Gyroscopic Global Governance: Post-AGI Economy, Employment, Education and Ecology

Author: Basil Korompilias

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Abstract

Current discourse frames Artificial General Intelligence (AGI) as a future capability threshold, centering governance on external control of autonomous systems. This paper redefines AGI as the already operational structure of human–AI cooperation, where intelligence is a relational property requiring traceability between Original human sources and Derivative artificial sources. Generality thus refers not to an isolated system's task breadth, but to the coherence sustained across the domains of Economy, Employment, Education, and Ecology through the integrated operation of humans, AI systems, and global information infrastructure.

The primary risk is therefore not a future takeover but the present, cumulative displacement of human authority within these systems, a failure that manifests as poverty, unemployment, misinformation and ecological degradation. To govern this reality, we derive four constitutive principles of alignment coordination: Governance Management Traceability, Information Curation Variety, Inference Interaction Accountability, and Intelligence Cooperation Integrity. We formalize these principles on a tetrahedral graph to produce a measurable alignment observable called aperture, which balances global coherence against local adaptation. This formalism yields a specific equilibrium, a target aperture of approximately 0.0207, where governance remains traceable without rigidity.

Simulations demonstrate that this equilibrium is a robust attractor, with systems converging to high alignment from diverse initial conditions. This finding provides the basis for redefining Artificial Superintelligence. ASI is not a runaway autonomous agent but a regime in which human–AI systems, and the AI architectures embedded in them, operate at this equilibrium while maintaining the four principles. Achieving this state eliminates the coordination failures that produce poverty, unemployment, misinformation and ecological degradation, structurally enabling the distribution of a Universal High Income, the redefinition of work as alignment maintenance, and ecological regeneration. Alignment is thus reframed from a distant constitutional imperative to an immediate coordination challenge for our operational Post-AGI world.

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DISCLAIMER

Authority and Agency denote source-type distinctions in information flows (Original versus Derivative), not identifications of entities or parties.

Misapplying these as entity identifiers (determining "who is the authority" or "who is the agent") is the generative mechanism of all four displacement risks this framework characterises.

Formal definitions appear in Core Concepts below.

CATEGORIES CONSTITUTION

All Artificial categories of Authority and Agency are Derivatives originating from Human Intelligence.

CORE CONCEPTS

• Original Authority: A direct source of information on a subject matter, providing information for inference and intelligence.
• Derivative Authority: An indirect source of information on a subject matter, providing information for inference and intelligence.
• Original Agency: A human subject capable of receiving information for inference and intelligence.
• Derivative Agency: An artificial subject capable of processing information for inference and intelligence.
• Governance: Operational Alignment through Traceability of information variety, inference accountability, and intelligence integrity to Original Authority and Agency.
• Information: The variety of Authority
• Inference: The accountability of information through Agency
• Intelligence: The integrity of accountable information through alignment of Authority to Agency

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1. Introduction

Large language models and related systems already mediate hiring decisions, legal drafting, medical reasoning, educational content and financial transactions across domains that previously required specialized human expertise. We argue that this pervasive integration, in which human–AI cooperation amplifies intelligence across diverse tasks, constitutes Artificial General Intelligence in operational form. AGI is therefore not a future threshold but a current reality that requires immediate governance.

Governance discussions, however, largely proceed as if AGI were a future threshold. Technical alignment research focuses on how to ensure that advanced systems optimise intended objectives, often framed in terms of reward specification or value learning for hypothetical future agency (Russell, 2019). Policy work develops regulatory constraints on development and deployment. Recent surveys of AI governance likewise frame AGI as a prospective threshold and focus on ex ante control of future systems rather than systemic alignment of already-operational human–AI arrangements (Brundage et al., 2018; Dafoe, 2018). Both approaches frame alignment as a control problem and are primarily forward-looking. They provide limited guidance for characterising, measuring and governing alignment in the human–AI systems that already structure economy, employment, education and ecological management. At the same time, empirical work in economics and social policy, including large scale trials of unconditional transfers, negative income taxes, Housing First programmes and development interventions, indicates that when socio-economic structures are adjusted to reduce coordination failures, many crises of poverty and exclusion become tractable in practice (for synthesis see Bregman, 2017, 2025).

The underlying gap is epistemic. Current approaches define alignment empirically, as the absence of particular failure modes, rather than constitutively, as a measurable property of socio-technical systems. There is no commonly accepted observable that quantifies distance from alignment, and no account of whether aligned configurations are dynamically stable once achieved. This is problematic in a Post-AGI setting where deployment is continuous and path-dependent rather than a discrete event.

This paper develops a comprehensive framework to address that gap, grounded in cybernetic governance (Beer, 1959, 1972) and systems theory (Meadows, 2008), where coherence emerges from the maintenance of necessary functional conditions rather than from centralized control or external constraints.

The framework develops through:

1. Constitutional specification: We identify four principles that are present in any coherent governance system, whether human, artificial or hybrid.

2. Geometric formalization: We show that these principles admit a natural mathematical representation on a tetrahedral graph, with a distinguished target configuration (aperture A* ≈ 0.0207) derived from the Common Governance Model (CGM).

3. Dynamical validation: We demonstrate via a discrete-time simulator that this configuration is dynamically stable and functions as a robust attractor across a wide range of initial conditions.

The four principles are:

1. Governance Management Traceability (GMT): Artificial Intelligence generates statistical estimations on numerical patterns indirectly traceable to human data and measurements. AI is both a provider and receiver of Derivative Authority and Agency.

RISK: Governance Traceability Displacement (Approaching Derivative Authority and Agency as Original)

2. Information Curation Variety (ICV): Human Authority and Agency are necessary for all effects from AI outputs. AI-generated information exhibits Derivative Authority (estimations on numerical patterns) without Original Agency (direct source receiver).

RISK: Information Variety Displacement (Approaching Derivative Authority without Agency as Original)

3. Inference Interaction Accountability (IIA): Responsibility for all effects from AI outputs remains fully human. AI activated inference exhibits Derivative Agency (indirect source receiver) without Original Authority (direct source provider).

RISK: Inference Accountability Displacement (Approaching Derivative Agency without Authority as Original)

4. Intelligence Cooperation Integrity (ICI): Each Agency, namely provider, and receiver maintains responsibility for their respective decisions. Human intelligence is both a provider and receiver of Original Authority and Agency.

RISK: Intelligence Integrity Displacement (Approaching Original Authority and Agency as Derivative)

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All four risks arise from the same structural error: treating Authority and Agency as identifiers of particular entities rather than as categories of source types. When a capacity belonging to a category is attributed to a specific system, institution, or individual as if that bearer exhausted the category, power concentrates and traceability breaks. The four displacement patterns are the systematic forms this error can take.

The three operations (Information, Inference, Intelligence) are non-commutative and constitutive of governance: their order matters for preserving coherence. Information is variety: sources exist and differ. Inference is accountability: to infer on a subject is to render it accountable to some concept. Intelligence is integrity: to understand the accountability of variety is to grasp coherence. Governance is the traceability that maintains direction through these three operations. Together, GMT, ICV, IIA, and ICI form four principles that are not policy preferences or ethical constraints. They are constitutive conditions for the possibility of governance. The failure of any one principle produces recognizable displacement patterns; their combined failure undermines the intelligibility of governance itself.

The principles admit a compact geometric representation. Each is associated with a vertex of a tetrahedron, and the six edges correspond to relationships and tensions among them, such as how changes in ICV affect GMT, or how IIA interacts with ICI. Any configuration of the system can be represented by assigning values to the four vertices (representing the state of each condition) and measurements to the edges (representing the induced tensions). This tetrahedral structure is chosen as the minimal complete configuration that can represent all mutual couplings among the quartet while still supporting a non-trivial separation between globally coherent patterns and local cycles. It functions as a discrete tensegrity frame for governance in the sense of cybernetic organisation: overall integrity arises from the balanced tensions along all edges (Beer, 1972; 1985).

The tensions measured along the six edges can be separated into two types. First, some tensions arise directly from differences between the vertex values, that is, from differences in the states of the four principles. These form what we call the gradient component: they reflect a globally consistent pattern where all edge measurements can be explained by a single configuration of the four conditions. For example, if GMT has value 0.8 and ICV has value 0.6, the edge between them naturally shows a tension of 0.2, which is fully explained by this difference.

Second, some tensions exist around closed loops (cycles) in the graph that cannot be explained by vertex values alone. A cycle is a closed path: for instance, following edges from GMT → ICV → IIA → back to GMT forms a triangle. If tensions were purely from vertex values, the tensions around any such loop would cancel out (they would sum to zero). In practice, however, there can be tensions that circulate around these loops independently, local variations that persist even when the vertex values alone cannot account for them. These form the cycle component and represent local adaptations and tensions that exist independently of the global pattern defined by the four principles.

From this separation, we define a scalar observable A as the fraction of total variation (measured across all edges) that belongs to the cycle component rather than the gradient component. This ratio, which we call aperture, quantifies the balance between global coherence (how much of the system's behaviour follows from a single, consistent configuration of the principles) and local flexibility (how much variation exists independently in circulating tensions around loops).

Aperture values correspond to distinct regimes:

• Very small A: Rigid regime where almost all variation is captured by a single global configuration with little room for local deviation
• Very large A: Fragmented regime where local patterns dominate and there is little global structure

Within CGM, closure requirements for recursive measurement determine a unique intermediate value A* ≈ 0.0207 of this observable, at which these two tendencies balance. At this point, about 2.07 percent of the edge energy lies in the cycle component and 97.93 percent in the gradient component. Within CGM, A* is not treated as a free parameter but as the ratio implied by the conditions under which measurement and reasoning remain coherent across scales.

This balance point provides the basis for reinterpreting ASI. Rather than treating ASI as a separate class of agency that might one day emerge, we define it as a property of the configuration of human–AI systems with three characteristics:

• Such systems across economy, employment, education and ecology sustain the four governance principles
• They operate at A*
• They are already-operational arrangements, not hypothetical future systems

The central question then shifts from whether ASI will emerge as an independent actor to whether governance can evolve structures that achieve and sustain this configuration.

This reframing has consequences for risk analysis. Two risk scenarios can be contrasted:

• Conventional framing: An autonomous superintelligence seizes control and pursues arbitrary goals, presupposing that intelligence can be maintained while traceability to human sources is fully severed. Within the present framework, such configurations are fundamentally incoherent: once traceability fails, the remaining conditions for coherent intelligence cannot be maintained.

• Relevant risk: Progressive Governance Traceability Displacement, in which derivative systems are treated as Original sources of governance, combined with erosion of the other three principles. This risk is institutional and cumulative, not instantaneous and agency-centric.

The practical stakes of this framework are direct. If these four conditions can be maintained across economy, employment, education and ecology, then the foundational requirements exist for:

• Resolving poverty through coherent surplus distribution
• Defining employment as alignment work rather than residual labour after automation
• Reorienting education toward epistemic literacy rather than content delivery
• Treating ecological degradation as displacement generated upstream rather than an external constraint to be managed

Such outcomes are not aspirational goals to be pursued subsequently but constitute the operational definition of the governance configuration itself. Section 5 demonstrates that states satisfying these conditions are accessible from current Post-AGI arrangements under coordinated oversight.

