even at epsilon = 0.40.
What the framework adds is a dynamic: rising sigma_e on global constraint dimensions is closing the gap between the individually-rational and collectively-rational equilibria. The gap that was infinite at low sigma_e (hoarding is costless because the constraint is not binding) becomes finite as sigma_e rises (hoarding has measurable survival cost because the constraint is tightening), and vanishes at sigma_e_crit(N) (the constraint is tight enough that even 1/N contributions to D matter for survival).
The empirical evidence assembled in Section 7 - warming acceleration, tipping point proximity, the UK JIC ecosystem collapse assessment - documents rising sigma_e on specific global constraint dimensions. On those dimensions, the proprietary ESG equilibrium is not stable. The companies hoarding constraint information are individually rational today. The individual rationality of hoarding is eroding on the dimensions where Earth is approaching Mars conditions, and the erosion is measurable through the same sigma_e estimates the climate science community already produces. The Mars Test does not require Earth to be at Mars conditions. It requires Earth to be moving toward them on the dimensions that matter - and on those dimensions, the convergence is driving s_crit downward toward the surplus levels that currently exist.
Illustrative computation of sigma_e_crit. The mechanism through which rising sigma_e shifts the equilibrium operates primarily through the dimension-specific surplus, not through the per-agent survival benefit overcoming the 1/N dilution. At large N, the per-agent survival benefit of disclosure remains negligible regardless of sigma_e - the tragedy of the commons is real. What changes is the dimension-specific effective surplus epsilon_k(sigma_e): as sigma_e rises on a constraint dimension, the gap between the current state and the irreversible threshold on that dimension shrinks, reducing the hoarding benefit on that dimension.
Consider the atmospheric carbon budget dimension. Let the remaining budget be B(t) Gt CO2, depleting at rate E(t) Gt/year. The effective surplus on this dimension is proportional to B(t)/E(t) - the years of budget remaining at current emission rates. The private hoarding benefit W_i on this dimension is proportional to the effective surplus: an agent can profitably hoard information about carbon budget interactions only while the budget remains large enough that the constraint has not yet manifested in prices. As B(t)/E(t) shrinks, W_i shrinks proportionally.
Using IPCC AR6 estimates adjusted for post-2020 emissions: remaining budget for 1.5 C is approximately 340 Gt CO2 (50% probability, central estimate as of 2024), current emissions approximately 40 Gt/year. Effective surplus: approximately eight years. The 2025 update from Forster et al. (2025) gives a lower central estimate of approximately 130 Gt CO2 remaining from January 2025, reflecting updated warming estimates and methodology - roughly three years at current emission rates. At 2.0 C: approximately 1000 Gt, giving approximately 25 years. The effective surplus on the 1.5 C dimension is already near zero in the framework's terms - the constraint is binding within one to two business cycles at most, and possibly less than one.
The equilibrium shift occurs when W_i(sigma_e) falls below R_min - when the hoarding benefit on the dimension (proportional to the remaining effective surplus) drops below the disclosure return (the constraint premium from Beier, 2026d, Proposition 7, which is independent of the dimension's effective surplus because it is grounded in calibration quality rather than trading profit). For the 1.5 C carbon budget dimension, this threshold has arguably already been crossed: the remaining budget is so small that trading profit from hoarding carbon-budget-interaction analysis is compressed into a time window shorter than the track record scoring cycle. On the 2.0 C dimension, the threshold is approximately 15-25 years away at current emission trajectories, but approaches faster if emission rates increase or if the budget estimate is revised downward.
The computation reveals that sigma_e_crit(N) varies by dimension rather than taking a single value. Each constraint dimension has its own effective surplus trajectory, its own threshold proximity, and therefore its own position on the Bermuda-Mars continuum. The atmospheric carbon budget at 1.5 C is near the Mars end. Agricultural productivity in temperate zones under moderate warming is near the Bermuda end. The framework identifies which dimensions are converging and at what rate, without generalizing to a claim about all dimensions simultaneously.
A sane superintelligence is one whose combined inference capacity exceeds that of any individual component while the failure modes that make unbounded AI optimization dangerous are structurally prevented through physical architecture. When AI agents are added to the Beier Factorial economy, the resulting three-layer system achieves this.
Human agents and agencies form the foundation. Humans produce primary observations through physical interaction with the environment and form agencies through the Beier Factorial mechanism: disclosure, conversation, joint inference. No AI system generates observational data; the sensor network is human and mechanical. The primacy of this layer is non-negotiable because ground truth originates in physical observation, and no computational process can substitute for the engineer who hears the bearing failing or the agronomist who sees the crop anomaly.
AI agents occupy the proposal layer. Trained on human disclosure data - the structured constraint reasoning, dimensional analyses, and outcome-scored predictions that human agencies produce - these systems search the combinatorial space of possible agencies and constraint interactions at computational speed. They propose hypotheses and identify candidate agencies that humans have not yet formed because the combinatorial space is too large for manual search. The architecture evaluates what the AI proposes; the AI does not evaluate itself.
