PRIORITY FILING - CONSOLIDATED EDITION
A fully revised and formatted version will follow.
Gregory Caldwell Beier
Susarb LLC, Cambridge, Massachusetts
July 2026
Part of the formal foundations of Origin Chain of Thought (OCOT).
© 2026 Gregory Caldwell Beier. Licensed under CC BY-NC-ND 4.0.
The three papers consolidated here answer one question from three directions: where can the coordination architecture live, and what happens to environments that cannot host it. The political topology paper grounds the answer in permitted conditions rather than desirability, deriving five host conditions and classifying regimes as participation-capacity classes, with the instability of partial hosting stated as a falsifiable claim rather than a preference. The sustainability paper removes a standing temptation by showing that sustainability is not a fourth coordination domain but a functional of the Scaling facets across markets, politics, and technology together, computable where the scalar is silent, and unreconstructable in an environment that cannot host one of its constituent domains. The selectorate paper derives the disclosure incentive from coalition size and finds that the resulting ordering of regimes coincides with the topology classification reached independently.
The coincidence is the filing's finding. Two derivations that share no premises, one from hosting conditions and one from coalition incentives, produce the same boundary around where maintained public extropy can rise. Corroboration of that kind is rare enough in this program to be worth publishing as a unit, and the unit is what this filing is.
The substrate that OCOT builds is often described as neutral infrastructure, a protocol that any environment could adopt the way any computer could run a markup language. It is not neutral, and this paper makes the non-neutrality precise. The substrate places five conditions on its host environment, each inherited from a result already established: permissionless publication, a public-scope option, a persistent attributed identity the host cannot revoke or falsify, tamper-evident records, and tolerance of assessments that contradict the host's official position. The paper defines a host's participation capacity as the set of constraint domains on which it permits all five, and shows that regime types are compatibility classes for this capacity. An open environment that permits the five across markets, governance, and technology has full participation capacity. An authoritarian environment that permits the five on domains it does not treat as threats to its hold on power but suppresses dissent on governance has a participation capacity that excludes the politics layer. A totalitarian environment that controls identity and publication and tolerates no unapproved dissent has empty participation capacity. The result is structural, derived from which conditions each environment permits rather than from any ranking of environments by desirability, and the framework's non-neutrality is located exactly: it enters through the dissent condition and the identity conditions that closed environments restrict by their nature. The paper closes with a falsifiable prediction, offered as a prediction and not a theorem, that partial hosting is unstable, because the infrastructure the substrate requires is domain-general and the cost of suppressing political content on an otherwise open channel rises with the channel's economic value.
Keywords: participation capacity, regime type, dissent, permissionless publication, persistent identity, coordination, political topology, OCOT
A markup language carries a recipe and a manifesto with equal indifference. The format does not inspect the content, and the same standard that serves a cooking blog serves a samizdat. A reader who assumes the OCOT substrate is neutral in this way assumes that any environment could host it, that the question of adoption is a question of will and infrastructure and not of political form. The assumption is wrong, and the wrongness is structural rather than incidental.
The substrate is not a passive format. It is a mechanism, and a mechanism functions only when its preconditions hold. The results already established show that the substrate's guarantees, the redundancy that corrects dishonest scope, the anti-enclosure that keeps a commons open, the honest scoring that the strike-time secures, depend on conditions the host environment either permits or does not. An environment that forbids a precondition does not host a degraded version of the substrate on the affected domain. It fails to host the substrate there at all, because the guarantee that made the substrate work is gone. This paper identifies the preconditions, defines the capacity an environment has to host the substrate as the set of domains on which it permits them, and shows that political form bounds that capacity. The framework is not neutral about its hosts, and the honest course is to say where the non-neutrality enters and why, rather than to present as universal a mechanism that is not.
The conditions the substrate places on a host are not new requirements introduced here. Each is the host-environment counterpart of a result the structural papers proved.
Proposition P-1 (The five host conditions). The substrate functions on a constraint domain only if the host environment permits, for assessments on that domain, all of the following: permissionless publication, so that any author with a persistent identity can strike and transmit a Tensor on the domain; a public-scope option, so that any author can publish on the domain at public disposition; a persistent attributed identity that the host cannot revoke or falsify; tamper-evident records, so that the host cannot alter a struck record's strike-time or content; and tolerance of dissent, so that an author can publish an assessment on the domain that contradicts the host's official position without the publication being suppressed or the author prevented from continuing.