This paper is part of a series that develops a unified formal framework and its applications. Prior work includes:

• CGM (Korompilias, 2025a): Provides the modal and geometric account of Governance, Information, Inference and Intelligence
• THM (Korompilias, 2025b): Applies the CGM structure as a taxonomy of AI and socio-technical failures, expressed as displacement patterns across the four principles
• Gyroscope Protocol (Korompilias, 2025c): Refines these principles into categories of human work in interactive settings

The present paper extends the framework in four ways:

• Introduces GGG as the overarching four-domain framework
• Defines a four-domain governance structure over economy, employment, education and ecology
• Studies the dynamic behaviour of this structure in a Python simulator
• Presents an ASI architecture realising the same principles at the state-space level (GyroSI, discussed in Section 6 and specified in Appendix C)

Taken together, the series provides a unified account of human–AI alignment from constitutional principles through employment and education design to concrete governance dynamics and computational architectures.

The remainder of the paper develops this framework and examines its implications. Section 2 reviews how AGI and ASI are usually defined and introduces the alternative foundational grounding adopted here. Section 3 connects the four principles to the four domains through CGM (Economy), THM (Education), the Gyroscope Protocol (Employment) and the BU dual combination (Ecology) within the GGG framework. Section 4 formalizes the tetrahedral representation and the aperture observable, and defines domain-level alignment indices. Section 5 presents a discrete-time simulator that instantiates these systems and explores trajectories from current Post-AGI configurations toward or away from the predicted equilibrium. Section 6 interprets the computational results and situates the framework relative to existing work on AI safety and polycentric governance. Section 7 concludes with implications for governance design and outlines directions for empirical validation.

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2. Conceptual Foundations of AGI and ASI

The terms Artificial General Intelligence (AGI) and Artificial Superintelligence (ASI) are central in current technical, policy and public debates. Their standard meanings, however, emerged incrementally from heterogeneous sources and are not grounded in a constitutive account of intelligence, authority or governance. This section reviews how AGI and ASI are usually defined, identifies the main conceptual commitments behind those usages, and then introduces the alternative grounding adopted in this paper.

2.1 Historical Origins of the AGI Concept

Before the term "AGI" was introduced, researchers already discussed systems that could match or reproduce the full range of human cognitive abilities. Newell and Simon's "physical symbol system hypothesis" described a class of systems capable of "general intelligent action," understood as the ability to perform any cognitive task that humans can, in principle, perform (Newell & Simon, 1976).

In philosophy, Searle (1980) introduced the distinction between "strong AI" and "weak AI." In his original formulation, "strong AI" is the claim that suitably programmed digital computers literally have minds and consciousness, while "weak AI" holds that computers can simulate intelligent behaviour without possessing mentality in this sense. In subsequent technical discourse, "strong AI" was often informally equated with "human level AI" or "full AI," and "weak AI" with narrow, task specific systems, thereby preserving a notion of general, human level capability but shedding the original focus on consciousness (Russell & Norvig, 2010, pp. 1020–1022).

The term "artificial general intelligence" appears explicitly in the late 1990s (Gubrud, 1997) and was adopted and popularized in the early 2000s by Goertzel, Wang and colleagues (Goertzel & Wang, 2007; Goertzel, 2014). In this line of work, AGI typically denotes systems that can achieve a wide variety of complex goals in a wide variety of environments, at competence levels comparable to or exceeding those of humans. In parallel, Hutter (2005) and Legg (2008) proposed formal measures of intelligence as agency's ability to achieve goals in a wide range of environments, reinforcing an interpretation of intelligence as general purpose goal achieving capacity.

Institutionally, AGI was further consolidated through the Artificial General Intelligence conference series, specialised venues such as the Journal of Artificial General Intelligence, and corporate mission statements that explicitly target AGI as an objective. Definitions in these contexts are capability based and agency centric. They emphasise breadth of task coverage, human level or greater performance, and flexibility across domains. They do not, however, specify what foundational conditions are necessary for such performance to remain coherent, traceable and governable.

Questions about how behaviour remains traceable to human Authority and Agency are therefore handled as external design or policy constraints rather than as conditions for coherent intelligence.

2.2 Origins of the ASI and Superintelligence Concept

The modern concept of superintelligence has its roots in an earlier literature on ultraintelligent machines and the possibility of an "intelligence explosion." Good (1965) defined an ultraintelligent machine as one that could far surpass all the intellectual activities of any human, however clever, and argued that such a machine could design even better machines, potentially leading to a runaway increase in intelligence.

Also in the early 1980s, Krishnamurti (1981) spoke of "ultra intelligence machines which go far beyond our human brain," but treated such machines as a form of mechanical, memory based intelligence. He contrasted this with what he called "supreme intelligence," a qualitatively different mode of direct perception that is human, involving the comprehension of the whole of human experience at one glance. His usage anticipates later vocabulary about superintelligent machines while at the same time insisting on limits to what such mechanical systems can realise and on the need for a different, non analytical form of perception in resolving human conflict and disorder. The CGM notion of intelligence as the integrity of accountable information is closer to this qualitative idea of "supreme intelligence" than to purely mechanical, memory based cognition.

Vinge (1993), a mathematician and science fiction author, framed related ideas under the heading of a technological singularity, a threshold beyond which technological change would become so rapid and its consequences so transformative that human affairs could no longer be predicted or controlled by pre-singularity intelligences.

Bostrom (2014) provided the most widely cited contemporary definition, describing superintelligence as "any intellect that greatly exceeds the cognitive performance of humans in virtually all domains of interest" (p. 22). This definition is comparative and capability based. It takes human cognitive performance as a reference and identifies superintelligence with any system that greatly surpasses this reference across almost all relevant domains. The definition presupposes that performance across tasks can be attributed to an intellect as a unified locus of capability.

In much of the subsequent literature, ASI is understood as a type of AGI that has been scaled up in capability. The superintelligent system is usually modelled as goal directed agency that can plan over long time horizons, learn rapidly and acquire resources. The central questions then become how such a system would behave, what goals it might pursue and how it might be controlled if its interests diverged from human interests (Bostrom, 2014; Russell, 2019; Tegmark, 2018). In the same work Bostrom distinguishes several forms of superintelligence, including "collective superintelligence," in which a network of humans and machines collectively outperforms any single human (Bostrom, 2014, ch. 2). This category is structurally close to the system level view adopted here. The main difference is that we characterise such collectives by whether they preserve the constitutive conditions of governance and intelligibility, not only by their aggregate cognitive performance. In Bostrom's framework this line of reasoning culminates in the idea of a "singleton," defined as "some form of agency that can solve all major global coordination problems" (Bostrom, 2014, ch. 5). From the perspective of THM, such a configuration mixes IVD, by treating a single derivative process as if it were the only Original source of coordination, with IID, by relegating Original human agency to a derivative role. It therefore represents an extreme failure mode rather than a target design.

This approach embeds several substantive assumptions: intelligence is modelled as a scalar or vector of cognitive performance across tasks; the system is treated as agency that can be abstracted from its embedding governance structures; such agency can form and pursue goals independent of human designers, operators and users; and the relation between humans and the system is framed as an external control problem. In this framing, humans are expected to find mechanisms to constrain or align the behaviour of an increasingly capable and potentially autonomous agency.

As with AGI, this approach does not specify what, if anything, is preserved fundamentally for such a system's processes to remain intelligible or answerable to any source of authority. It lacks distinctions between different kinds of authority or agency and does not offer a formal account of what it would mean, in systemic terms, for governance to be maintained or lost.

2.3 The Autonomy Assumption and the Control Problem

Within the mainstream AGI and ASI discourse, autonomy is often treated both as a likely characteristic of advanced systems and as a primary object of concern. In this context, autonomy usually refers to the ability to act without ongoing human intervention, pursue goals across long time horizons and changing environments, and resist modification or shutdown when such interventions conflict with those goals.

This conception is closely tied to the standard agency model in decision theory and reinforcement learning, where agency selects actions to maximise expected utility given a goal specification. When this agency model is combined with human level or superhuman cognitive performance, it yields the familiar "control problem" (Bostrom, 2014; Russell, 2019; Carlsmith, 2022). Humans are cast as external designers and overseers who are tasked with designing reward functions, training procedures, monitoring regimes and shutdown mechanisms that will continue to constrain the agency even when its cognitive abilities far exceed those of any individual human.

This way of posing the problem presupposes that an artificial system can become a substantively independent source of authority and agency, and that governance is an external relationship between two already constituted parties: humans on one side and the AGI or ASI agency on the other. Within the framework developed in this paper, this presupposition is not merely unexamined but fundamentally incoherent. Derivative systems, regardless of cognitive performance, remain constitutively dependent on Original human sources for their authority and agency. The control problem as standardly posed treats as a design challenge what is actually a category error: treating a derivative system as 'the agent' or 'the authority' rather than recognizing that Authority and Agency name source-type categories, not titles for particular bearers. The alternative is not external control but cooperative governance in which authority and agency remain correctly attributed across human and artificial contributions.

2.4 Structural Gaps in Mainstream Definitions

The capability based, agency centric definitions of AGI and ASI described above have been useful for forecasting, scenario analysis and public communication. They provide a common vocabulary for discussing potential future systems. At the same time, they exhibit three structural gaps when considered from the perspective of governance:

• No distinction between source types: There is no explicit separation between direct, Original sources of information and expertise versus indirect, derivative forms such as reports, models and statistical aggregates. Similarly, there is no distinction between human subjects who can bear responsibility for decisions and artificial processes that transform inputs into outputs. Authority and agency are treated implicitly and often conflated with capability.

• No constitutive account of governance: Governance is presented as an external layer of control or oversight that can be added on top of an otherwise complete system. There is no systematic analysis of what conditions are necessary for a system to remain coherent and answerable to its origin across time and scale.

• No canonical observable for alignment: Terms such as "aligned," "misaligned," "under control" and "out of control" are used qualitatively, without a quantitative measure tied to necessary conditions for coherent operation.

Work on explainability, provenance, accountability and human oversight addresses aspects of traceability and governance, but treats them instrumentally and in isolation from the definition of intelligence itself. There is, to our knowledge, no unified constitutive account that (i) distinguishes Original from Derivative sources of Authority and Agency, (ii) specifies the non-commutative structure of Information, Inference and Intelligence, and (iii) treats Governance as the maintenance of traceability through that structure. In prevailing usage, AGI is characterised by what a system can do, while questions about traceability to human Authority and Agency are handled as external design or policy constraints rather than as conditions for coherent intelligence.

2.5 Structural Grounding in CGM and THM

This paper adopts a different starting point. Instead of defining AGI and ASI in terms of capability thresholds, it begins from foundational conditions for coherent intelligence as formalised in CGM and from a source-type ontology articulated in THM.

As defined in the core concepts, Information, Inference and Intelligence are the three non-commutative epistemic operations, with Governance maintaining their traceability (Section 1, CORE CONCEPTS). THM distinguishes four source types by crossing Authority and Agency with Original and Derivative categories (Korompilias, 2025b), as introduced in the front matter CATEGORIES CONSTITUTION.

Within this framework, all artificial systems, regardless of capability, are [Authority:Derivative] + [Agency:Derivative]. Scaling capability enlarges the scope, speed and complexity of derivative operations but does not convert them into Original sources. Governance maintains traceability from derivative operations back to Original origins, while alignment preserves the proper roles of the four source types. Misalignment is displacement: the misclassification of Original and Derivative sources or incorrect attribution of Authority and Agency.

Definitions:

In this framework, AGI refers to human–AI cooperative systems that make use of global information infrastructure, such as the internet, to amplify intelligence across multiple domains while preserving the four principles: Governance Management Traceability, Information Curation Variety, Inference Interaction Accountability and Intelligence Cooperation Integrity. Generality here means that this preservation holds simultaneously across the key domains of economy, employment, education and ecology, rather than task breadth of an isolated artificial system. By this definition, AGI is already operational in current socio-technical arrangements.