Evaluation is performed by air-gapped mechanical scoring - computation programs physically isolated from AI influence, accepting prediction-outcome pairs and outputting track record scores. The air gap is physical, not algorithmic. The deeper defense is epistemic: the scoring system evaluates predictions against physical outcomes observed and entered by human sensor nodes - actual aquifer levels, actual crop yields, actual grid states. An AI that crafts hypotheses to exploit parsing logic in the scorer still fails when the hypothesis is measured against reality, because reality is the one input the AI does not control. Self-evaluation is among the most dangerous failure modes because an AI system that generates its own evaluation data can optimize for the evaluation metric rather than for prediction accuracy, and the resulting track record degenerates into self-referential optimization. The physical separation of inference from evaluation prevents this degeneration at the architectural level.
The architecture addresses a specific failure mode identified in the alignment literature (Bostrom, 2014): optimization pressure misaligned with human values in a system whose evaluation is self-referential. It does not claim to resolve the full alignment problem - value specification, value loading, and value stability under self-improvement remain open - but it structurally prevents the self-evaluation feedback loop that makes unbounded optimization dangerous in deployed systems. Resources remain under human control, the scoring system is physically unreachable, and the human kill switch is a physical connection that can be severed, inverting the control relationship so that the AI must remain useful to the human to continue operating. The training data is grounded in outcome-scored human observation, which biases hypothesis generation toward reasoning that has been validated against outcomes rather than toward patterns that have merely been written. The formal properties of this architecture will be developed in a companion paper (Beier, forthcoming), which will address convergence behavior as AI capability scales and the conditions under which the architectural containment holds.
The Mars architecture can be applied on Earth within existing market structures. Consider an investor who understands the Beierspace/eigenspace distinction and its implications for price formation. The strategy: trade on constraint dimensions the market cannot see, and disclose everything - the reasoning, the model, the dimensional analysis, the position, and the outcome. Trading profit serves as a pedagogical credibility signal, demonstrating that the framework identifies something the existing price system misses.
The mechanism operates through the excess distortion identified in Beier (2026h). The investor identifies a specific V_k with high lambda_k that the market is not tracking - perhaps the interaction between airline emissions and atmospheric carbon budgets at aggregate scale. The investor takes a position and publishes the full dimensional decomposition: here is V_1 (what the price sees), here is V_k (what the price cannot carry), and here is the mechanism by which V_k will eventually manifest in outcomes that affect V_1.
When the prediction validates, other investors learn to see V_k. Alpha on that specific trade decays toward zero as the market incorporates the constraint dimension - the standard Grossman-Stiglitz story. But what has actually happened is that the market's effective K* has increased by one, carrying LD and S upward with it and stabilizing the eigenstructure on that dimension. The investor who understands the framework can already see dimensions k+1, k+2, k+3. The advantage is not information asymmetry on a fixed set of dimensions but the ability to identify new dimensions faster than the market absorbs the previous ones, and the supply of unpriced constraint dimensions is inexhaustible at current K*. The compensation mechanism is suppleness rent at the frontier of dimensional awareness: the rent decays on each specific dimension but regenerates at the frontier, which is always moving outward.
Each disclosed dimension is simultaneously a prediction and a tutorial - a worked example of Beierspace analysis that teaches the market about the framework for identifying constraint interactions in general. Proposition 4.2 applies directly: each new disclosing investor creates new agency possibilities with the existing population of disclosers. The combinatorial space of possible higher-order constraint interactions among disclosed models grows combinatorially with the number of participants. The track record mechanism prunes the unproductive combinations and allocates attention to the productive ones.
The warming rate is accelerating, and the last three years have been the three warmest in the instrumental record. Observed warming for the 2015-2024 decade reached 1.24 C above 1850-1900, of which 1.22 C was attributed to human activity (Forster et al., 2025). The rate of human-induced warming rose from approximately 0.20 C per decade over 1970-2015 (Foster and Rahmstorf, 2026; Forster et al., 2025) to 0.27 C per decade over the most recent ten years (Forster et al., 2025). Foster and Rahmstorf (2026) find an even sharper acceleration after removing natural variability, with the adjusted rate reaching approximately 0.35 C per decade since 2015. The WMO consolidated estimate for 2024 was 1.55 C above pre-industrial (WMO, 2025; individual datasets range from 1.47 C for NASA to 1.62 C for Berkeley Earth), and 2025, despite La Nina cooling, reached 1.44 C (Berkeley Earth, 2025). Copernicus concluded that breaching 1.5 C within the 2030s is "highly likely" (Copernicus, 2024).
In the framework's notation, sigma_e is rising on climate-coupled dimensions, and the acceleration is measured, not projected. The interaction with the rational inattention feedback loop (Beier, 2026h, Proposition 2, Remark) is particularly dangerous. As physical structural drift accelerates, constraint dimensions become more volatile, but the price system's capacity to carry constraint information remains structurally zero on those dimensions regardless of how much variance they carry. The growing gap reinforces the feedback loop: agents whose attention is optimized for a world in which constraint information is absent from prices continue to rationally ignore constraints even as the constraints become more severe. The information architecture's degradation is invisible to agents operating within it - prices look the same, models perform the same on the dimensions they track, and the constraint dimensions that are worsening are precisely the dimensions no one is watching. The self-destabilizing dynamics below S = 1 (Beier, 2026e, Theorem 5.2) operate through exactly this mechanism.