Proof sketch. Each condition is necessary because a prior guarantee fails without it. Permissionless publication is required by the redundancy defense: an under-scoped record is corrected by a third party who publishes at the correct scope, and if publication requires the host's permission, the host can deny the correction (Beier, 2026, "The Transmit Facet," Proposition D-3). The public-scope option is required by anti-enclosure: without it, a coalition that controls the largest available group can enclose the domain, and on a domain the host controls, the host is that coalition (Beier, 2026, "The Transmit Facet," Proposition D-4). Persistent unfalsifiable identity is required for the track record to be a valid calibration signal: a track record the host can erase or forge carries no information about an author's calibration, because the host can manufacture standing or destroy it (Beier, 2026b; Beier, 2026r). Tamper-evident records are required for honest strike-time scoring: if the host can alter a record after it is struck, the host can rewrite the scored claim (Beier, 2026, "Strike-Time and Transmit-Time," Proposition T-2). Dissent tolerance is required for the substrate's coordination function on the domain: the function is to surface where the consensus or the official assessment is wrong, and an assessment that contradicts the official position is precisely what an environment intolerant of dissent suppresses, which removes the correction the substrate exists to provide. Remove any one condition and the corresponding guarantee fails on the domain, so the substrate does not function there. End sketch.
The five are not a wish list for a congenial political environment. They are the conditions under which the specific guarantees of the specific mechanism hold. A host that denies permissionless publication has not made the substrate less convenient; it has removed the redundancy that the substrate's self-correction depends on. The conditions are load-bearing in the literal sense that the proofs of the earlier papers rest on them.
The conditions vary by domain within a single host. An environment may permit dissenting assessments about aquifer depletion while forbidding dissenting assessments about the legitimacy of its government. The capacity to host the substrate is therefore not a single bit per environment but a set of domains.
Definition (Participation capacity). The participation capacity of a host environment is the set of constraint domains on which the environment permits all five conditions of Proposition P-1.
Proposition P-2 (Regime types are compatibility classes). Regime types partition by their participation capacity. An open environment that permits the five conditions across the domains of markets, governance, and technology has participation capacity equal to the full domain space. An authoritarian environment that permits the five conditions on domains it does not treat as threats to its hold on power, typically markets and technology, but suppresses dissent on governance, has participation capacity that excludes the politics layer. A totalitarian environment that controls identity and publication comprehensively and tolerates no unapproved dissent on any domain has empty participation capacity. The partition follows from which conditions each environment permits, derived from Proposition P-1, and does not rank environments by desirability.
Proof sketch. Apply the definition to each case. An open environment that permits permissionless attributed public publication of dissenting, tamper-evident assessments across all three domains satisfies the five conditions on every domain, so every domain lies in its participation capacity. An authoritarian environment, defined here by its suppression of challenges to its hold on power while permitting economic and technical activity, satisfies the dissent condition on markets and technology, where assessments do not challenge that hold, but violates the dissent condition on governance, where they do; the governance domains therefore fail condition five and lie outside the participation capacity, while the market and technology domains remain inside it. A totalitarian environment, defined by comprehensive control of identity and of publication, violates the permissionless-publication, public-option, persistent-identity, and dissent conditions on any domain it has not approved, so no domain outside state approval satisfies the five conditions and the participation capacity is empty. The classification is a consequence of the conditions each environment permits and is silent on whether any environment is better than another; it states only which domains each can host. End sketch.
The framework is not neutral, and the non-neutrality is now locatable. It does not enter through a hidden preference for one political form expressed in the substrate's design. It enters through condition five, dissent tolerance, and through the identity and publication conditions, which closed environments restrict by their nature and open ones do not. An environment that suppresses assessments contradicting its official positions cannot host the substrate on the domains where those positions lie, because the substrate's function on a domain is to carry exactly such assessments and score them against outcomes. The structure Sen (1999) identified, that famines do not occur in functioning democracies with a free press, is the same result read on a single domain: where the politics layer can carry a dissenting assessment of official policy, the coordination failure is surfaced and corrected, and where it cannot, it is not. The substrate generalizes that mechanism across domains, and its participation capacity is bounded wherever the dissent the mechanism requires is forbidden.
The authoritarian case in Proposition P-2 is the interesting one, because it is a partial host: it carries the substrate on some domains and not others. Whether partial hosting is stable is a question the structural results raise but do not settle, and the framework's answer is a prediction rather than a theorem.
Proposition P-3 (Instability of partial hosting, as a falsifiable prediction). The infrastructure the substrate requires is domain-general: the same persistent identity, public-publication channel, and tamper-evident record that carry an assessment on water carry an assessment on governance. An environment that hosts the market and technology layers therefore builds infrastructure that structurally permits the politics layer, and excluding the politics layer requires suppressing specific content on a channel that is otherwise open. The framework predicts that partial hosting is unstable, because the cost of suppressing political content on an open channel rises as the channel's economic and technical value grows. The prediction is offered as a prediction and is falsifiable.