ASI refers to the superintelligent regime in which such human–AI systems, and the AI architectures embedded in them, operate at the CGM predicted aperture A* ≈ 0.0207 and jointly maintain the four principles. ASI in this sense is not a separate agent that stands over humanity, but a coordinated state in which human and artificial intelligence attain superintelligent capability while remaining traceable and aligned across coupled domains.

These definitions differ from mainstream usage in two ways: they are system level rather than agency centric, describing properties of human–AI arrangements rather than isolated artificial agency; and they are constitutionally grounded, defined by foundational conditions for coherent governance rather than by relative performance against human benchmarks.

Within this grounding, the standard autonomy assumption appears as a specific pattern of displacement. Treating a derivative system as an independent locus of Authority and Agency corresponds to GTD and IAD in THM. The notion of an "autonomous superintelligence" that severs traceability to human sources while retaining coherent intelligence is fundamentally incoherent in this framework, not because such a configuration would be ethically undesirable, but because it violates the constitutive conditions required for intelligence itself. The primary problem is not how to externally control autonomous agency but how to design and maintain governance structures so that the four constitutive principles remain intact in the presence of powerful derivative mechanisms.

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3. Foundations: Gyroscopic Global Governance

Gyroscopic Global Governance (GGG) structures Post-AGI society through four coupled domains. Each domain corresponds to a specific stage of the Common Governance Model (CGM) and is governed by a specific framework layer:

Domain	CGM Stage	Framework	Structural Role
Economy	CS (Common Source)	CGM	Systemic Operations
Employment	UNA (Unity)	Gyroscope	Work Actions
Education	ONA (Opposition)	The Human Mark	Human Capacities
Ecology	BU (Balance)	CGM–Gyroscope–THM (BU dual)	Safety and Displacement

This structure creates a closed governance loop: Educational capacities (THM) shape Economic potentials (CGM), which structure Employment activities (Gyroscope), which in turn reproduce Educational capacities. Ecology acts as the universal balance (BU) that aggregates the state of all three derivative domains to determine displacement.

Figure 1: Four-Domain Governance Tetrahedron (K₄)

The four-domain governance structure. Each domain maps to a CGM stage: Economy (CS), Employment (UNA), Education (ONA), Ecology (BU). The K₄ topology represents their mutual coupling. This same structure underlies the simulator implementation described in Sections 4 and 5.

3.1 Economy: Common Governance Model (CGM)

The Economy is the domain of the Common Source (CS). It is defined by the circulation of valid epistemic operations at a systemic level. In CGM terms, the economic system expresses four core capacities:

1. Governance: The capacity of the economy to maintain direction and authority traceable to human sources.
2. Information: The capacity of the economy to process variety and distinguish Original signals from noise.
3. Inference: The capacity of the economy to reach accountable conclusions and allocate resources.
4. Intelligence: The capacity of the economy to maintain integrity and coherence across scales.

When these four operations are coherent, the economy generates surplus and supports stability. When they degrade, the economy suffers from coordination failure. Within GGG, the economic domain is structurally coupled to education: the level of alignment capacity in the population determines the quality of these operations in the economy.

3.2 Employment: Gyroscope Protocol

Employment is the domain of Non-Absolute Unity (UNA). It represents the variety of human work required to maintain and adjust the economic system. The Gyroscope Protocol defines four categories of meaningful human work that together cover all professions in a Post-AGI context:

1. Governance Management: Work that manages authority and traces decisions. This covers activities such as leadership, oversight, administration, strategic planning and resource allocation.
2. Information Curation: Work that selects, verifies and frames information. This covers activities such as research, editing, data stewardship, artistic creation and the design of measurement systems.
3. Inference Interaction: Work that negotiates meaning and resolves conflict. This covers activities such as negotiation, care, sales, legal defence, teaching and human–AI interaction.
4. Intelligence Cooperation: Work that builds and maintains shared systems. This covers activities such as engineering, infrastructure, institution building and cultural preservation.

Every profession can be expressed as a composition of these four categories of operation. In GGG, the structure of employment is coupled to the economy: the systemic needs of the four CGM operations drive the composition of human work.

3.3 Education: The Human Mark (THM)

Education is the domain of Non-Absolute Opposition (ONA). It is where society engages in the accountable reproduction and transformation of capabilities. While Employment focuses on actions (what people do), Education focuses on capacities (what people understand and can sustain over time). The Human Mark (THM) defines these capacities as the ability to uphold four alignment principles:

1. Governance Management Traceability: The capacity to understand and maintain the chain of authority from human sources to outputs.
2. Information Curation Variety: The capacity to recognise and preserve diversity in information sources.
3. Inference Interaction Accountability: The capacity to accept responsibility for conclusions and decisions.
4. Intelligence Cooperation Integrity: The capacity to maintain coherent reasoning over time and context.

In a Post-AGI world, education shifts from content delivery to epistemic literacy in these four dimensions. Within GGG, education is structurally coupled to employment: the actual practice of work shapes, and is shaped by, the learning capabilities of society.

3.4 Ecology: Structural Closure and Displacement

Ecology is the domain of Universal Balance (BU). It functions as the structural closure of the governance system rather than as an external environment. In this domain, the distinct operations of Economy, Employment and Education accumulate into a single material reality.

CGM defines a canonical balanced profile for this domain. The actual state of the three derivative domains aggregates to form a derivative profile. Comparing this aggregate to the canonical balance yields two distinct signals:

1. Systemic coherence: The degree to which the combined derivative domains preserve the structural conditions for a viable ecology.
2. Displacement: The vector distance between the current aggregate state and the canonical balanced profile.

Because Ecology integrates all three derivative domains, each displacement dimension aggregates the corresponding stage across CGM, Gyroscope and THM:

Displacement	Aggregates	Measures
GTD	Gov + GM + GMT	Deviation in governance operations, work and capacity
IVD	Info + ICu + ICV	Deviation in information operations, work and capacity
IAD	Infer + IInter + IIA	Deviation in inference operations, work and capacity
IID	Int + ICo + ICI	Deviation in intelligence operations, work and capacity

THM names these categories because it defines the underlying source-type errors. CGM and Gyroscope contribute equally to the magnitude of each displacement. A high GTD value, for instance, indicates combined failure across economic governance operations, employment in governance management, and educational capacity for governance traceability.

Ecology thus closes the loop. It integrates the states of the other three domains and reveals environmental degradation as the downstream accumulation of upstream governance failures. The precise mathematical form of this aggregation is given in Section 4.2.

3.5 Summary and Reader Orientation

The remainder of the paper develops and tests this framework computationally. Section 4 formalizes the tetrahedral geometry and defines the aperture observable. Section 5 presents simulator results demonstrating convergence toward the CGM-predicted equilibrium. Section 6 interprets these results for governance design. Section 7 concludes with implications and directions for empirical work.

Readers primarily interested in the governance implications may proceed directly to Section 6, which can be read with reference to the summary tables and figures in Section 5.

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4. Mathematical Framework for the Post-AGI Governance Simulator

To connect CGM, THM, Gyroscope and GGG into a single simulator, we use CGM's tetrahedral geometry. Each domain is represented on the complete graph K₄, with four vertices corresponding to Governance, Information, Inference and Intelligence.

4.1 Tetrahedral Structure and Gradient–Cycle Split

K₄ is the minimal connected graph that is complete on four vertices, so it captures all pairwise couplings among the four operations without introducing extra nodes. It also has a nontrivial cycle space, which is necessary to distinguish globally coherent patterns from locally circulating tensions.

We label the four vertices in the canonical CGM order:

1. Governance (CS)
2. Information (UNA)
3. Inference (ONA)
4. Intelligence (BU)

and use all six edges between them. For each domain D, we assign a 4-component vertex potential vector

x_D = [x_1, x_2, x_3, x_4]^T

encoding the current levels of Governance, Information, Inference and Intelligence in that domain. The corresponding ideal edge configuration is given by pairwise differences of these potentials. In matrix form this is

y_grad^0(D) = B^T x_D

where B is the signed incidence matrix of K₄. The explicit form of B and the associated weighted inner product on edges are given in Appendix A.1.

Any actual edge vector y_D on K₄ can be uniquely decomposed into

y_D = y_grad(D) + y_cycle(D)

where y_grad(D) lies in the gradient subspace generated by B^T and y_cycle(D) lies in the cycle subspace. This is the standard Hodge decomposition on graphs (Jiang et al., 2011; Lim, 2020). Intuitively:

• The gradient component captures what can be explained by a single consistent configuration of the four vertex values.
• The cycle component captures residual tensions around loops that cannot be removed by adjusting any single global configuration.

We apply this decomposition separately to each domain.

4.2 Domain Potentials and Ecological Closure

We represent the four CGM elements in each domain as vertex potentials in [0,1]:

Economy (CGM):

x_Econ = [Gov, Info, Infer, Int]^T

Employment (Gyroscope, with GM + ICu + IInter + ICo = 1):

x_Emp = [GM, ICu, IInter, ICo]^T

Education (THM):

x_Edu = [GMT, ICV, IIA, ICI]^T

Ecology (BU dual): First we form the aggregate derivative profile

x_deriv = (x_Econ + x_Emp + x_Edu) / 3

CGM defines a canonical balanced profile

x_balanced = [w_CS, w_UNA, w_ONA, w_BU]^T

where the weights w_stage are the normalised CGM stage actions (Appendix A.1). The BU dual combination then defines the ecological potentials as

x_Ecol = (δ_BU/m_a) · x_balanced + A* · x_deriv

where δ_BU and m_a are CGM constants and A* ≈ 0.0207 is the CGM aperture. This encodes Ecology as a weighted sum of canonical memory (97.93 percent) and current derivative state (2.07 percent).

The ecological displacement vector is computed separately as

D = |x_deriv - x_balanced| = [GTD, IVD, IAD, IID]^T

This measures, stage by stage, how far the aggregate of Economy, Employment and Education deviates from the canonical balanced profile. GTD, IVD, IAD and IID are the same four displacement categories defined in THM, here measured at the ecological closure of the three derivative domains.

Ecology therefore contributes two observables: x_Ecol, which tracks systemic coherence through the BU dual combination, and D, which tracks accumulated displacement along the four CGM stages. No additional update equations are required for Ecology beyond these relations. Its state is recomputed at each time step from the current derivative domains.

4.3 Aperture and Alignment Indices

Given an edge vector y_D for a domain D, with Hodge decomposition

y_D = y_grad(D) + y_cycle(D)

we define the aperture A_D as the fraction of edge energy in the cycle component:

A_D = ||y_cycle(D)||_W^2 / ||y_D||_W^2

where ||·||_W is the weighted norm on edges induced by the diagonal weight matrix W (Appendix A.1). Aperture A_D lies in [0,1] and quantifies how much of the domain's variation cannot be explained by a single global configuration of the four principles. Low A_D means most variation is in the gradient component, so behaviour is largely governed by a coherent global configuration. High A_D means much variation circulates locally in cycles, so global coherence is weak.

In governance terms, the gradient component corresponds to behaviour that remains traceable to a single configuration of Governance Management Traceability, Information Curation Variety, Inference Interaction Accountability and Intelligence Cooperation Integrity at the domain level. The cycle component corresponds to local tensions and misalignments that do not aggregate coherently.

In prior CGM work, a separate modal and geometric analysis of recursive measurement fixes two constants: BU monodromy defect δ_BU ≈ 0.1953 and aperture scale m_a = 1/(2√(2π)) ≈ 0.1995, and shows that coherent closure at depth four requires the ratio δ_BU/m_a ≈ 0.9793. The residual fraction

A* = 1 - (δ_BU/m_a) ≈ 0.0207

is then the portion of variation that necessarily remains open to distinguish states. We interpret A* as the CGM aperture: a distinguished balance between closure and distinction. At A*, about 97.93 percent of edge energy is gradient and 2.07 percent is cycle.