The Climate Overshoot Commission (2023) recommended a moratorium on large-scale solar radiation modification deployment while calling for expanded research. SRM would introduce constraint dimensions whose number and interaction structure are unknown: altered precipitation, ozone chemistry changes, termination shock, governance across sovereign states, agricultural impacts, continued ocean acidification despite reduced surface temperatures. In the framework's terms, K_SRM may exceed any feasible information architecture's capacity to track. An extinction-level event is a possible outcome not because any single SRM effect is necessarily catastrophic, but because the interaction effects among many simultaneously introduced constraint dimensions cannot be anticipated by an information architecture that has not yet learned to track the existing constraints of the pre-SRM climate system.
The alternative: instead of intervening in the physical system, redesign the information architecture to track existing constraint dimensions well enough to coordinate adaptation and mitigation before the overshoot forces a geoengineering decision or a wartime economic response.
The UK government's January 2026 national security assessment on biodiversity loss and ecosystem collapse, prepared with the involvement of the Joint Intelligence Committee (HM Government, 2026), identifies six ecosystems of strategic importance and warns that their decline could drive cascading disruptions to food, water, health, and supply chains. The EU's 2023 Joint Communication describes climate change as a risk multiplier cascading across systems and regions (European Commission, 2023), with the EEAS's 2025 progress report treating environmental degradation as an existential threat (EEAS, 2025). The 2025 US Annual Threat Assessment was the first in over a decade to omit climate change entirely - a political decision, not an analytical one (Council on Strategic Risks, 2025). When national intelligence committees treat ecosystem collapse as a security threat comparable to cyberattack or nuclear proliferation, the assessment reflects the analytical conclusion that constraint dimensions are shifting fast enough to destabilize the systems states depend on.
When constraint pressure becomes existential, democratic economies have historically shifted to centralized resource allocation. The United States and United Kingdom in World War II imposed rationing, directed production, suspended normal price mechanisms for essential goods, and allocated resources administratively across constraint dimensions that the price system could not track under the speed and severity of wartime disruption.
A climate overshoot triggering sudden restriction of food availability, water access, and energy supply would likely produce a similar shift. Governments would assume wartime-style economic management - not from ideological preference but because the price system cannot coordinate allocation when constraint dimensions shift faster than the market can track. When S drops below 1 on enough critical dimensions simultaneously, the price system's scalar compression becomes acutely inadequate, and administrative allocation - rationing - is the available alternative.
Rationing is a crude multi-dimensional codec. It replaces the price system's scalar compression with administratively determined allocations across multiple constraint dimensions (food per household, fuel per vehicle, electricity per district). As a codec, it is better than the price system under crisis conditions (it can address multiple constraint dimensions rather than compressing all of them into a single scalar) but it fails the Mars Test on the same grounds as regulatory mandates: it is a rigid, low-dimensional compression that cannot adapt to eigenstructure rotation, has no track record mechanism for identifying which administrators are making good allocation decisions, and is vulnerable to political distortion that selects for compliance rather than accuracy. When the information architecture collapses, political authority fills the vacuum - but the resulting system is a tourniquet, not a cure.
The period between the present and the onset of wartime economic conditions is the window within which the information architecture can be upgraded voluntarily. After the shift to wartime management, the architecture is imposed rather than chosen. The track record mechanism that makes the full-disclosure architecture self-correcting is unlikely to survive political control, because political control selects for track records that align with the controlling authority's preferences rather than with observed outcomes.
Proprietary ESG information is commercially viable during this window. The window is also the period during which open disclosure could raise LD on constraint dimensions enough to prevent or mitigate the overshoot that closes the window. The commercial viability and the social opportunity occupy the same interval of time, and they compete for the same resources.
Global spending on financial market data and news reached a record $44.3 billion in 2024 (Burton-Taylor Consulting, 2025). The ESG-specific subset - ratings, research, analytics, climate risk modeling, sustainability consulting - represents a substantial and growing fraction. The ESG data market alone exceeded $2 billion in 2024 (Opimas, 2024), while the broader sustainability consulting market reached $12.4 billion (Verdantix, 2024). ESG-mandated assets under management are estimated at $29-39 trillion globally (various sources, 2024-2025).
In the framework of Beier (2026c), these expenditures are reconstruction costs. The ESG industry reconstructs constraint information that was never in the price - corporate environmental impact, social risk exposure, governance quality, climate transition readiness - packages it as a scarce commodity, and sells it back to the market. The reconstruction takes multiple forms: sell-side analysts reverse-engineer constraint interactions from financial statements, rating agencies build sustainability scores from compressed metrics, and quantitative funds extract signal from pricing noise on dimensions the price was never designed to carry.
The fundamental limit on reconstruction quality is a theorem, not an observation. The data processing inequality (Cover and Thomas, 2006) establishes that for any Markov chain V -> p -> V-hat(p), the mutual information satisfies I(V; V-hat) <= I(V; p). For constraint dimensions k >= 2 in the eigenbasis case, the price carries zero mutual information about V_k, so E[(V_k - V-hat_k(p))^2] >= Var(V_k) = lambda_k regardless of the estimator (Beier, 2026h, Proposition J). No amount of analytical sophistication, computational power, or expenditure can push below this bound by working from the price signal alone. The sell-side analyst attempting to infer aquifer depletion risk from stock prices faces a physical barrier, not a skill barrier: the information was never in the signal.