Argument. The conditions of Proposition P-1 are properties of an infrastructure, not of a domain. A persistent identity system that lets an analyst accumulate a track record on water risk is the same system that would let an analyst accumulate a track record on institutional resilience; a public-publication channel that carries a chip-supply assessment is the same channel that would carry a governance assessment; a tamper-evident record store does not inspect the subject of what it stores. An environment that builds this infrastructure to host the economically valuable domains has built the means of hosting the politically sensitive ones, and its exclusion of the politics layer is therefore not an absence of capacity but an active suppression of particular content on a channel that is technically open to it. The framework's prediction is that this suppression grows more costly as the channel grows more valuable, because the same author base, identity system, and publication norms that make the channel valuable for markets and technology make selective political suppression conspicuous and hard to enforce without degrading the channel's value for the permitted domains. An environment may sustain partial hosting indefinitely by accepting the economic cost of a less open channel, and the framework treats partial hosting as under tension whose magnitude grows with the channel's value rather than as necessarily collapsing. The claim is contestable, and its test is whether environments that adopt the substrate for economic coordination find the boundary against political coordination cheap or expensive to hold over time. End argument.
The prediction is the one place in this paper where the framework reaches past what the prior results establish, and it is marked as such. Propositions P-1 and P-2 are structural consequences of the mechanism's preconditions. Proposition P-3 is a claim about how those preconditions behave under economic pressure, and it is offered for testing rather than asserted as proved. The honest statement is that the substrate's infrastructure does not partition by domain, that partial hosts therefore suppress rather than lack, and that whether the suppression holds is an empirical question the adoption of the substrate will answer.
The participation capacity of a host bounds the domains on which the substrate can coordinate, and the bound has a consequence for the coordination the framework is ultimately about. The North Star holds that sustainable coordination emerges from aggregating the Scaling assessments across the three domains of markets, governance, and technology, so an environment that cannot host the politics layer loses part of the aggregate from which sustainability is read. The next paper develops that aggregation and shows why sustainability is not a fourth domain to be observed directly but a quantity that emerges from the Scaling facets of the three, which is what makes the participation-capacity result of this paper bear on the framework's central claim about what the substrate is for.
The political topology of the substrate is the recognition that a coordination mechanism is not neutral about the environments that can run it. The mechanism requires that its participants be able to publish, attributably and permissionlessly, assessments that contradict power, and the environments that forbid this cannot host the part of the substrate that would carry such assessments. Naming that boundary is not a political position taken by the framework. It is a structural property of a mechanism whose function is to surface where the official account is wrong.
The North Star of the framework holds that the substrate serves sustainable coordination across three domains, markets, governance, and technology, and that sustainability is not itself a fourth domain. The distinction has been asserted without being made precise, and it matters, because treating sustainability as a fourth domain would imply a separate observable to be measured directly, while treating it as an emergent aggregate implies it is reconstructed from the three domains' assessments. This paper makes the distinction precise. Sustainability over a horizon is the property that the constraint trajectories implied by the systemic interaction effects across the three domains stay within their irreversibility thresholds, and the systemic interaction effects are exactly what the Scaling facet carries, so sustainability is a functional of the Scaling facets aggregated across the three domains and not an independently observable quantity. The aggregation is more than a sum, because the domains are coupled and the coupling terms carry information no single domain's Scaling facet holds, which the composition algebra combines across domains. A consequence follows directly from the participation-capacity result: an environment that cannot host the Scaling assessments of one domain cannot reconstruct sustainability fully, because the aggregate is evaluated on a strict subset that omits the unhosted domain's contribution and the coupling terms that involve it, so an environment which degrades the politics layer systematically mis-estimates sustainability by the political coupling it cannot see. The emergent quantity is computable from the commons and its approach to a threshold is forecastable, where the scalar price carries no information about constraint trajectories at all, so sustainability moves from a quantity that was neither directly observable nor reconstructable to one that is reconstructable from the Scaling facets the architecture collects.
Keywords: sustainability, Scaling facet, emergence, coordination domains, planetary boundaries, coupling, participation capacity, OCOT
The framework names three domains in which coordination happens: markets, where prices coordinate exchange, governance, where collective decisions coordinate authority, and technology, where capability coordinates what becomes possible. It then makes a claim about a fourth thing, sustainability, and the claim is that sustainability is not a fourth domain. The phrasing has carried the intuition without the content, and the content is what determines whether the claim is right.