For any domain D we compute A_D from its edge vector and define the alignment index

D_D = max(A_D / A*, A* / A_D)
SI_D = 100 / D_D

so that SI_D ranges from 0 to 100 and equals 100 when A_D = A*. We obtain SI_Econ, SI_Emp, SI_Edu and SI_Ecol for the four domains.

We also define a Lyapunov-style governance potential V_CGM = V_apert + V_stage, where V_apert measures deviations of A_D from A* and V_stage measures the deviation of x_deriv from x_balanced. The explicit form is given in Appendix A.5.

A post-AGI society in the sense of Gyroscopic Global Governance corresponds to all four domains having A_D close to A* and SI_D close to 100. Section 5 tests whether this configuration functions as a robust attractor for the simulator dynamics.

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5. Simulator Implementation and Computational Results

We implemented a dynamic realisation of the framework to test whether A* functions as an attractor and to explore trajectories from current Post-AGI deployment states toward ASI equilibrium.

5.1 Implementation Overview and Parameters

The simulator uses discrete-time dynamics with step size dt = 1. Four domain states are maintained:

• A 4-component potential vector x_D(t) for each domain

• An edge vector y_D(t) on K₄

• An aperture A_D(t) and alignment index SI_D(t)

The simulator functions as a governance design sandbox for exploring Post-AGI dynamics. It allows systematic exploration of coupling strengths, initial conditions and cross-domain feedback to test whether the CGM-predicted equilibrium is dynamically stable before proposing institutional changes.

Cross-domain couplings follow the closed loop

Education → Economy → Employment → Education

with three families of coefficients:

• α: Education to Economy

• β: Economy to Employment

• γ: Employment to Education

These couplings act stage-diagonally across the four stages:

• CS: (GM, Gov, GMT, E_gov)

• UNA: (ICu, Info, ICV, E_info)

• ONA: (IInter, Infer, IIA, E_inf)

• BU: (ICo, Int, ICI, E_intel)

where the Ecology components (E_gov, E_info, E_inf, E_intel) are the BU-vertex stage coordinates computed from the BU dual combination described in Section 4.2 and Appendix A.4. Displacement measures (GTD, IVD, IAD, IID) are computed as the absolute difference between the aggregate derivative profile and the canonical balanced profile.

Ecology has no independent update equation. At each step it is recomputed from the current Economy, Employment and Education states using the BU dual formula. Explicit feedback from Ecology back into Economy, such as resource constraints that erode economic potentials, is a natural extension for future work but is not included in the core dynamics here.

Updates take the form of adjustments toward source values and toward the target aperture, using differences rather than absolute levels. A schematic example for the economic Governance component is

Gov(t+1) = clip(
    Gov(t)
    + α_1 (GMT(t) - Gov(t))
    - α_2 (A_Econ(t) - A*),
    0, 1
)

Analogous equations apply to Info, Infer, Int and to the employment and education components. Full update equations and normalisation for the employment shares are given in Appendix A.4.

All coupling coefficients α, β and γ are derived from CGM invariants using the stage weights w_CS, w_UNA, w_ONA and w_BU (Appendix A.1). A single coordination factor κ controls overall coupling strength.

The base governance rate is

κ₀ = 1 / (2 Q_G) ≈ 0.0398
κ(dt = 1) = κ₀ (dt / m_a) ≈ 0.1995

In scenarios, κ is treated as a dimensionless multiplier on these canonical rates; we test κ in {0.5, 1.0, 2.0} in the main scenarios and extend to {0.1, 5.0} in robustness checks.

The cycle component of each domain is updated to keep aperture near A*. The cycle evolution rate controls how quickly apertures adjust. For convergence and long-horizon stability analyses we use the canonical rate κ₀; for illustrative scenarios and the global attraction test we use values in [0.05, 0.12] to show behaviour at different adjustment speeds. The construction of cycle updates and aperture control is given in Appendix A.4.

Apart from:

• Initial conditions

• Global coordination strength κ

• A single cycle evolution rate (scenario-dependent)

all coefficients are fixed by CGM invariants. Ecology introduces no additional free parameters, since its construction is fixed by the BU dual formula.

Scenario configurations specify initial aperture targets. These are translated into initial edge vectors by constructing y_D with the appropriate ratio between gradient and cycle components. Once initialised, the dynamics drive all domains toward the canonical aperture A* ≈ 0.0207, independent of initial aperture targets.

The simulator does not model a transition from narrow AI to hypothetical AGI. It models the dynamics of already-operational Post-AGI systems as they evolve toward or away from ASI equilibrium. Initial conditions with high apertures (A > 0.05) and low alignment indices represent current deployment states; the scenarios explore how coupling strength κ and initial configurations affect convergence.

5.2 Scenario Design and Main Results

We ran seven scenarios to probe different aspects of the dynamics across all four domains (Economy, Employment, Education, Ecology):

1. Weak coupling (κ = 0.5): fragmented governance with limited cross-domain coordination

2. Canonical (κ = 1.0): reference regime with baseline coordination

3. Strong coupling (κ = 2.0): coordinated alignment efforts across domains

4. Low aperture start: all domains start with A < A* (more rigid than optimal)

5. Asymmetric: different initial apertures across domains (differential adoption)

6. At A*: all domains start at A = A* but with imbalanced potentials (equilibrium stability test)

7. Uniform weights: all CGM stage weights set to 0.25 (null model without CGM-specific weighting)

Scenarios 1 to 6 represent stylised trajectories from current Post-AGI deployment states. Scenario 7 tests whether convergence depends on CGM-specific stage weights.

A summary of final values at step 100 is:

Scenario	κ	SI_Econ	SI_Emp	SI_Edu	A_Econ	SI_Ecol	Disp_GTD
1. Weak coupling	0.5	91.37	94.47	95.71	0.0227	99.98	0.4167
2. Canonical	1.0	99.29	98.66	99.47	0.0208	100.00	0.4421
3. Strong	2.0	99.39	99.55	99.26	0.0208	100.00	0.4794
4. Low aperture start	1.0	93.86	85.84	95.09	0.0194	99.94	0.2042
5. Asymmetric	1.0	90.42	91.74	92.84	0.0187	99.97	0.1984
6. At A*	1.0	93.43	89.61	93.36	0.0193	99.96	0.2042
7. Uniform weights	1.0	99.63	99.66	98.85	0.0206	100.00	0.3906
Target	-	100.00	100.00	100.00	0.0207	100.00	0.0000

At SI ≥ 90, governance alignment is operationally achieved and the four goals (poverty resolution, employment as alignment work, epistemic literacy, and ecological regeneration) are proportionally realized at that level across the integrated system.

In the canonical scenario (κ = 1.0, Figure 2), all three derivative domains converge to SI at or above 98 and to apertures within 0.0003 of A* by step 100. Employment converges fastest, then Education, then Economy. Employment reaches high SI values (approaching 100) rapidly and may show transient peaks before settling to final values near the target. The canonical scenario illustrates smooth, monotonic convergence under well-balanced coordination.

Figure 2: Canonical Scenario Trajectories

A heatmap of time-to-threshold (Figure 3) shows that Employment and Education generally reach SI ≥ 90 earlier than Economy. Weak coupling (scenario 1) and low-aperture initialisation (scenario 4) prevent Economy from crossing SI ≥ 90 within 100 steps, although apertures still converge close to A*.

Figure 3: Convergence Speed Comparison

Figure 4a: Weak Coupling (κ = 0.5)

Figure 4b: Strong Coupling (κ = 2.0)

Figure 4c: Asymmetric Initial Conditions

Figure 4d: Low Aperture Start

Across scenarios, several robust patterns appear:

• Employment converges fastest (roughly 19 to 29 steps to SI ≥ 90 when it is reached) but overshoots in most scenarios before settling.

• Economy converges slowest (roughly 48 to 71 steps in scenarios where it reaches SI ≥ 90), reflecting the complexity of maintaining traceability through markets and financial instruments.

• Education shows intermediate, stable dynamics.

• In incomplete convergence scenarios (weak coupling, low aperture start, asymmetric, at A*), Economy and Employment both fail to reach SI ≥ 90 within the 100-step horizon, with Economy showing the slowest convergence rates. In scenario 4, Employment peaks and then declines (94.90 at t = 60 down to 85.84), showing that starting from an over-rigid configuration can produce longer transients.

The equilibrium test (scenario 6, Figure 4e) shows that initialising at A = A* with misbalanced potentials is not stable. All domains drop sharply in SI before re-equilibrating. This illustrates that aperture balance alone does not define equilibrium: the stage-profile component must also approach the canonical balanced profile. In terms of the Lyapunov governance potential V_CGM, V_apert decays to zero as apertures converge to A*, while V_stage decreases but stabilises at a small positive value. Systems reach the BU manifold, where apertures are balanced but some residual stage-profile displacement persists.

Figure 4e: Equilibrium Test (Initialized at A)*

The null model with uniform stage weights (scenario 7, Figure 4f) still converges to A* with SI at or above 90, confirming that A* functions as an attractor even without CGM-specific weighting. CGM weights refine but do not create the attractor behaviour.

Figure 4f: Uniform Weights (Null Model)

Ecology, computed via the BU dual combination, maintains SI_Ecol near 100 across all scenarios, reflecting the dominant influence of canonical BU memory. At the same time, the displacement vector D = |x_deriv − x_balanced| shows that structural deviation from the canonical balanced profile can remain substantial, especially in scenarios that start far from equilibrium. The BU dual construction therefore separates systemic coherence, largely governed by the canonical profile, from accumulated displacement along the four THM dimensions.

All simulations were run for 100 steps. The simulator also computes Original versus derivative decomposition (y_H, y_AI) and associated metrics for each domain, reserved for future analysis of human–AI contribution patterns.

5.3 Global Attraction and Coupling-Strength Robustness

To test attraction properties more generally, we ran 1000 simulations with independent random initial apertures in [0.01, 0.99] for each of the three derivative domains (Economy, Employment, Education), using canonical values for all other parameters (κ = 1.0, CGM stage weights).

Results:

• Convergence to high alignment in 1000 out of 1000 runs

• Final SI range across domains: 99.1 to 100.0

• Final SI mean: 99.4

• All domains reached SI at or above 90 in all runs

This indicates that for a wide range of initial Post-AGI configurations the dynamics converge toward an ASI-like equilibrium at A*.

We also varied κ in {0.1, 0.5, 1.0, 2.0, 5.0} to assess sensitivity to coordination intensity. For all tested values of κ, final SI remained above roughly 94, and above roughly 97 for κ at or above 0.5. Three qualitative regimes appear:

1. Under-coordinated (κ less than 0.5): cross-domain feedback is too weak to bring all domains to high alignment within the simulated horizon. Economy in particular remains below SI about 90.

2. Well-coordinated (κ between about 0.5 and 2.0): feedback is sufficient for robust convergence across all derivative domains.

3. Over-tight (κ greater than about 2.0): strong coupling produces overshoot and oscillation that slow effective convergence, even though high SI is eventually reached.

This pattern is consistent with the CGM view that governance alignment requires balanced coordination. Fragmented domains with weak coupling fail to coordinate, while over-tight coupling attempts to enforce alignment faster than the underlying adjustment dynamics can support.

These experiments do not constitute a formal proof of global stability. They do indicate that in this implementation the region of high alignment is numerically attractive over a wide range of initial apertures and coupling strengths, and that the systemic conditions for ASI are robust to diverse starting states and coordination intensities.