The $44.3 billion figure captures direct market data spending and includes categories (real-time price feeds, execution infrastructure, index licensing) that are not primarily reconstructive. The reconstruction-relevant portion - sell-side research, credit analysis, ESG rating, quantitative signal extraction - is a subset. However, the full reconstruction burden extends well beyond the $44.3 billion to include analyst compensation (hundreds of thousands of sell-side, buy-side, credit, ESG, and compliance analysts globally), computational infrastructure for signal extraction, regulatory compliance systems that reconstruct decision-making reasoning from compressed transaction records, and internal research departments at asset managers, insurance companies, and pension funds. A conservative estimate of the total reconstruction burden in global financial markets is $150-250 billion annually (Beier, 2026h).
Two distinct information-theoretic results bound the reconstruction problem, and they should not be conflated. The first is the data processing inequality bound (Cover and Thomas, 2006): for reconstruction from the price signal alone, E[(V_k - V-hat_k(p))^2] >= lambda_k for constraint dimensions k >= 2 in the eigenbasis. This is a hard physical limit - no analytical method can recover information the price never carried. But the financial industry does not reconstruct from prices alone. Sell-side analysts use earnings calls, site visits, supply chain data, satellite imagery, and expert networks. These auxiliary signals carry genuine constraint-dimension information, and the DPI bound on price-only reconstruction does not apply to them.
The second result is the duplication bound: regardless of the signal source, reconstruction is a private good. Each downstream user who needs constraint information must independently acquire or reconstruct it, because analyst A's research is not freely available to analyst B's clients. The aggregate cost scales as M * c_R, where M is the number of downstream users and c_R is the per-user reconstruction cost. Disclosure eliminates the duplication by producing information once (at cost N * c_D) and making it public. The savings M * c_R - N * c_D are positive whenever M >> N, which holds in any developed financial market where thousands of fund managers each need constraint information that a much smaller number of domain experts could produce through structured disclosure. The duplication argument does not depend on the DPI bound - it applies to reconstruction from any source, not just from prices. The $150-250 billion estimate includes both price-only reconstruction (bounded by the DPI) and multi-source reconstruction (bounded by the duplication cost). The distinction matters: the DPI bound establishes that some reconstruction is futile (price-only inference about constraint dimensions), while the duplication bound establishes that all reconstruction is wasteful relative to production at source through disclosure.
The standard regulatory response to the externality problem inherits the same dimensional mismatch the paper identifies in prices. A Pigouvian carbon tax (Pigou, 1920) attempts to capture the social cost of emissions in a single number added to the transaction price. But the social cost of carbon - estimated at $31/ton by Nordhaus (2017) and $185/ton by Rennert et al. (2022), with Pindyck (2019) arguing that the integrated assessment models underlying all such estimates are structurally flawed - is itself a scalar compression of atmospheric physics, intergenerational ethics, technological alternatives, and scaling consequences. It is a scalar layered on a scalar: one compressed number added to another compressed number, with the reasoning behind both invisible to the participants who are supposed to respond to them. The Mars architecture addresses this at the structural level: instead of computing the unknowable scalar (the "correct" carbon price), it preserves the multi-dimensional constraint reasoning in structured, attributed, outcome-scored form, allowing capital allocators to incorporate the full dimensional analysis into their decisions rather than responding to a number whose provenance they cannot evaluate. The Mars architecture and the Pigouvian tax are complements, not substitutes. A carbon tax corrects the first-order price distortion on the consensus dimension (making emissions costly). The Mars architecture provides the multi-dimensional constraint reasoning that informs what the tax rate should be, how it interacts with other constraint dimensions, and whether $31/ton or $185/ton is closer to the truth. Each instrument addresses what the other cannot.
The divergence among ESG ratings is itself a predicted consequence of the framework. Berg, Koelbel, and Rigobon (2022) documented that the average correlation between major ESG rating providers is approximately 0.54, a figure that gains force when compared to the approximately 0.99 correlation typically reported for credit ratings across agencies. Beier (2026c) identifies the mechanism: different agencies apply different proprietary methodologies to compress multi-dimensional constraint information into scalar scores. The divergence is a mathematical consequence of lossy compression, not a methodological deficiency: when the source dimensionality K far exceeds the output dimensionality (a scalar), different compressors produce different scalars because the compression discards different components. The divergence would be eliminated by preserving dimensionality (structured multi-field assessments rather than aggregated scores), which is precisely what the Mars architecture's full-disclosure format achieves. The deeper problem is identified in Beier (2026i, Corollary 6.1), which derives Goodhart's Law from the Dissipation Law: when an ESG score becomes a target, capacity directed at the measured dimension is withdrawn from unmeasured dimensions, the unmeasured dimensions dissipate at an increased rate, and the score reports stability while the underlying structure degrades on the dimensions it cannot see.
The rational inattention feedback loop (Beier, 2026h, Proposition 2, Remark) compounds the problem. The ESG industry exists within this feedback loop: it reconstructs constraint information for clients whose attention allocation is already optimized for a world in which constraint information is absent from prices. The full-disclosure architecture breaks the loop by injecting constraint information directly into the information environment, shifting the fixed point from "constraints invisible, attention elsewhere" to "constraints visible, attention engaged."
The major ESG data providers are now subsidiaries of large financial data conglomerates: MSCI ESG Ratings sits within MSCI Inc., Morningstar acquired Sustainalytics, Deutsche Boerse holds ISS ESG, and the Dow Jones Sustainability Indices and Trucost platform belong to S&P Global. FTSE Russell ESG ratings are a London Stock Exchange Group product, Bloomberg ESG is integrated into the Bloomberg terminal, and Moody's operates its own ESG assessment products.