The stakes of the distinction are concrete. If sustainability were a fourth domain, it would have its own coordination, its own transactions, and its own observable that an instrument could read directly, the way a price reads a market. The work would then be to build a sustainability observatory alongside the three domain observatories. If instead sustainability is an emergent aggregate, it has no transactions of its own and no direct observable, and the work is to reconstruct it from the assessments the three domains already produce. The two readings point to different programs. This paper argues the second is correct, by showing that sustainability is a definite function of the Scaling facets of the three domains, that the function requires their coupling and not merely their sum, that an environment missing one domain cannot evaluate the function, and that the function is computable from the commons in a way the scalar signal never permitted.
Take the three domains as state spaces carrying constraint dimensions: the market domain M, the governance domain P, and the technology domain T, each with its own constraint variables and each evolving over time. A constraint dimension has an irreversibility threshold, a boundary beyond which the system transitions to a state from which return is difficult, slow, or impossible, the thresholds the Basin Transition and Threshold Economics analyses treat (Beier, 2026, "Basin Transition Economics"). Sustainability over a horizon is then the following property.
Definition (Sustainability). A configuration of the three domains is sustainable over a horizon when the constraint trajectories implied by the systemic interaction effects across M, P, and T remain within their irreversibility thresholds throughout the horizon.
The definition is the one the planetary-boundaries framework expresses for the biophysical case, that a system is in a safe operating space when its coupled subsystems stay within their boundaries (Rockstrom et al., 2009), generalized from the biophysical subsystems to the three coordination domains. Sustainability is a predicate on the joint long-horizon trajectory of the three domains, and the question is what carries the information needed to evaluate the predicate.
The information that determines the joint trajectory is the systemic interaction effect, and the architecture has a single home for that information.
Proposition SU-1 (Sustainability is read from the Scaling facets). Sustainability is a functional of the Scaling facets of the three domains and is not an independently observable quantity. There is no sustainability transaction and no sustainability facet; the quantity is reconstructed from the Scaling assessments of markets, governance, and technology.
Proof sketch. Sustainability is a predicate on the joint long-horizon trajectory of the three domains, by the definition of Section 2. The joint trajectory is governed by the systemic interaction effects, how each domain's aggregate behavior bears on the constraint dimensions over time, rather than by the individual transactions, which carry only transaction-level information. The Scaling facet is the only facet of a Tensor that states the systemic interaction effect, the assessment of what happens as the analyzed condition operates at scale and meets the other systems scaling beside it, which the other facets do not carry (Beier, 2026ah; Beier, 2026ai). The information required to evaluate the sustainability predicate is therefore contained in the Scaling facets, aggregated across the three domains, and the predicate is a functional of those facets. No separate observable carries it, because sustainability is not a coordination domain with transactions of its own but a property of how the three domains' aggregates evolve, which is exactly the property the Scaling facets assess. End sketch.
The result settles the fourth-domain question. Sustainability has no transactions, so it is not a domain. It is a property of the three domains' aggregate trajectories, and the assessments that carry aggregate trajectories are the Scaling facets. To read sustainability is to aggregate the Scaling facets across markets, governance, and technology and to evaluate whether the implied trajectories stay within thresholds, which is reconstruction from existing assessments rather than measurement of a new observable. The program the architecture needs is therefore not a sustainability observatory but the collection of Scaling assessments across the three domains the substrate already serves.
Reconstructing sustainability is not as simple as adding the three domains' sustainability assessments, because the domains do not evolve independently.
Proposition SU-2 (Coupling makes the aggregate more than a sum). The sustainability functional is not the sum of per-domain assessments, because the three domains are coupled and the coupling terms carry information no single domain's Scaling facet holds. Evaluating the functional requires composing Scaling assessments across domains, and the composition recovers the cross-domain coupling that the per-domain assessments omit.
Proof sketch. The joint trajectory depends on how the domains interact, not only on how each behaves alone: a market trajectory bears on a governance trajectory, which bears on a technology trajectory, and the constraint dimensions respond to the joint motion. A sum of per-domain Scaling assessments captures each domain's within-domain interaction effects but omits the cross-domain coupling, the conditional dependence between domains that the Constraint Coupling analysis showed to be where the most dangerous and least visible failures occur (Beier, 2026am). The omitted coupling carries information, the conditional mutual information between the domains' trajectories, that appears in none of the per-domain assessments taken alone. Recovering it requires Scaling assessments that reason across domains and the composition that combines records from different domains into a joint assessment, which the composition algebra supplies through its aggregation over the lineage (Beier, 2026, "The Composition Algebra"). The aggregate sustainability signal therefore includes the coupling information that a sum would miss, and is more informative than the per-domain assessments combined additively. End sketch.