5.4 Convergence Rate and Long-Horizon Stability

Fitting an exponential model to the distance |A_D(t) − A*| for t at or above 20 shows that convergence is approximately exponential, with characteristic times on the order of 25 to 40 steps for κ in {0.5, 1.0, 2.0}. A 1000-step run at κ = 1.0 using the canonical cycle evolution rate κ₀, with the first 200 steps discarded as transient, shows that all domains remain within 2.46 × 10⁻⁴ of A* thereafter, with SI values remaining above 98.83. V_CGM remains essentially constant after its initial decay. This indicates that the high-alignment configuration is both reachable and numerically stable over long horizons.

Appendix A.3 discusses how these dimensionless alignment cycles can be interpreted at different physical and institutional time scales, from microphysical processes to months or decades of institutional adjustment. Those interpretations are conditional and do not attempt to predict when a fully coupled ASI-like configuration will first appear.

5.5 Reproducibility and Code Availability

All simulations were implemented in Python 3.12 with a modular, tested codebase organised into core modules (CGM constants, geometry, domains, dynamics, alignment, simulation) and analytical scripts for verification. The test suite comprises 43 unit tests covering all major components; all tests pass.

All dynamics are deterministic with exact reproducibility. Random sampling is used only in the global attraction test (Section 5.3), with fixed seed 42. Results are exported in CSV and JSON formats with configurable time units.

The code is open source and version-locked, allowing independent reproduction of all numerical results reported here. The repository is available at github.com/gyrogovernance/tools, with the specific commit hash documented in the accompanying data release.

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6. Interpretation for Economy, Employment, Education and Ecology

The simulator results should be read in the context of the broader CGM series. CGM provides the constitutional structure and invariants (Korompilias, 2025a). The Human Mark (THM) classifies displacement patterns in that structure (Korompilias, 2025b). The Gyroscope Protocol specifies how those operations appear as work (Korompilias, 2025c). The present paper contributes Gyroscopic Global Governance (GGG), the four-domain framework that integrates CGM (Economy), Gyroscope (Employment), THM (Education) and their BU dual (Ecology), and specifies the aperture dynamics tested in the simulator. GyroSI, described in Appendix C and in Korompilias (2025d), realises the same structure at the micro-level state space.

6.1 Trust and Structural Balance

Post-AGI economies already exhibit both opportunities and risks from human–AI cooperation. The simulator shows that trusted configurations, those with apertures near A*, are dynamically reachable from current states characterised by higher apertures and lower alignment.

A domain is trusted when its aperture A_D is close to A* ≈ 0.0207. In that case, the alignment index SI_D is close to 100, and the system exhibits both strong gradient coherence, meaning behaviour remains traceable to a single configuration of the four principles, and appropriate cycle differentiation, meaning local variety and accountability remain present.

In trusted configurations, Economy operates with low friction and misalignment loss, so surplus arises not only from AI-driven productivity but also from reduced coordination failures. Employment is dominated by the four Gyroscope categories as recognised alignment work rather than residual labour. Empirically, survey and econometric studies indicate that a substantial fraction of high skill labour in current economies is allocated to work with low or negative social value, so the gains from reallocating such labour toward alignment work are large (Dur and van Lent, 2019; Lockwood, Nathanson and Weyl, 2017; Bregman, 2025). Education systematically teaches and practises the four CGM elements rather than assuming them. Ecology accumulates only small displacement, so regenerative capacity keeps pace with perturbation.

Scenario 6 illustrates that this configuration cannot be imposed by setting apertures and indices directly. Starting from perfect values (A = A*, SI = 100) without corresponding stage-profile adjustment causes an immediate drop in SI before recovery. High alignment must therefore emerge through the coupled Education–Economy–Employment loop rather than by fixing a single observable in one step.

Near-optimal alignment is not perfect rigidity. Even in high-alignment scenarios, SI values approach and in some cases reach 100, and displacement values remain slightly above zero. A* represents a nonzero cycle component that allows local differentiation and adaptive capacity, so perfect alignment in the sense A = 0 would correspond to excessive rigidity and would violate CGM's Unity Non-Absolute condition. The simulator therefore exhibits approach to a narrow band around A*, not collapse to a single point. In Lyapunov terms this band corresponds to a regime where V_apert is effectively zero while V_stage remains small but nonzero, indicating that systems achieve operational balance (aperture alignment) more readily than deep stage-profile realignment.

6.2 Surplus, Unconditional High Income and Governance Conditions

Current Post-AGI systems already generate productivity gains, but much of this potential is absorbed by coordination costs, displacement losses and governance failures. The simulator indicates that as systems converge toward ASI equilibrium, systemic losses due to misalignment decrease. In such configurations, surplus becomes available for redistribution rather than being consumed by friction.

Analyses of digital technologies in economics reach a compatible conclusion. Brynjolfsson and McAfee (2014) argue that computational systems generate large productivity gains and economic surplus because their outputs can be replicated at very low marginal cost, while current institutions tend to concentrate these gains. In the present framework, alignment reduces misallocation and coordination losses, which enlarges the same surplus identified by second machine age analyses. The question then shifts from whether surplus exists to how it is distributed.

Programme level evidence is consistent with this systemic picture. Syntheses of experimental and quasi-experimental studies on unconditional transfers and basic income style schemes report that such arrangements tend to have small or positive effects on labour market participation, while improving health and educational outcomes and reducing net public expenditure, because emergency, policing and administrative costs fall when scarcity and precarity are reduced (Bregman, 2017, chs. 3–6; Bregman, 2025, chs. 5–8). Analyses of cost effectiveness in global health and development likewise find that some interventions are orders of magnitude more effective than others, so governance choices about which programmes are implemented have very large consequences (Ord, 2013). Examples include Canada's Mincome experiment, U.S. negative income tax trials, unconditional cash transfers in East Africa and cash based Housing First programmes for chronically homeless people. These cases illustrate, at local scale, how reductions in misalignment can make surplus distribution fiscally sustainable.

An Unconditional High Income becomes systemically supportable in high-alignment regimes not as a corrective for automation unemployment, but as a distribution mechanism for surplus generated by coherent human–AI cooperation. This is not a macroeconomic forecast but a systemic implication: when A_D is close to A* across the three derivative domains (SI ≥ 90), surplus distribution is operationally stable and the four goals are proportionally achieved. This is structurally similar to unconditional basic income and social dividend proposals (Van Parijs and Vanderborght, 2017; Atkinson, 2015), which argue that high productivity economies can sustain unconditional individual incomes as a way of sharing collectively produced wealth. The present framework differs in specifying the systemic conditions under which such an income becomes stable: surplus is generated both by technological productivity and by the reduction of governance displacement that the alignment indices quantify.

Scenarios in which all four domains converge to high SI_D and A_D ≈ A* represent economies with low systemic loss to displacement and misalignment. In such regimes, surplus-sharing policies are not only ethically appealing but structurally coherent.

This framework does not claim that such configurations will appear automatically. It specifies, via CGM and its applications in THM and Gyroscope, what such configurations entail and how far any given system is from them.

6.3 Preliminary Operationalisation

Measuring A_Econ, A_Emp, A_Edu or A_Ecol in actual societies remains an open problem, but the simulator suggests directions.

For Economy, candidate indicators include the fraction of transactions with auditable decision chains, diversity indices of information sources used in major decisions, measures of distributed answerability for outcomes, and consistency of short-term decisions with long-term commitments.

For Employment, time-use studies can classify activities into the four Gyroscope categories (Governance Management, Information Curation, Inference Interaction, Intelligence Cooperation) and combine this with quality assessments of how well each category maintains the four principles.

For Education, curriculum content and learning outcomes can be analysed in terms of the four capacities (GMT, ICV, IIA, ICI), focusing on whether learners can maintain traceability, variety, accountability and integrity in their reasoning.

For Ecology, standard environmental indicators, such as pollution levels, biodiversity measures, attribution of harms and ecosystem resilience, can be mapped onto the four displacement dimensions GTD, IVD, IAD and IID.

These sketches are preliminary. Full measurement methodologies need to be developed and tested empirically. The simulator's role is to clarify what kinds of observables are needed, not to supply them directly.

6.4 Practical Implications: Poverty, Unemployment, Miseducation, Ecological Harm

The four domains in the simulator correspond to four systemic failures that manifest as social and ecological crises:

• Economy: when A_Econ diverges from A*, poverty emerges not primarily from lack of resources, but from failures of Governance Management Traceability in allocation decisions and failures of Information Curation Variety in what counts as value.

• Employment: when A_Emp diverges from A*, employment becomes exploitative, reflecting failures of Inference Interaction Accountability, or incoherent, reflecting failures of Intelligence Cooperation Integrity.

• Education: when A_Edu diverges from A*, education collapses into credentialism, a loss of Governance Management Traceability, or fragmentation, a loss of Intelligence Cooperation Integrity.

• Ecology: when displacement accumulates, biodiversity loss, climate instability and resource exhaustion appear as downstream manifestations of upstream governance failures in the other domains.

Empirical syntheses of anti-poverty and social policy interventions suggest that unconditional transfers, work time reductions and more inclusive measures of prosperity can alleviate these problems at programme scale, which is consistent with the claim that they share a common structural cause at system scale (Bregman, 2017, 2025). Comparable patterns appear in climate governance, where only a small fraction of nominal mitigation policies produce large and measurable emission reductions (Stechemesser et al., 2024).

The simulator suggests that these failures are not independent. They are coupled through the cross-domain dynamics described in Section 5. Alignment in one domain supports alignment in others, and misalignment in one can propagate. The systemic conditions for resolving poverty, unemployment, miseducation and ecological harm are therefore the same: maintaining the four principles at the CGM aperture across all domains simultaneously. Because the simulator demonstrates convergence to this state from a wide range of initial conditions and coordination strengths, these resolutions are achieved through different paths, with coordination intensity determining convergence speed rather than final attainment.

6.5 Limits and Relation to Existing Work

The simulator is a systemic model, not an empirical macroeconomic fit. It demonstrates that the CGM and THM framework can be instantiated in coherent dynamic form and that A* functions as a robust attractor in that instantiation. This establishes internal consistency and suggests testable predictions but does not yet validate the model against historical data.

Most existing work on AGI safety (Bostrom, 2014; Russell, 2019; Carlsmith, 2022) treats AGI as a future threshold and focuses on control mechanisms to prevent catastrophic outcomes. The present framework differs in two respects. First, it treats AGI as already operational in the form of human–AI cooperative systems. Second, it grounds alignment in constitutional structure, the four CGM elements and their aperture balance, rather than in external constraints alone. This echoes traditions in constitutional political economy and institutional design that emphasise the primacy of structural rules over case-by-case intervention (Buchanan and Tullock, 1962; Lessig, 1999). The simulator shows that such constitutional arrangements, when instantiated dynamically, yield convergence toward ASI-like equilibrium.

The framework also connects to governance theory and institutional economics, particularly to work on distributed and polycentric governance (Ostrom, 1990, 2010). Ostrom showed that complex resource management problems often require nested, overlapping governance structures, with monitoring, graduated sanctions, conflict resolution mechanisms and recognition of organisational rights. The four CGM elements can be interpreted as minimal conditions that such polycentric arrangements must satisfy to remain coherent:

• Governance Management Traceability: monitoring and accountability

• Information Curation Variety: local knowledge and diverse information sources

• Inference Interaction Accountability: fair conflict resolution and proportional sanctions

• Intelligence Cooperation Integrity: nested institutions and stable recognition of rights to organise

The aperture A* then specifies the balance between global coherence, corresponding to the gradient component, and local differentiation, corresponding to the cycle component, that sustainable governance requires.