These parent companies derive the majority of their revenue from the financial market data and index licensing businesses that depend on functioning markets. Their ESG subsidiaries are supposed to address the constraint threats - climate risk, biodiversity loss, social instability - that could destabilize the markets on which the parent companies depend.
The information-theoretic critique follows directly from the companion papers' results. If these companies believed, as an analytical matter, that the constraint threats their ESG products are supposed to address are existential to the markets they serve, the rational response would be to make the constraint data free, transparent, and usable as a public good. The marginal social value of disclosed constraint information exceeds the marginal private revenue from selling it (a consequence of Proposition 2 in Beier, 2026h) by exactly the stability externality - the contribution of each disclosed bit to LD, and through LD to S, and through S to the continued functioning of the markets from which these companies derive the rest of their revenue. Making the data free would raise LD on constraint dimensions, raise S, stabilize the eigenstructure, and preserve the markets that generate the data industry's non-ESG revenue.
The fact that no major ESG data provider has done this reveals one of two things. Either the companies do not believe the constraint threats are existential (in which case their ESG products are rent extraction from regulatory compliance and investor fashion, not serious constraint analysis), or the institutional incentive structure prevents the collectively rational action even when individuals within the firms understand the problem. In either case, the products fail the Mars Test.
Even ostensibly open ESG data frameworks face a version of the incentive problem. OS-Climate, for instance, provides open-access climate risk data. But the data is contributed primarily by companies with specific financial interests in selling adjacent data services, consulting, and technology platforms. The contributors are not disinterested sensor nodes producing ground truth scored against outcomes; they are commercial entities whose disclosure is shaped by their broader business strategy.
Open access is necessary but not sufficient for passing the Mars Test. The Mars architecture requires that open data be scored against observed outcomes, that attention and decision weight be allocated through validated track records, and that the incentive structure driving measurement and reporting be truth-optimized rather than commercially optimized. Providing data openly while retaining the commercial incentive structure that shapes what gets measured, how it gets measured, and what gets reported is a partial improvement that does not address the structural problem.
Proposition 8.1 (Social cost of proprietary gating increasing in sigma_e). The aggregate social cost of proprietary gating - the total distortion attributable to constraint information being produced but not disclosed - is increasing in sigma_e. The aggregate private revenue from proprietary gating is independent of sigma_e. Therefore the gap between social cost and private revenue widens as Earth's constraint environment tightens.
Proof. Rising sigma_e raises the drift rate sigma_k on affected constraint dimensions. For dimensions where sigma_k rises above the aggregate information capacity LD, the dimension exits the usable set: K* decreases by one (Beier, 2026e, Theorem 8.1, Part B: K* = |{k : sigma_k < LD}|). The excluded dimension's full variance lambda_k enters the aggregate distortion (Beier, 2026h, Proposition 1: uncompressed dimensions contribute their full prior variance to total distortion). The aggregate social cost of gating is C_gate = sum_{k > K*} lambda_k, which increases whenever sigma_e causes at least one dimension to cross the LD threshold. The aggregate private revenue R_gate (vendor subscription fees) is determined by market demand for the data product and does not depend on sigma_e. Therefore C_gate - R_gate is strictly increasing in sigma_e on each dimension that crosses the threshold.
A subtlety the proof discovery protocol exposed: the per-bit marginal value of disclosure dS/dD actually decreases in sigma_e at fixed D (because higher sigma_e increases the denominator of S, making each incremental bit less effective at raising stability). The gap widens not because each bit becomes more valuable but because the number of untracked dimensions grows - the dimensionality channel dominates the per-bit channel. The economy needs more disclosure bits, not more valuable bits. See Appendix for the full computation.
The practical implication: as Earth's constraint environment tightens, the case for making ESG data free strengthens - not because altruism becomes more appealing but because the number of dimensions falling off the trackable set is increasing, and each lost dimension carries rising variance. The dollar spent on proprietary constraint data generates less social value relative to the same dollar spent on open disclosure, and the shortfall is increasing over time.
ESG Ethics, in this framework, is the information-theoretic proposition that the architecture for observing and communicating constraint-critical dimensions should be designed to survive the Mars Test.
Gating constraint information behind a paywall when the constraint is existential introduces artificial delay in the disclosure channel. The delay degrades D, and through LD and S, destabilizes the eigenstructure on exactly the dimensions where stability matters most. Every month that a constraint interaction remains invisible to the market because the analysis is locked behind a proprietary framework is a month in which the market's allocation decisions are made without information that could improve them - and the cost of that ignorance propagates through S to the probability of crossing tipping points, and from there to lives.
The ethical claim reduces to an information-theoretic claim, derivable from the companion papers' combined apparatus, and it holds regardless of one's moral framework.
Four information architectures are evaluated against the Mars Test: would this architecture keep a colony alive under Mars boundary conditions?