The coupling is why sustainability cannot be decomposed into independent sectoral targets and summed, an approach that treats each domain's safe operating space in isolation. The domains interact, and the interaction is where the compound failures live, so the aggregate that determines sustainability has to carry the cross-domain terms. The composition algebra is the instrument that carries them, combining a market Scaling assessment, a governance Scaling assessment, and a technology Scaling assessment into a joint assessment whose lineage records that it draws on all three, which is the reconstruction the sustainability functional requires.
The reconstruction depends on having the Scaling facets of all three domains, and the participation-capacity result says that some environments cannot host one of them.
Proposition SU-3 (Truncation under missing participation capacity). An environment that cannot host the Scaling assessments of one domain cannot reconstruct sustainability fully. The functional is then evaluated on a strict subset that omits the unhosted domain's direct contribution and the coupling terms that involve it, so the reconstructed sustainability is truncated, and the truncation is largest when the missing domain is strongly coupled to the others.
Proof sketch. Sustainability is the functional of all three domains' Scaling facets together with their coupling, by Propositions SU-1 and SU-2. An environment's participation capacity is the set of domains on which it permits the conditions the substrate requires, and an environment that suppresses dissenting assessment on a domain cannot host that domain's Scaling facets, by the political-topology result (Beier, 2026, "The Political Topology of the Substrate," Propositions P-1 and P-2). When one domain's Scaling facets are absent, the functional is evaluated on the remaining domains, which omits the absent domain's direct contribution and every coupling term that involves it, since a coupling term between the absent domain and another cannot be formed without the absent domain's assessment. The reconstructed sustainability is therefore computed on a strict subset of the information the full functional requires, which truncates it, and the size of the truncation grows with the strength of the absent domain's coupling to the others, because strongly coupled domains contribute larger coupling terms that the truncation discards. End sketch.
The result connects the framework's political non-neutrality to its central quantity. An environment that degrades the governance layer, in the authoritarian case the political-topology paper described, does not merely lose coordination on governance. It loses the governance Scaling facets and every coupling term between governance and the other two domains, so its reconstruction of sustainability is missing the political contribution and the political coupling, which it cannot recover by observing markets and technology perfectly. The environment systematically mis-estimates sustainability by the political coupling it structurally cannot see, and the mis-estimate is worst precisely where governance is most coupled to the biophysical and technological trajectories, which is the case for the constraint dimensions on which sustainability most depends. The capacity to host the politics layer is therefore not a political preference but a condition for reading sustainability at all.
The final result is that the emergent quantity, unlike the scalar it replaces, can actually be read.
Proposition SU-4 (Computability and forecastability). The sustainability aggregate is computable from the commons by aggregating the Scaling-facet trajectories across domains and evaluating the threshold predicate, and its approach to a threshold is forecastable, where the scalar price carries no information about constraint trajectories. Sustainability moves from a quantity that was neither directly observable nor reconstructable to one that is reconstructable from the Scaling facets the architecture collects.
Proof sketch. The aggregation of Scaling-facet trajectories across domains is the composition-algebra operation of Proposition SU-2, which is computable on the commons given a domain ontology that supplies the constraint coordinates (Beier, 2026, "The Composition Algebra," Proposition C-2). Evaluating the threshold predicate on the aggregated trajectory is a comparison of the trajectory against the irreversibility thresholds, which is computable once the trajectory is formed. The approach to a threshold is forecastable because the aggregated Scaling trajectory makes the constraint parameter that governs a basin transition observable, converting the transition from a zero-warning discontinuity to a forecastable approach, which the Basin Transition analysis established for the single-domain case and which the aggregation extends across domains (Beier, 2026, "Basin Transition Economics"). The scalar price, by contrast, carries strictly positive excess distortion on the constraint dimensions and so carries no information about their trajectories (Beier, 2026h), which is why sustainability was unreadable from prices. The Scaling facets carry the trajectories, the composition algebra aggregates them, and the threshold predicate evaluates them, so the emergent quantity is reconstructable from what the architecture collects. End sketch.
The contrast with the scalar is the point. A price system cannot read sustainability, not because sustainability is unmeasurable in principle but because the scalar channel destroys the constraint-trajectory information that sustainability is a function of. The architecture restores that information in the Scaling facets, and the sustainability aggregate is the reconstruction those facets make possible. Sustainability was neither a thing an instrument measured directly nor a thing the price let one infer, and the Scaling facets change the second of those, turning sustainability into a quantity that a commons of structured assessment can reconstruct and watch approach its thresholds.