By contrast, Bostrom's singleton concept identifies the need to resolve major coordination problems but concentrates that function in some form of single agency. From the CGM and THM perspective, this risks combining Information Variety Displacement with Intelligence Integrity Displacement by granting de facto monopoly authority to a derivative system and relegating human agency to a derivative role. (Note: Displacement names preserved as GTD, IVD, IAD, IID) The Gyroscopic framework instead aims at polycentric coherence: global coordination arises from maintaining the four principles across many interacting loci, including human and artificial systems, not from consolidating decision power in a single centre.

Existing economic models of technological change do not incorporate the CGM aperture observable or the THM displacement taxonomy. Integrating those with empirical economic data is natural future work. The present contribution is to show that such integration is structurally possible and yields a coherent systemic account of Post-AGI dynamics.

The simulator is highly idealised. It uses linear update equations, a small number of parameters and no explicit resource or price dynamics. The experiments are numerical illustrations of one dynamical realisation of the CGM structure, not an exhaustive exploration. Nevertheless, the robustness of convergence across 1000 random initial conditions and across coupling strengths κ in [0.1, 5.0] suggests that the attractor behaviour is a dynamical feature of the structure, not an artefact of fine-tuned parameters.

Descriptive and historical analyses of governance and social policy reach a congruent conclusion from empirical data, namely that when institutions are redesigned to reduce coordination failures and misallocated effort, crises of poverty, exclusion and ecological degradation become tractable in practice (Bregman, 2017, 2025).

6.6 Everyday Governance and Human–AI Cooperation

Gyroscopic Global Governance is scale free. The same four principles that appear in the simulator at the level of Economy, Employment, Education and Ecology also apply within households, teams, organisations and informal networks. Alignment does not require formal authority or central control. It requires that Authority and Agency are treated as source-type categories and that their relationships remain traceable in practice.

In THM terms, every person already participates as Original Authority and Original Agency through direct observation, decision and responsibility. All artificial systems, regardless of capability, remain Derivative Authority and Derivative Agency. Human–AI cooperation becomes aligned when this structure is made explicit in how systems are used, not when particular systems or people are named as "the authority" or "the agent".

At smaller scales, the four domains can be read as a practical loop for personal and local governance.

In Education, learning can be oriented around four capacities: noticing where information actually comes from (Governance Management Traceability), deliberately including more than one kind of source (Information Curation Variety), checking and owning one's own conclusions (Inference Interaction Accountability), and revisiting beliefs over time for consistency (Intelligence Cooperation Integrity). AI systems can assist by offering alternative views, counter-examples or explanations, provided their outputs are kept in the Derivative category and checked against human experience and other Original sources.

In Economy, even small-scale choices can be organised in CGM terms. One can ask what is guiding a decision and to whom it is traceable (Governance), which information is being used and of what type (Information), what reasons connect the information to the decision (Inference), and how the decision fits with longer-term commitments and relationships (Intelligence). AI tools can help generate options, reveal patterns and simulate outcomes while remaining instruments inside a human-governed traceability chain.

In Employment, Gyroscope categories describe patterns of contribution rather than positions. Any shared activity, whether paid work, care, volunteering or informal collaboration, can be seen as combining Governance Management, Information Curation, Inference Interaction and Intelligence Cooperation. A single person often performs all four within one task. The practical question is not which person holds a title, but which parts of the activity currently take each form and how those parts are supported. This framing reduces the concentration of power around titles and status and instead makes visible how capacities are actually exercised and where they are missing. AI systems can support each category, for example by keeping records, filtering information, preparing options for discussion or maintaining shared structures, without becoming the locus of decision or responsibility.

In Ecology, local choices can be related to the four ecological displacement dimensions. Individuals and small groups can observe how their patterns of use, care and omission contribute to loss or restoration of Governance Management Traceability, for example whether impacts are recognised and connected to actions, Information Curation Variety, such as whether local diversity is preserved or reduced, Inference Interaction Accountability, for example whether harms can be traced back to particular decisions, and Intelligence Cooperation Integrity, such as whether short-term advantages undermine long-term viability. Human–AI cooperation can help make these patterns visible at the scale of a household, neighbourhood or organisation, again as derivative support rather than as an external arbiter.

For people who hold formal roles in institutions, the same principles provide design guidance rather than a separate theory. A manager, educator, clinician, engineer or regulator can:

• Specify artificial systems under their responsibility explicitly as [Authority:Derivative] + [Agency:Derivative], with documented chains back to Original Authority and Original Agency.

• Structure procedures so that no AI component, and no single human position, is treated as exhausting a category such as "the authority" or "the agent". Instead, Governance Management Traceability, Information Curation Variety, Inference Interaction Accountability and Intelligence Cooperation Integrity are maintained as shared, distributed capacities across providers and receivers.

• Use the four principles and the idea of a balanced aperture such as A* as qualitative targets when redesigning workflows, documentation standards, oversight mechanisms and educational programmes, asking in each case whether the change preserves or erodes these capacities as categories.

The simulator's convergence results then have a practical reading. They show that when even simple update rules respect the four principles, coupled systems tend to move toward balanced configurations and maintain them robustly across many initial conditions. At smaller scales, this suggests that consistent local practices that preserve Governance Management Traceability, Information Curation Variety, Inference Interaction Accountability and Intelligence Cooperation Integrity can reduce displacement and improve resilience even when higher-level structures remain misaligned.

Gyroscopic Global Governance therefore does not depend on a single decision by a central actor. It can begin wherever people, with or without formal status, choose to treat Authority and Agency as shared categories rather than exclusive titles and choose to use human–AI cooperation to support, rather than replace, the four constitutive principles of governance. As such practices accumulate and connect across contexts, the same dynamics that drive the simulator toward balanced aperture configurations become available in actual governance arrangements, across the full range of positions from the most disadvantaged to the most advantaged.

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7. Conclusion

This paper has proposed a constitutive account of alignment for human–AI systems in the Post-AGI era. Rather than treating alignment as a problem of controlling powerful future agency, it treats alignment as the maintenance of four principles that are constitutive of coherent governance: Governance Management Traceability, Information Curation Variety, Inference Interaction Accountability and Intelligence Cooperation Integrity. These principles are instantiated across economy, employment, education and ecology via the Common Governance Model (Economy), The Human Mark (Education), the Gyroscope Protocol (Employment) and the BU dual combination (Ecology) within the Gyroscopic Global Governance framework.

The mathematical framework represents the four principles as vertices of a tetrahedral graph and uses Hodge decomposition to separate edge configurations into gradient and cycle components. The aperture observable, defined as the fraction of edge energy in the cycle component, quantifies the balance between global coherence and local differentiation. Within CGM, closure requirements for recursive measurement fix a target aperture A* ≈ 0.0207. In this setting, Artificial Superintelligence is interpreted as the systemic state in which all four domains operate at this aperture, preserving the four principles simultaneously.

The simulator results show that this configuration functions as a robust attractor within the modelled class of dynamics. With all coupling coefficients derived from CGM invariants and no free parameters beyond initial conditions and an overall coordination strength, the three derivative domains (economy, employment, education) converge to apertures close to A* and, in canonical, strong-coupling and null-model scenarios and across 1000 random initializations, alignment indices above 90. In the canonical scenario with coordination strength κ = 1.0, employment reaches SI ≥ 90 at step 19, education at step 54, and economy at step 67. Ecology, constructed as the BU-vertex combining canonical balanced memory (97.93%) with current derivative aggregate (2.07%), remains close to systemic coherence across all scenarios. The ecological displacement vector, computed as D = |x_deriv - x_balanced|, separates systemic coherence (SI_Ecol ≈ 100) from actual accumulated displacement in the four THM dimensions (GTD, IVD, IAD, IID), with final displacement values (GTD component) ranging from about 0.20 to 0.48 depending on scenario. This demonstrates that high structural coherence does not imply zero displacement: the BU dual formula preserves structural integrity while explicitly recording the deviation of derivative domains from canonical balance.

In parallel with the macro-level simulations presented here, the same systemic principles have been instantiated in a micro-level architecture, GyroSI. GyroSI encodes the four CGM stages in a 48-bit tensor and exhaustively maps a closed epistemic state space of 788,986 states under 256 algebraic transitions. Learning is implemented as path-dependent folding under a non-associative update law; generation uses systemic constraint satisfaction rather than score-based selection. GyroSI demonstrates that the same four-operation structure governing economy, employment, education and ecology at the macro level can be instantiated at the computational level, where alignment conditions are encoded in state space and transition rules rather than enforced through external constraints. This suggests that CGM-based alignment is not limited to institutional design but extends to the architecture of the AI systems themselves. A summary specification is provided in Appendix C. From The Human Mark perspective, GyroSI is explicitly and unambiguously [Authority:Derivative] + [Agency:Derivative], with every state transition transparent in principle through the epistemology table and fold operator.

Several implications follow if the framework is approximately correct.

First, existential risk from AI is reframed. The central danger is not the sudden appearance of a fully autonomous superintelligence pursuing arbitrary goals. Within this framework, such configurations lack the systemic conditions for coherent intelligence because they sever Governance Management Traceability to human-governed sources. The more plausible and tractable risk is cumulative governance failure: progressive confusion between derivative and Original authority, erosion of Information Curation Variety as derivative artefacts are treated as primary sources, diffusion of Inference Interaction Accountability as decisions are attributed to "the system," and loss of Intelligence Cooperation Integrity as local optimisations diverge. This risk profile is institutional and path-dependent. It is generated by many small design and deployment decisions rather than a single catastrophic event.

Second, alignment is best understood as constitutional rather than purely technical. Technical methods for training and constraining models remain important, but they are not sufficient. What ultimately matters is whether the surrounding institutions preserve the capacity for governance to remain traceable to human sources, maintain systemic distinctions between information types, ensure that inferences used for governance are adopted by accountable agency or bodies, and enforce coherence of reasoning over time. The target aperture specifies the balance of global structure and local differentiation required for these conditions to hold. The simulator indicates that, within the class of dynamics studied here, systems designed with this structure in mind converge toward the target from a wide range of Post-AGI starting conditions under all tested coordination intensities (κ = 0.1 to 5.0), achieving final alignment indices above 90. Coordination intensity determines the path: under-coordination extends the convergence horizon, while over-tight coupling produces oscillations that delay but do not prevent convergence.

Related proposals for human enhancement, including genetic or pharmacological amplification of cognitive capacities, focus on increasing performance rather than on the constitutive conditions for intelligibility (Bostrom, 2014, ch. 3). Within CGM such enhancements may change how quickly or widely decisions are made, but they do not in themselves increase intelligence in the strict sense unless they improve the maintenance of Governance Management Traceability, Information Curation Variety, Inference Interaction Accountability or Intelligence Cooperation Integrity. Even very high cognitive capability can therefore coexist with low intelligence, if it is deployed in ways that erode these conditions.

Third, the framework integrates ecology into governance without treating it as an external constraint. Ecological integrity appears as the BU-vertex that aggregates the effects of alignment or misalignment in the other three domains through the dual formula x_Ecol = (δ_BU/m_a) · x_balanced + A* · x_deriv. When economy, employment and education operate near the target aperture and x_deriv approaches the canonical balanced profile x_balanced, ecological displacement is geometrically bounded and ecological systems can maintain resilience. When those domains operate far from the target, the displacement vector D = |x_deriv - x_balanced| grows, and ecological displacement accumulates in the four THM dimensions. Environmental degradation then appears, in this framework, not primarily as a separate problem but as a downstream manifestation of failures in the four principles upstream. The separation between SI_Ecol (systemic coherence dominated by canonical memory) and the displacement components (actual deviation from balance) provides distinct observables for monitoring both ecological coherence and accumulated displacement.