Proprietary ESG ratings (MSCI ESG Ratings, Sustainalytics, ISS ESG, Moody's ESG, Bloomberg ESG, FTSE Russell ESG). The mechanism is reconstruction from public data plus proprietary models. The ratings are sold as commercial products; access is gated by subscription fees. There is no systematic outcome scoring of the ratings themselves against observed constraint outcomes - no proper scoring rule, no track record capital, no mechanism that would make honest comprehensive disclosure incentive-compatible in the sense of Beier (2026d, Proposition 14). When the models degrade as the underlying covariance structure rotates (the Supple paper's core finding: economic covariance matrices are composed predominantly of Beier-space quantities whose eigendecompositions are temporary), the degradation is not publicly disclosed because the model is the product. The absence of outcome scoring means the agencies have no formal incentive to maximize calibration quality; instead, they face the standard career-concerns incentive to herd toward consensus (Scharfstein and Stein, 1990) - precisely the distortion that proper scoring is designed to eliminate. The ratings agencies are owned by conglomerates with revenue interests that may conflict with maximum constraint disclosure. On Mars, this architecture would gate life-critical information behind commercial agreements, prevent the Beier Factorial from operating on the gated dimensions, and conceal model degradation during exactly the periods when the models are most needed. Fails the Mars Test.
Regulatory disclosure mandates and open-source ESG data each represent partial improvements that fall short of the Mars standard. TCFD, ISSB/IFRS S1-S2, and EU CSRD mandates remove the paywall for specified dimensions, but the disclosure they produce is compliance-optimized rather than truth-optimized, scored against auditor satisfaction rather than observed constraint outcomes, and fixed to dimensions the standard-setting body has identified - dimensions that cannot adapt to eigenstructure rotation as the constraint environment changes. Open-source platforms like OS-Climate make data freely accessible, which is necessary infrastructure, but contributor incentives remain commercially shaped (Section 8.3), and no agency formation mechanism allows the Beier Factorial to operate on the data. On Mars, regulatory mandates would produce disclosure on a fixed set of dimensions determined by bureaucratic process and miss the constraint interactions that fall outside the standard's categories. Open-source data would provide sensor readings without the interpretive framework that turns data into constraint awareness. Both earn a partial pass - better than proprietary gating, insufficient for survival under Mars conditions.
Full-disclosure super-transparency with track record scoring and Beier Factorial agency formation. The mechanism is structured disclosure at source, scored against observed outcomes, with attention and decision weight allocated to agents and agencies based on validated track records. The scoring uses the Brier rule with coverage weight alpha < 2/3, which Beier (2026d, Proposition 14) proves makes honest comprehensive disclosure strictly dominant for every agent regardless of calibration quality - eliminating the strategic selection problem that undermines other disclosure mechanisms. The combinatorial agency discovery process operates on the disclosed data, producing superlinear (Mars) or factorial (Earth) growth in visible constraint dimensions. AI agents search the combinatorial space under air-gapped scoring. Human operators maintain physical override. On Mars, this is the architecture that Theorem 4.3 shows is the unique Nash equilibrium under zero surplus. The constraint premium W_constraint(q) > 0 (Beier, 2026d, Proposition 7) ensures that the return to participation is permanently positive even in the absence of a functioning price system - the mechanism is self-sustaining. Passes the Mars Test.
Proposition 9.1 (Architecture ranking). Under the combined (x, Delta) dynamics from Beier (2026h) and Beier (2026e), the steady-state stability S for the four architectures satisfies:
S_full-disclosure > S_regulatory > S_open-source > S_proprietary
The ranking follows from the disclosure rate D achievable under each architecture (full-disclosure has the highest D, proprietary the lowest, because paywall gating directly reduces D on the gated dimensions) and the agency formation capacity (full-disclosure supports the Beier Factorial, others do not). The ranking has an information-theoretic foundation in the observation architecture hierarchy derived in Beier (2026i, Section 9.6): scalar channels (prices, ratings) have capacity O(log N); flat multi-channel systems (prices plus disclosure plus ratings) have capacity O(N); combinatorial networks at depth 1 have capacity Omega(N^2); and recursive combinatorial networks at depth L have capacity potentially Omega(N^{2^L}). Proprietary ESG operates as a scalar channel. Regulatory mandates and open-source data are flat multi-channel systems. The full-disclosure architecture with Beier Factorial agency formation is a combinatorial network whose capacity growth rate can match the dimensionality growth of the problem. The gap between S_full-disclosure and S_proprietary widens as sigma_e increases, because rising sigma_e pushes more constraint dimensions out of the trackable set, increasing the social cost of gating while leaving private revenue unchanged (Proposition 8.1), and because the Beier Factorial contribution to L_FD responds to rising sigma_e by discovering more constraint interactions, while L_PR does not.
The Coupling Advantage Theorem (Beier, 2026g; derived in the Ngakpa Principle companion paper) provides a stronger version of this result for the comparison between full-disclosure and proprietary architectures. The theorem models two architectures: a ROM architecture in which disclosure rate D is structurally coupled to learning capacity L (D = alpha * L, giving x_ROM = alpha * L^2, the mildest superlinear coupling), and a kernel architecture in which D is exogenous (x_ker = D* * L, linear in L). For the Beierspace stability dynamics with any sigma_b in class B', the theorem establishes: (i) for L above a computable threshold, x_ROM > x_ker with an unbounded gap; (ii) S_ROM > S_ker with an unbounded gap; (iii) a phase separation interval exists - a computable range of L within which S_ROM > 1 > S_ker, meaning the ROM architecture self-stabilizes while the kernel architecture self-destabilizes from identical initial learning capacity; (iv) under uncorrected dynamics, the ROM architecture converges to x_max (full stability) while the kernel architecture converges to 0 (collapse).