The emergent-aggregate account closes the North Star's structure. The substrate serves three coordination domains, each carrying its own Scaling facets, and sustainability is the functional of those facets across the three, reconstructed through the composition algebra, bounded by the participation capacity of the host, and computable in a way the scalar never allowed. Sustainability is not a fourth domain to be observed but a property of the three domains' aggregate trajectories that the architecture reads from the assessments it already collects.
The account leaves the dynamics of the aggregate for further work. The sustainability functional evolves as the three domains evolve and as the commons that assesses them improves, and the improvement results imply that the reconstruction sharpens over time, both because human authors calibrate their Scaling assessments and because the models trained on the commons read the constraint structure more sharply. Whether the reconstruction converges fast enough to forecast the thresholds before they bind, in the long-horizon domains where the thresholds are irreversible and the resolution is slow, is the question on which the framework's claim to serve sustainable coordination finally rests, and it is an empirical question the commons, once built, will answer.
The political-topology analysis classified regimes by their structural capacity to host the disclosure substrate, an open society hosting it fully, an authoritarian one excluding the political layer, a totalitarian one unable to host it at all. This paper reaches the same ordering from a different starting point, the selectorate theory of political survival, and the agreement between two independent analyses is the paper's main reason for being written. The selectorate theory explains regime behavior through the size of the coalition a leader needs to retain power, with small-coalition regimes provisioning private benefits to their narrow coalition and large-coalition regimes provisioning public goods to a broad one. The paper shows that coalition size determines a regime's incentive toward the coordination information in the public sphere, which is the extropy a political system maintains. A small-coalition regime has an incentive to suppress that extropy, because the coordination information disclosure provides would enable the broad collective action that threatens a narrow coalition's private extraction, while a large-coalition regime has the opposite incentive, because it already provisions public goods and depends on the broad coordination that disclosure supports. Maintained public extropy therefore rises with coalition size, low under narrow coalitions and high under broad ones, and this ordering coincides with the host-capacity ordering of the political-topology analysis, because the same feature, the breadth of the basis on which power rests, drives both the capacity to host disclosure and the incentive to sustain it. Two analyses built on different foundations, one on structural host conditions and one on coalition incentives, order regimes the same way, which corroborates both, and the paper states the correspondence as structural rather than precise, because the extropy measure applied to political systems is coarser than the measure applied to a price.
Keywords: selectorate theory, coalition size, public extropy, regime classification, political topology, corroboration, OCOT
The political-topology analysis ordered regimes by a structural criterion, whether the conditions the disclosure substrate requires, persistent identity, durable records, open transmission, and the rest, can hold under the regime, and concluded that open societies host the substrate fully, authoritarian societies exclude the political layer while permitting disclosure elsewhere, and totalitarian societies cannot host it at all (Beier, 2026, "The Political Topology of the Substrate"). That analysis derived the ordering from the regime's permitted conditions, not from any judgment about which regime is preferable, and it left open whether the ordering would also follow from the incentives regimes face rather than the conditions they permit.
This paper shows that it does, by reaching the same ordering from the selectorate theory of political survival, which explains regime behavior through the size of the coalition a leader needs to keep power (Bueno de Mesquita et al., 2003). The theory holds that a leader retains office by satisfying a winning coalition drawn from a larger selectorate, that small coalitions are satisfied with private benefits directed to their members, and that large coalitions can be satisfied only with public goods, because private benefits spread across a large coalition are worth little per member. The paper connects coalition size to the regime's incentive toward public-sphere coordination information, shows that maintained public extropy rises with coalition size, and shows that the resulting ordering coincides with the host-capacity ordering of the topology analysis. The coincidence is the point: two analyses with different foundations agree, and the agreement corroborates both.
The first result connects the selectorate structure to disclosure.
Proposition SE-1 (Coalition size and disclosure incentive). A small-coalition regime has an incentive to suppress public-sphere coordination information, because that information enables the broad collective action that threatens a narrow coalition's private extraction. A large-coalition regime has the opposite incentive, because it provisions public goods and depends on the broad coordination that the information supports. The incentive to sustain public-sphere coordination information increases with coalition size.