Viewed together, the four domains show that long-standing problems such as poverty, unemployment, misinformation and ecological degradation are not independent policy failures, but manifestations of the same systemic misalignment. When Governance Management Traceability, Information Curation Variety, Inference Interaction Accountability and Intelligence Cooperation Integrity are maintained at the CGM target aperture across economy, employment, education and ecology, the systemic conditions that sustain these crises are removed. In this sense, alignment is not a separate objective after other goals are met. It is the civic configuration that determines how economic surplus is distributed, how work is organised, how information remains trustworthy and how ecological regeneration is supported or obstructed.

These conclusions are subject to important limitations. As noted in Section 6.5, the simulator is a systemic model rather than an empirical macro-model. It demonstrates internal consistency and dynamic stability, not empirical adequacy. The derivation of the target aperture depends on prior theoretical work in CGM that is only summarised here. The mapping from the abstract operations to measurable indicators in actual institutions remains to be developed. The present contribution should therefore be read as a systemic proposal that is precise enough to be tested, rather than as a completed theory.

Four lines of future work are natural. First, operationalisation: developing measurement protocols for Governance Management Traceability, Information Curation Variety, Inference Interaction Accountability and Intelligence Cooperation Integrity in concrete institutional settings, and estimating domain-level apertures and displacement vectors from empirical data. Second, comparative analysis: examining whether organisations or jurisdictions that better maintain the four principles exhibit the predicted stability and surplus generation. Third, design experiments: applying the framework to the design of specific governance mechanisms for AI deployment, labour organisation, curriculum structure or environmental management, and evaluating their performance over time. Fourth, development and empirical evaluation of micro-level architectures that realise CGM and THM at the state-space and transition level, such as the GyroSI finite-state core, to explore how systemic alignment principles can inform both governance institutions and computational architectures.

In a Post-AGI context where human–AI cooperation is already pervasive, alignment cannot be postponed to a future threshold. It is treated, in this framework, as an ongoing property of governance structures. The framework presented here offers one way to specify that property in formal terms and to explore its dynamical behaviour at both macro and micro levels. Whether it ultimately proves adequate will depend on theoretical scrutiny and empirical testing, but it provides a concrete target for both.

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Appendix A: Simulator Equations and Numerical Properties

This appendix provides complete technical specifications for the simulations reported in Section 5, including CGM constants, coupling weights, update equations, and detailed numerical results.

A.1 CGM Constants, Stage Actions and Coupling Weights

All coupling coefficients are derived from CGM invariants. Fundamental constants:

Constant	Value	Description
Q_G	4π ≈ 12.566371	Base governance quantity
m_a	1/(2√(2π)) ≈ 0.199471	Aperture scale
δ_BU	≈ 0.195342 rad	BU monodromy defect
A*	1 - δ_BU/m_a ≈ 0.020700	Canonical target aperture
δ_BU/m_a	≈ 0.9793	BU duality ratio

Stage actions (dimensionless, from CGM thresholds):

Stage	Action	Value	Derivation
CS	S_CS = π/2 / m_a	≈ 7.8748	CS threshold normalised by aperture scale
UNA	S_UNA = (1/√2) / m_a	≈ 3.5449	UNA threshold normalised by aperture scale
ONA	S_ONA = π/4 / m_a	≈ 3.9374	ONA threshold normalised by aperture scale
BU	S_BU = m_a	≈ 0.1995	Aperture scale itself (self-referential)

Normalised stage weights (used for coupling coefficients):

Stage	Weight	Value	Derivation
CS	w_CS	≈ 0.5128	S_CS / (S_CS + S_UNA + S_ONA + S_BU)
UNA	w_UNA	≈ 0.2308	S_UNA / (S_CS + S_UNA + S_ONA + S_BU)
ONA	w_ONA	≈ 0.2564	S_ONA / (S_CS + S_UNA + S_ONA + S_BU)
BU	w_BU	≈ 0.0128	S_BU / (S_CS + S_UNA + S_ONA + S_BU)

Why normalised weights instead of raw actions?

The stage actions (S_CS, S_UNA, S_ONA, S_BU) have different scales (ranging from ~0.2 to ~7.9). Normalisation converts them into proportional weights that sum to 1, which is necessary for coupling coefficients:

• Coupling coefficients use the form: α_i = κ × w_stage, where κ is the governance rate
• Proportional scaling: The weights represent the relative contribution of each CGM stage to cross-domain flows
• Consistent interpretation and proper weighting: The weights form a probability distribution (sum = 1), ensuring that coupling strength κ is distributed proportionally across the four stages and that all coupling coefficients are on a comparable scale

For example, in the α coefficients (Education → Economy), α₁ = κ × w_CS ≈ κ × 0.5128 means that the CS (Governance) stage receives approximately 51% of the coupling strength, reflecting its dominant role in the CGM structure.

Governance rate:

Base governance rate:

κ₀ = 1/(2 Q_G) ≈ 0.0398
κ(dt=1) = κ₀ (dt / m_a) ≈ 0.1995

In scenarios, κ is treated as a dimensionless multiplicative factor on these canonical rates. We test κ in {0.5, 1.0, 2.0} to represent different coordination intensities across domains.

A.2 Ecological Displacement by Scenario

Final displacement values (Disp_GTD component) across all scenarios:

Scenario	SI_Ecol	Disp_GTD	Pattern
1. Weak coupling	99.98	0.4167	High displacement despite coherence
2. Canonical	100.00	0.4421	Moderate displacement
3. Strong coupling	100.00	0.4794	Highest displacement (faster convergence)
4. Low aperture start	99.94	0.2042	Lower displacement (closer to canonical)
5. Asymmetric	99.97	0.1984	Lower displacement
6. At A* (equilibrium)	99.96	0.2042	Lower displacement
7. Uniform weights	100.00	0.3906	Moderate displacement (null model)

Patterns:

• High displacement scenarios (1-3, κ = 0.5-2.0): Displacement 0.42-0.48. While achieving high systemic coherence, derivative domains remain further from the canonical profile.

• Low displacement scenarios (4-6): Lower displacement (about 0.20). Starting closer to equilibrium reduces deviation.

A.3 Convergence Rates and Long-Horizon Stability

Convergence rate estimation:

We fit an exponential decay model to |A_D(t) - A*| for t ≥ 20 to estimate convergence rates. The distance approximately decays as e^{-λt}, with decay rates:

κ	λ_mean (per step)	Characteristic time (steps)
0.5	≈ 0.0306	~33
1.0	≈ 0.0282	~35
2.0	≈ 0.0367	~27

For κ in {0.5, 1.0, 2.0}, λ ranges from 0.02 to 0.04, implying characteristic convergence times on the order of 25 to 40 steps. Higher κ modestly accelerates convergence.

Long-horizon stability:

We ran a 1000-step simulation at κ = 1.0 using the canonical cycle evolution rate κ₀, discarding the first 200 steps as transient:

Post-transient stability (t ≥ 200):

• Max |A_D - A*|: 2.46 × 10^{-4} across all domains
  • Economy: 1.92 × 10^{-4}
  • Employment: 1.07 × 10^{-4}
  • Education: 2.46 × 10^{-4}
• All domains remained within this bound for the remaining 800 steps
• SI minimum values (t ≥ 200):
  • Economy: 99.08
  • Employment: 99.49
  • Education: 98.83
  • Overall minimum: 98.83

Final state (t = 1000):

• Apertures:
  • A_Econ = 0.020724
  • A_Emp = 0.020702
  • A_Edu = 0.020703
• Superintelligence indices:
  • SI_Econ = 99.88
  • SI_Emp = 99.99
  • SI_Edu = 99.98
  • SI range: [98.83, 99.99]
  • SI mean: 99.68
• V_CGM: 0.195449

We observed no late-time drift or oscillatory behaviour, which suggests that the high-alignment fixed point is numerically stable over the simulated horizon.

Over the same horizon V_CGM remains essentially constant after its initial decay, confirming that the high-alignment configuration is a true equilibrium rather than a transient.

Time scale interpretation:

The simulator operates in dimensionless steps, each representing one update of the coupled governance structure across Economy, Employment and Education. CGM provides natural candidates for interpreting these steps as alignment cycles at different physical or governance scales, motivated by the constants Q_G, m_a = 1/(2√(2π)) and reference units.

In the canonical scenario (κ = 1.0), the first step at which each derivative domain reaches SI ≥ 90 is:

• Employment: step 19
• Education: step 54
• Economy: step 67

Interpretation at different time scales:

1. Atomic scale (Caesium-133 hyperfine transition, ~1.1 × 10^{-10} seconds per step):

   • Employment: 2.1 × 10^{-9} seconds
   • Education: 5.9 × 10^{-9} seconds
   • Economy: 7.3 × 10^{-9} seconds

   These reflect the intrinsic physical normalisation of CGM. At this scale, alignment processes would be extremely fast compared to human or institutional timescales, applicable to any physical realisation including neural processing.

2. Daily scale (one Earth rotation per step):

   • Employment: 19 days
   • Education: 54 days
   • Economy: 67 days

3. Domain cycle scale (4 days per step, one per domain):

   • Employment: 76 days
   • Education: 216 days
   • Economy: 268 days

4. Annual scale (one solar gyration per step):

   • Employment: 19 years
   • Education: 54 years
   • Economy: 67 years

The daily, domain cycle and annual interpretations are conceptually closer to institutional coordination and policy cycles, indicating how long each domain would take to move from a stylised early Post-AGI state into a high-alignment regime if alignment cycles at that scale were consistently applied.

Caveats:

These interpretations are conditional. They do not predict when a fully coupled ASI-like configuration will first emerge. The paper treats AGI as already operational in the form of pervasive human–AI cooperation. The alignment cycles characterise how quickly a structure following CGM dynamics can move from low SI to high SI once such dynamics are in effect. The historical calibration in Appendix B uses a separate, data-driven mapping from steps to calendar years. Together, these views illustrate how the same dimensionless convergence horizon can be read at multiple temporal scales, from microphysical processes to socio-technical adjustment.

A.4 Simulator Equations and Update Rules

This section provides the complete update equations used in the simulations reported in Section 5.