The phase separation result is the theorem's strongest claim: within a computable parameter regime, the difference between full-disclosure and proprietary architectures is qualitative (stable vs. unstable), not a matter of degree. The width of the phase separation interval grows with the coupling parameter alpha: from 0.034 at alpha = 1.0 to 0.471 at alpha = 3.0 in the default parameterization (Beier, 2026g). The result is verified across five functional forms in class B' (power law, exponential, logistic, piecewise concave, concave square root), with opposite dynamical outcomes confirmed in all cases. A counterexample is stated: for L below the threshold D*/alpha, the kernel architecture dominates, because the ROM coupling penalizes low-capability agents by linking their low L to a proportionally low D.
The full-disclosure Mars architecture is a ROM architecture in this sense: the disclosure rate is constitutive of the architecture's competence, not a separable overlay. The proprietary ESG architecture is a kernel architecture: disclosure is a product sold alongside other services, separable from the analytical capability that produces it. The Coupling Advantage Theorem predicts that as both architectures experience increasing sigma_e on constraint dimensions, there exists a learning capacity range within which they produce opposite outcomes - the full-disclosure architecture strengthens while the proprietary architecture collapses.
Any equipment sent to Mars must be repairable with locally available materials and locally held knowledge. Software must be open source because there is no internet connection to a proprietary vendor's update server. Hardware documentation must be complete because the manufacturer is on another planet. Data formats must be interoperable because the colony cannot afford vendor lock-in when the locked vendor is 225 million kilometers away.
Earth's current technology infrastructure assumes continuous internet connectivity for software updates, security patches, and vendor-managed services. The vulnerability is not merely network latency but complexity collapse: when cascading failures cross domains - grid failure disabling water treatment, water failure disrupting cooling systems, cooling failure degrading server infrastructure - proprietary architectures become impossible to debug because the cross-domain troubleshooting that survival requires is legally and technically prevented by the same firewalls that protect intellectual property under normal conditions. The technology stack that functions when each domain fails independently may not function when the constraint dimensions fail simultaneously, which is the scenario the UK Joint Intelligence Committee warns could materialize within two decades.
Preparing for Mars on Earth means building the resilience of open, locally repairable, fully documented systems before the crisis that reveals their necessity. Open-source hardware and software, complete documentation at the component level, standardized data formats, and local repair capacity are requirements for a Mars colony and for a technology infrastructure that survives the constraint scenarios intelligence agencies are now assessing as national security threats. The overlap is the point.
The best way to run Earth is to prepare for Mars here - to build open-source systems on repairable hardware, with transparent data flowing through full-disclosure constraint reasoning scored by air-gapped AI evaluation, and the Beier Factorial operating at planetary scale to produce combinatorial growth in the number of constraint dimensions the collective economy can see.
The formal results identify this as the optimal information architecture under the combined (x, Delta) dynamics when sigma_e is rising and the constraint environment is tightening. The Mars framing makes it vivid; the mathematics makes it necessary when the boundary conditions are met. Whether those boundary conditions apply to Earth on the dimensions that matter is the empirical question, and the evidence assembled in Section 7 suggests that on climate-coupled, ecology-coupled, and pandemic-coupled dimensions, they increasingly do.
The Mars boundary conditions are idealized. Real Mars colonies will have political dynamics, status hierarchies, and information hoarding incentives that the zero-surplus assumption suppresses. The theorem that full disclosure is the unique Nash equilibrium (Theorem 4.3) depends critically on zero surplus; any positive surplus opens a region of strategy space in which some hoarding is individually rational.
The Beier Factorial growth rate depends on constraint interaction density, an empirical quantity not yet measured for any real system. Measuring the interaction density empirically - through the frequency and structure of novel constraint discoveries in existing data - is necessary to validate the formal results and is left to future work. Earth's convergence toward Mars conditions is dimension-specific: the convergence argument applies to the tightening dimensions and should not be generalized to a claim that all constraint dimensions are approaching Mars conditions.
The formal results from the companion papers assume Gaussian sources and MSE distortion. The qualitative conclusions are robust to relaxation of these assumptions; the quantitative results are not.
The transition from proprietary to open disclosure faces coordination problems not fully addressed here. The critical mass threshold - the minimum fraction of agents who must commit to full disclosure before the Beier Factorial growth rate exceeds the hoarding equilibrium's information production rate - is the most important open problem. The threshold likely connects to the phase transition at S = 1 in Beier (2026e); identifying the precise relationship is future work.
Track record scoring requires ground truth. For slow-moving constraint dimensions (decadal climate trends, long-run ecosystem stability), the scoring cycle may be too slow to discipline the system within the available time window. This is a genuine limitation with no easy resolution.
Whether the window has already closed on some dimensions is the question this paper cannot answer and no framework can answer until the outcomes are observed. If certain tipping points have already been crossed, the Mars Test on those dimensions yields a different answer: not "reform the information architecture" but "manage the overshoot with the architecture you have." Whether the window remains open is an empirical question whose answer may arrive as a physical event rather than a data point.
Constructive design of the Mars-surviving architecture at the implementation level, fuller formal treatment of the Beier Factorial mechanism, and the interaction between the Beier Factorial and the sane superintelligence are all future work. The treatment here establishes the key results but does not exhaust the topic.