Proof sketch. A small-coalition regime provisions private benefits to its narrow coalition and retains power by preventing the formation of a coalition that could displace it (Bueno de Mesquita et al., 2003). Public-sphere coordination information, the disclosure that lets actors outside the coalition see the constraint state and coordinate around it, is precisely what enables a broad challenger coalition to form and to act, so a small-coalition regime has an incentive to suppress it, because the information threatens the narrow coalition's hold and the private extraction it protects. A large-coalition regime provisions public goods, because a large coalition cannot be satisfied by private benefits, and the provision of public goods depends on the broad coordination that disclosure supports, so a large-coalition regime has an incentive to sustain public-sphere coordination information rather than suppress it. The disclosure incentive therefore moves with coalition size, from suppression under narrow coalitions to sustenance under broad ones, and increases monotonically in the size of the coalition the regime depends on. End sketch.
The result ties a regime's posture toward disclosure to the structure of its survival. A regime does not suppress or sustain coordination information arbitrarily but according to whether the information threatens or supports the coalition that keeps it in power, and the selectorate theory supplies the link: narrow coalitions are threatened by the broad coordination disclosure enables, and broad coalitions depend on it. The posture toward disclosure is thus not an independent feature of a regime but a consequence of its coalition size, which the next result carries to the extropy the regime maintains.
The second result states the consequence for the extropy measure.
Proposition SE-2 (Maintained extropy and coalition size). The public-sphere extropy a regime maintains increases with the size of its winning coalition. Small-coalition regimes maintain low public extropy, because their suppression incentive removes coordination information from the public sphere, and large-coalition regimes maintain high public extropy, because their incentive sustains it.
Proof sketch. The public extropy a regime maintains is the coordination information present in its public sphere, the produced information net of what the regime suppresses. By Proposition SE-1, the suppression incentive decreases with coalition size, from strong suppression under narrow coalitions to sustenance under broad ones, so the share of produced coordination information that survives into the public sphere increases with coalition size. The maintained public extropy, being the surviving share, therefore increases with coalition size: it is low under narrow coalitions, where suppression removes most coordination information, and high under broad coalitions, where the regime's own incentive sustains it. The extropy a political system maintains is thus an increasing function of the breadth of the coalition on which the regime's power rests, with the narrowest regimes maintaining the least and the broadest the most. End sketch.
The result gives the extropy measure a political reading. The coordination information available in a society's public sphere is not fixed by the society's productive or technological capacity alone but is shaped by the regime's incentive to sustain or suppress it, and that incentive is set by coalition size, so the maintained public extropy is a function of the regime's structure. A society capable of producing rich coordination information may maintain little of it in the public sphere under a narrow-coalition regime that suppresses it, and the same society may maintain much of it under a broad-coalition regime that sustains it, which means the maintained extropy reflects the political structure as much as the productive one. The next result connects this ordering to the topology analysis.
The third result is the corroboration.
Proposition SE-3 (Agreement with host capacity). The coalition-size ordering of maintained public extropy coincides with the host-capacity ordering of the political-topology analysis. Both order regimes the same way, broad-coalition open regimes maintaining and hosting high extropy, narrow-coalition authoritarian regimes suppressing and excluding it, minimal-coalition totalitarian regimes maintaining and hosting almost none, because the same feature drives both the capacity to host disclosure and the incentive to sustain it.
Proof sketch. The political-topology analysis ordered regimes by their structural capacity to host the substrate, from open regimes that host it fully through authoritarian regimes that exclude the political layer to totalitarian regimes that cannot host it (Beier, 2026, "The Political Topology of the Substrate," Proposition P-2). The present analysis orders regimes by maintained public extropy as a function of coalition size, from broad-coalition regimes that maintain high extropy through narrow-coalition regimes that maintain low extropy to minimal-coalition regimes that maintain almost none, by Proposition SE-2. The two orderings coincide because the feature that drives each is the same: the breadth of the basis on which power rests. A regime whose power rests on a broad coalition both can host disclosure, because broad-based power does not depend on suppressing the constraint state, and has the incentive to sustain it, because it provisions the public goods disclosure supports, while a regime whose power rests on a narrow coalition both excludes disclosure structurally and has the incentive to suppress it. The structural capacity of the topology analysis and the incentive of the selectorate analysis are therefore two expressions of the same underlying feature, so the two analyses produce the same ordering, and each corroborates the other. End sketch.
The agreement is the result the paper exists to establish. The topology analysis derived the regime ordering from the conditions a regime permits, the selectorate analysis derives it from the incentives a regime faces, and the two are independent in their foundations, one structural and one strategic, yet they order regimes identically. Two independent derivations of the same ordering corroborate the ordering more than either alone, because an ordering that follows from both the conditions and the incentives is less likely to be an artifact of either framework. The convergence also locates what the orderings share, the breadth of the power base, which is the feature that both determines whether a regime can host disclosure and determines whether it wants to, so the political topology and the selectorate extropy are two views of a single structural fact about how broadly power is distributed.