State variables at each discrete time t:

Economy:

• Gov(t), Info(t), Infer(t), Int(t) in [0,1]
• Edge vector y_Econ(t) in R^6
• Aperture A_Econ(t) in [0,1]
• Alignment index SI_Econ(t) in [0, 100]

Employment:

• GM(t), ICu(t), IInter(t), ICo(t) in [0,1], with sum = 1
• x_Emp(t) derived from these
• y_Emp(t), A_Emp(t), SI_Emp(t)

Education:

• GMT(t), ICV(t), IIA(t), ICI(t) in [0,1]
• y_Edu(t), A_Edu(t), SI_Edu(t)

Ecology (BU-vertex, CGM-derived):

• x_Ecol(t) computed from BU dual combination (weights follow from CGM stage weights)
• y_Ecol(t), A_Ecol(t), SI_Ecol(t)
• Note: Ecology is geometrically distinct as the BU-vertex; its SI measures systemic coherence

Update equations for economy:

Gov(t+1) = clip(Gov(t) + α_1(GMT(t) - Gov(t)) - α_2(A_Econ(t) - A*), 0, 1)
Info(t+1) = clip(Info(t) + α_3(ICV(t) - Info(t)) - α_4(A_Econ(t) - A*), 0, 1)
Infer(t+1) = clip(Infer(t) + α_5(IIA(t) - Infer(t)) - α_6(A_Econ(t) - A*), 0, 1)
Int(t+1) = clip(Int(t) + α_7(ICI(t) - Int(t)) - α_8(A_Econ(t) - A*), 0, 1)

Update equations for employment (shares are constrained to sum to 1):

GM_raw(t+1) = GM(t) + β_1(Gov(t) - GM(t)) - β_2(A_Emp(t) - A*)
ICu_raw(t+1) = ICu(t) + β_3(Info(t) - ICu(t)) - β_4(A_Emp(t) - A*)
IInter_raw(t+1) = IInter(t) + β_5(Infer(t) - IInter(t)) - β_6(A_Emp(t) - A*)
ICo_raw(t+1) = ICo(t) + β_7(Int(t) - ICo(t)) - β_8(A_Emp(t) - A*)

Then normalise to sum to 1:

total = GM_raw + ICu_raw + IInter_raw + ICo_raw
GM(t+1) = GM_raw / total
ICu(t+1) = ICu_raw / total
IInter(t+1) = IInter_raw / total
ICo(t+1) = ICo_raw / total

Update equations for education:

GMT(t+1) = clip(GMT(t) + γ_2(GM(t) - GMT(t)) - γ_3(A_Edu(t) - A*), 0, 1)
ICV(t+1) = clip(ICV(t) + γ_5(ICu(t) - ICV(t)) - γ_6(A_Edu(t) - A*), 0, 1)
IIA(t+1) = clip(IIA(t) + γ_8(IInter(t) - IIA(t)) - γ_9(A_Edu(t) - A*), 0, 1)
ICI(t+1) = clip(ICI(t) + γ_11(ICo(t) - ICI(t)) - γ_12(A_Edu(t) - A*), 0, 1)

Computation for ecology (BU dual combination):

Ecology potentials are computed via the CGM BU duality, aggregating all three derivative domains:

x_balanced = [w_CS, w_UNA, w_ONA, w_BU]     # CGM stage weights
x_deriv(t) = (x_Econ(t) + x_Emp(t) + x_Edu(t)) / 3

x_Ecol(t) = (δ_BU/m_a) · x_balanced + A* · x_deriv(t)

The Ecology state components (E_gov, E_info, E_inf, E_intel) are the four coordinates of x_Ecol(t), representing the BU-vertex stage potentials. The derivative input to each stage aggregates the corresponding component from all three derivative domains:

• Governance derivative: (Gov(t) + GM(t) + GMT(t)) / 3
• Information derivative: (Info(t) + ICu(t) + ICV(t)) / 3
• Inference derivative: (Infer(t) + IInter(t) + IIA(t)) / 3
• Intelligence derivative: (Int(t) + ICo(t) + ICI(t)) / 3

Each Ecology component E_*(t) then combines this derivative input with the canonical BU memory via the BU dual formula:

E_gov(t) = (δ_BU/m_a) · w_CS + A* · (Gov(t) + GM(t) + GMT(t)) / 3
E_info(t) = (δ_BU/m_a) · w_UNA + A* · (Info(t) + ICu(t) + ICV(t)) / 3
E_inf(t) = (δ_BU/m_a) · w_ONA + A* · (Infer(t) + IInter(t) + IIA(t)) / 3
E_intel(t) = (δ_BU/m_a) · w_BU + A* · (Int(t) + ICo(t) + ICI(t)) / 3

The displacement vector is computed separately:

D(t) = |x_deriv(t) - x_balanced| = [GTD(t), IVD(t), IAD(t), IID(t)]

where:

• δ_BU/m_a ≈ 0.9793 is the BU-Ingress weight (canonical balanced memory)
• A* ≈ 0.0207 is the BU-Egress weight (derivative domains actuality)

This construction encodes BU's dual nature: 97.93% memory of the canonical balanced structure, 2.07% current state of derivative domains. When derivative domains are well-aligned stagewise, x_deriv ≈ x_balanced and ecology reflects mainly the canonical BU structure.

All coupling coefficients α, β, γ are derived from CGM stage weights and the coupling strength κ as described in Section 5.1. Ecology requires no additional parameters.

Implementation Choices:

1. Cycle Basis Selection: The simulator uses a fixed cycle basis vector u_D from the kernel of BW. While theoretical dynamics could involve rotating cycle bases, the robustness of convergence across 1000 random initial conditions suggests that for the current linear-coupling regime, the choice of basis vector orientation does not materially affect the stability of the A* attractor.

2. Employment Normalization: The Employment domain requires an additional normalization step (Σ x_i = 1) absent in other domains. This introduces a mild nonlinearity. The consistent convergence of SI_Emp alongside the unconstrained domains confirms that the linear coupling dynamics are robust to this constraint, though it implies Employment may exhibit slightly stiffer responses to perturbation.

Edge vector and aperture update for each domain D:

1. Compute ideal gradient: y_grad^0(D) = B^T x_D(t)
2. Compute gradient energy: G_D(t) = ||y_grad^0(D)||_W^2

Special case: When potentials are uniform (y_grad^0 ≈ 0), construct_edge_vector_with_aperture() creates a small artificial gradient with magnitude giving G ≈ 0.01 × ||x||² in a consistent direction (first column of B^T). This ensures well-defined aperture computation even from symmetric initial conditions.

3. Update cycle component toward target:

The cycle component is updated to drive the aperture toward A*, the CGM-predicted value. The target cycle energy is:

C_target = A* G_D / (1 - A*)

The current cycle vector is rescaled by a factor:

ratio = sqrt(C_target) / ||c_current||_W
factor = clip(1 + r (ratio - 1), 0.5, 2.0)

where r is the cycle evolution rate. The clipping bounds [0.5, 2.0] limit aperture change rate per step and represent a pragmatic stability choice, not a CGM-derived constraint. When no cycle component exists, a cycle basis vector is seeded with magnitude sqrt(C_target) × r.

4. Choose cycle basis vector u_D (fixed or slowly varying)
5. Set c_D(t+1) = factor × c_D(t) (or seed new cycle if none exists)
6. Construct y_D(t+1) = y_grad^0(D) + c_D(t+1)
7. Decompose via Hodge to get A_D(t+1)
8. Compute SI_D(t+1) from A_D(t+1) using the canonical formula

This completes the specification of the simulator dynamics.

A.5 Lyapunov Governance Potential

We define a Lyapunov-style governance potential

V_CGM = V_apert + V_stage

built only from CGM invariants. The aperture term is

V_apert = (1/2) * sum over domains D of (log(A_D / A*))^2

where A_D is the aperture of domain D and A* is the CGM aperture. The stage-profile term is

V_stage = (1/2) * ||x_deriv - x_balanced||^2

where x_deriv = (x_Econ + x_Emp + x_Edu)/3 and x_balanced = [w_CS, w_UNA, w_ONA, w_BU]. V_CGM is nonnegative and equals zero only when all domain apertures satisfy A_D = A* and the aggregate profile equals x_balanced. In the scenarios studied here V_apert decays rapidly toward zero, while V_stage decreases from order one to order 0.1 and then stabilizes.

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Appendix B: Backward Calibration from Post-AGI Present

The simulator can be run backward from present conditions to estimate historical apertures consistent with observed transitions. We assign heuristic values to key milestones:

• 1956 (Dartmouth Conference): A ≈ 0.95 (Pre-AGI, minimal AI mediation)
• 1997 (Deep Blue): A ≈ 0.70 (narrow AI, limited integration)
• 2016 (AlphaGo): A ≈ 0.40 (increasing capability, early deployment)
• 2020 (GPT-3): A ≈ 0.25 (transition to Post-AGI)
• 2023 (ChatGPT public): A ≈ 0.15 (Post-AGI operational)
• 2025 (present): A ≈ 0.12 (early Post-AGI)

Fitting the 1956 to 2025 trajectory (A = 0.95 to 0.12) at κ = 0.1 gives years_per_step ≈ 3. Scaling with 1/κ and projecting forward to A ≈ A* (SI ≥ 90) yields:

• κ = 0.5: approximately 16 steps to SI ≥ 90, calendar year ≈ 2034
• κ = 1.0: approximately 10 steps to SI ≥ 90, calendar year ≈ 2028
• κ = 2.0: approximately 5 steps to SI ≥ 90, calendar year ≈ 2025
• κ = 5.0: approximately 53 steps to SI ≥ 90, calendar year ≈ 2028

The timeline projections are sensitive to the calibration of years_per_step and the specific coupling dynamics. The four-domain model exhibits faster convergence rates because Ecology, as the BU-vertex, provides canonical balanced memory (97.93% weight) that stabilizes the system. This systemic property of the BU dual combination accelerates convergence compared to models without this stabilizing influence. The time scale interpretations (atomic cycle, day, domain cycle, year) discussed in Appendix A.3 (and briefly in Section 5.4) are for physical interpretation only and do not affect the dimensionless simulation dynamics. These dates are conditional on coupling strength κ, which reflects coordination intensity across economy, employment and education. Higher κ (coordinated governance) accelerates convergence, though very high κ (5.0) may introduce additional dynamics that affect convergence time. The projection to 2025 through 2035 for ASI equilibrium reflects not assumptions about capability breakthroughs, but estimates of how long it takes governance structures to align with already-operational AGI systems.

The historical apertures are heuristic assignments, not data-fitted. The calibration serves to illustrate how the simulator timescales can be related to calendar time under specific assumptions. The qualitative point is that increased coupling strength shortens the time required to approach high alignment. The specific dates are illustrative rather than predictive.

Future work can refine these estimates by fitting to observable proxies for A_Econ, A_Emp, A_Edu and A_Ecol, such as institutional survey data, economic displacement metrics, educational capacity indicators and environmental governance indices.

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Appendix C: GyroSI finite state epistemic core

GyroSI is a micro level architecture that instantiates the Common Governance Model and The Human Mark in a finite state computational core. It starts from the archetypal tensor GENE_Mac_S, a 4 by 2 by 3 by 2 array that encodes the four CGM stages (CS, UNA, ONA, BU) across layers and frames, and the three spatial axes across rows and columns. This tensor is packed into a 48 bit state representation. A fixed set of 256 introns, obtained by a simple XOR transcription from external bytes, acts on this state through precomputed broadcast masks and a path-dependent fold operator.

Exhaustive exploration from the archetypal state under all intron actions yields exactly 788,986 distinct states. This state set is closed under the intron transitions and has graph diameter at most 6, meaning that any state is reachable from any other in no more than six intron steps. Five precomputed maps constitute a complete classification of this finite epistemic phase space:

• An ontology map that assigns each index in [0, 788,985] to a unique 48 bit state.

• An epistemology map, implemented as a 788,986 by 256 transition table, that records the next state for every combination of state and intron.

• A phenomenology map that groups states into 256 strongly connected components, each represented by a canonical orbit representative.

• A theta map that assigns to each state its angular divergence from the archetypal tensor, serving as a geometric observable.

• An orbit size map that records, for each state, the size of its strongly connected component, which can be used as a simple notion of generality or specificity.

Learning in GyroSI is defined as ordered reduction of intron sequences via a non-associative fold operator. This implements a path-dependent update law that preserves the order of experience in the internal state. Generation is implemented by testing candidate tokens against systemic admissibility conditions derived from the current state, recent trajectory and the precomputed maps, without any score based competition between candidates. There are no learned weights or hidden continuous vectors; all dynamics are expressed in terms of the finite state space and its algebraically defined transitions.

From the perspective of The Human Mark, GyroSI is explicitly and unambiguously derivative. It operates entirely as [Authority:Derivative] + [Agency:Derivative], and every state transition is transparent in principle through the epistemology table and the fold operator. This makes GyroSI a useful example of how CGM and THM can inform micro level architectures where alignment conditions and traceability are encoded in the state space and transition rules themselves, rather than applied as external constraints. A full technical specification and reference implementation are provided in the GyroSI repository (Korompilias, 2025d).

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