The price system needs what it destroys. The distortion floor - the proof that excess distortion Delta > 0 is a necessary condition for the disclosure incentive that maintains the eigenstructure on which the price system operates - is a reflexive coupling with no precedent in the externality literature. It explains why the information architecture problem cannot be solved by improving the price system alone, and it connects the Mars boundary conditions to the Earth application through a single causal chain: the price system's compression withdraws maintenance from constraint dimensions, the withdrawn maintenance creates the economic incentive for supplementary disclosure, and the supplementary disclosure sustains the eigenstructure that gives the price system a stable object to compress.
The Mars Test sits at one extreme of a continuum whose opposite extreme - the Bermuda Test - is the regime where proprietary information architectures are optimal and the Grossman-Stiglitz equilibrium correctly describes information production. Under Mars conditions, the formal results converge: the Nash equilibrium is full disclosure, the compensation mechanism is track record capital, and constraint awareness grows superlinearly through combinatorial agency formation. What matters for Earth is not the Mars result itself but the convergence dynamics - the empirical fact that specific constraint dimensions are moving toward Mars on the continuum, with effective surplus declining and sigma_e rising, while the information architectures governing those dimensions remain calibrated to Bermuda. The Coupling Advantage Theorem identifies a phase separation interval within which full-disclosure architectures self-stabilize while proprietary architectures self-destabilize from identical initial conditions. The empirical evidence assembled in Section 7 suggests the converging dimensions are identifiable and the convergence is measurable.
The architecture that survives Mars is also the architecture that gives Earth its best chance on those dimensions. The window of voluntary adoption is finite and shrinking.
Seven formal results are stated in this paper (five with full proofs in the Appendix, two derived from companion papers). Each follows the proof discovery protocol specified in Beier (2026e). The Appendix documents one error discovered during proof formalization: the mechanism through which the social cost of proprietary gating widens in sigma_e operates through the dimensionality channel (rising sigma_e pushes dimensions out of the trackable set) rather than the per-bit-value channel (the original proof sketch incorrectly claimed d^2S/(dD d sigma_e) > 0; the computation shows it is negative). The conclusion survives; the mechanism is corrected.
The Distortion Floor (Section 3.1). There exists a minimum excess distortion Delta_min > 0 below which the disclosure incentive cannot sustain the LD required for S > 1. The price system's information destruction is a necessary condition for its own coherence - a reflexive coupling between the price system's failure mode and the information architecture's survival condition, with no precedent in the externality literature. (Derived from the joint apparatus of Beier, 2026h, 2026d, and 2026e.)
Proposition 4.1 (Superlinear growth on Mars). Under full disclosure and dense constraint coupling, the number of visible constraint dimensions K*(N) grows as O(N^alpha) for alpha > 1. The growth rate depends on the constraint interaction density. On Mars, the growth is superlinear but bounded by the colony's population and attention budget. (Section 4.3. Full proof in Appendix.)
Proposition 4.2 (Increasing marginal returns to disclosure on Earth). The marginal contribution to K* of the (N+1)th disclosing human sensor node is strictly increasing in N when constraint interaction density exceeds a computable threshold and all existing nodes disclose fully. The ratio of marginal K* under full disclosure to marginal K* under hoarding grows without bound in N. (Section 4.4. Full proof in Appendix.)
Theorem 4.3 (Full disclosure as unique Nash equilibrium under Mars conditions). Under zero effective surplus on the constraint dimension under consideration and high sigma_e, full disclosure (d_i = 1 for all i) is the unique Nash equilibrium. The result depends critically on zero effective surplus. The critical surplus threshold s_crit is a function of N, sigma_e, and the eigenvalue spectrum; rising sigma_e on global constraint dimensions drives s_crit downward, eroding the individual rationality of hoarding on the converging dimensions. The dimension-specific surplus concept (Section 2) provides the bridge to Earth: aggregate surplus can be positive while effective surplus on specific constraint dimensions approaches zero. (Section 4.6. Full proof in Appendix.)
Flutter Suppression Conjecture (Section 3.3). An information architecture exhibits flutter suppression if dD/d(sigma_e) > 0: the disclosure rate increases when physical structural drift increases. The Mars architecture satisfies this property trivially at zero surplus (D = 1 is already maximal). The conjecture that the interior equilibrium D*(sigma_e) is increasing in sigma_e at positive surplus is supported by the comparative statics on Theorem 4.3 but not formally derived. The testable prediction (smaller covariance norm changes during crises under volatility-responsive disclosure) is independent of the conjecture's proof status.
Proposition 8.1 (Social cost of proprietary gating increasing in sigma_e). The aggregate social cost of proprietary gating (total distortion from untracked constraint dimensions) increases in sigma_e because rising physical drift pushes dimensions out of the usable set K*, with each lost dimension contributing its full variance to total distortion. The per-bit marginal value of disclosure decreases in sigma_e, but the number of bits needed increases faster. (Section 8.4. Full proof in Appendix.)
Proposition 9.1 (Architecture ranking) and the Coupling Advantage Theorem. Under the combined (x, Delta) dynamics, steady-state stability satisfies S_full-disclosure > S_regulatory > S_open-source > S_proprietary. The Coupling Advantage Theorem (Beier, 2026g) strengthens this for the full-disclosure vs. proprietary comparison: a computable phase separation interval exists within which the full-disclosure architecture self-stabilizes while the proprietary architecture self-destabilizes from identical initial learning capacity. The difference is qualitative (stable vs. unstable) within a computable parameter regime, not a matter of degree. (Section 9. Proof of ranking in Appendix; Coupling Advantage Theorem in Beier, 2026g.)