Coalition size sets a regime's incentive toward public-sphere coordination information, maintained public extropy rises with coalition size, and the resulting ordering of regimes coincides with the host-capacity ordering of the topology analysis, so the two independent analyses corroborate each other. The extropy a political system maintains is shaped by the breadth of the coalition on which its power rests, narrow coalitions suppressing the coordination information that would threaten their private extraction and broad coalitions sustaining the information their public-goods provision depends on, and this is the same feature that determines whether a regime can host the substrate at all.
The reading contributes to the diagnostic political work the program is developing, where the question of which political arrangements can sustain coordination is central. The selectorate analysis supplies a mechanism for the topology analysis's classification, explaining not only that open regimes host disclosure and closed ones do not but why the incentive runs that way, through the coalition structure that the selectorate theory identifies. The correspondence suggests that the program's claim about which environments host the substrate is not specific to the substrate but reflects a general feature of how broadly power is distributed, the same feature that the selectorate theory uses to explain public-goods provision, so the architecture's political dependence is an instance of a structure that political science already describes, and the convergence of the two analyses is a point of contact between the program and that literature rather than a claim the program makes alone.
Beier, G. C. (2026). "Basin Transition Economics: How Constraint Dimensions Cross Thresholds, Why the Price Cannot See Them Coming, and What the Disclosure Mechanism Changes." Working Paper.
Beier, G. C. (2026). "Strike-Time and Transmit-Time: The Information Economics of the Two-Timestamp Record." Working Paper.
Beier, G. C. (2026). "Sustainability as an Emergent Aggregate: Why Sustainability Is Not a Fourth Coordination Domain." Working Paper.
Beier, G. C. (2026). "The Composition Algebra: Lineage, Independence, and the Detection of Emergence." Working Paper.
Beier, G. C. (2026). "The Political Topology of the Substrate: Which Environments Can Host Structured Disclosure." Working Paper.
Beier, G. C. (2026). "The Political Topology of the Substrate: Why the Host Environment Bounds What Can Be Coordinated." Working Paper.
Beier, G. C. (2026). "The Transmit Facet: Disposition, Scope, and Why the Public Option Cannot Be Removed." Working Paper.
Beier, G. C. (2026a). "Dual Surfaces of the Price: Geometric Fidelity and the Judgment Kernel." Working Paper. Zenodo.
Beier, G. C. (2026ah). "Scaling Risk as the Fifth Consideration: Why Interaction Effects at Scale Constitute a Distinct Information Type the Price System Cannot Carry." Working Paper. Zenodo.
Beier, G. C. (2026ai). "The Mathematical Structure of Interaction Effects Across Scale." Working Paper. Zenodo.
Beier, G. C. (2026am). "When Constraint Domains Interact: The Economics of Cross-Domain Information Failure." Working Paper. Zenodo.
Beier, G. C. (2026b). "The Disclosure Incentive: How Track Record Capital Resolves the Grossman-Stiglitz Paradox and Reveals the Competition-Cooperation Synthesis Across Four Disciplines." Working Paper. Zenodo.
Beier, G. C. (2026h). "Excess Distortion in the Price System: A Rate-Distortion Analysis of Scalar Compression in Multi-Dimensional Constraint Environments." Working Paper. Zenodo.
Beier, G. C. (2026o). "The Constitution Axiom: Observation as the Origin of Coordination-Dependent Reality." Working Paper. Zenodo.
Beier, G. C. (2026q). "The Scalar Lobby: Political Economy of the Transition from Scalar to Multi-Dimensional Observation." Working Paper. Zenodo.
Beier, G. C. (2026r). "The Incentive Compatibility of the Disclosure Incentive: A Mechanism Design Foundation for the Judgment Market." Working Paper. Zenodo.
Bueno de Mesquita, B., Smith, A., Siverson, R. M., and Morrow, J. D. (2003). The Logic of Political Survival. Cambridge, MA: MIT Press.
Bueno de Mesquita, B., Smith, A., Siverson, R. M., and Morrow, J. D. (2003). The Logic of Political Survival. Cambridge: MIT Press.
Rockstrom, J., et al. (2009). "A Safe Operating Space for Humanity." Nature, 461, 472 through 475.
Sen, A. (1999). Development as Freedom. New York: Knopf.
Gregory Caldwell Beier
Susarb LLC, Cambridge, Massachusetts
July 2026