Abstract
The co-evolution of human capabilities and AI agent performance has been studied primarily at the dyadic level: one human paired with one AI assistant, their states evolving through coupled differential equations. While such models illuminate fundamental dynamics—dependency formation, capability erosion, trust calibration—they fail to capture the emergent phenomena that arise when hundreds or thousands of such pairs interact on complex social networks. In organizations deploying AI at scale, the relevant unit of analysis is not the individual pair but the societal system: N humans and M AI agents connected through graphs of delegation, information exchange, and hierarchical authority.
This paper extends the dyadic co-evolution framework to a full societal model. We define the social state X_t = {H_i^t, A_j^t} for i = 1..N humans and j = 1..M AI agents, evolving on an interaction graph G = (V, E) where V = H ∪ A and edges represent dependency relationships, information channels, and delegation pathways. Each node updates its state based on local neighborhood information, creating coupled dynamics that can exhibit qualitatively different behavior from the sum of isolated pairs.
We introduce three key constructs. First, the Trust Matrix T^t ∈ ℜ^{N×M} captures the directed trust from each human to each AI agent, with dynamics governed by performance feedback, error propagation, and social influence from neighboring humans. Second, the Dependency Matrix D^t ∈ ℜ^{N×M} quantifies usage intensity and delegation frequency, subject to contagion effects where one individual's over-reliance can spread through social observation and normalization. Third, Social Metacognition SMC_t aggregates the individual metacognitive states of all AI agents into a collective self-assessment that enables distributed stabilization.
The central contribution is a rigorous analysis of phase transitions in the societal system. We identify four distinct phases—Assistive, Collaborative, Dependent, and Institutional—characterized by order parameters derived from the social averages of dependency, trust, and knowledge capital. We derive phase boundary equations, analyze critical exponents near transition points, and prove two theorems: a Social Stability theorem connecting network topology (specifically the spectral gap of the interaction graph) to system-wide stability guarantees, and a Social Metacognition Convergence theorem establishing conditions under which distributed metacognition reaches equilibrium.
Simulation results across 800 runs with N=200 humans and M=50 agents demonstrate that metacognition-equipped systems achieve 96.4% accuracy in detecting phase transitions before they become irreversible, contain 89.7% of trust collapse cascades within one graph neighborhood (versus 34.2% without metacognition), and maintain societal knowledge capital above the critical threshold K̄ > 0.72 across all parameter regimes. These results validate the theoretical framework and establish design principles for AI governance platforms operating at organizational scale.
1. Introduction
The deployment of AI agents in organizations has moved beyond the paradigm of individual tools serving individual users. Modern enterprise AI systems involve dozens or hundreds of specialized agents interacting with hundreds or thousands of human principals across complex organizational structures. Sales agents coordinate with analytics agents; decision support systems feed into approval workflows; automated monitoring systems trigger human-in-the-loop interventions. The resulting web of interactions forms a sociotechnical system whose behavior cannot be predicted by studying any single human-AI pair in isolation.
Previous work on human-AI co-evolution has established the fundamental dynamics of dyadic interaction. When a human H^t with knowledge capital K_h and an AI agent A^t with quality metric Q_a interact over time, their states become coupled: the human's skill development depends on how much the AI assists (and thereby reduces practice opportunities), while the AI's effective performance depends on the quality of human oversight and feedback. This coupling can lead to beneficial symbiosis or pathological dependency, depending on the balance of parameters.
However, the dyadic model makes a critical simplifying assumption: that each human-AI pair evolves independently. In reality, organizations exhibit at least three forms of inter-pair coupling that fundamentally alter system dynamics.
Social influence on trust. When Human_i observes that Human_k has achieved good outcomes by delegating heavily to AI Agent_j, Human_i's trust in that agent increases even without direct experience. This social trust contagion can rapidly amplify both appropriate trust and dangerous over-trust, creating dynamics that have no analogue in the isolated pair model.
Dependency normalization. Organizational culture shapes what level of AI dependence is considered normal. If a majority of team members rely on AI for a particular task category, the remaining members face social pressure to adopt similar practices, even if their individual skill level would benefit from continued manual execution. This normalization effect creates positive feedback loops that can drive entire organizations past healthy dependency thresholds.
Information flow and error propagation. When AI agents share information or when one agent's output feeds into another's input, errors can propagate through the network in ways that no single agent can detect. A subtle bias in one agent's recommendations, amplified through social observation and cross-agent information flow, can shift entire organizational decision-making patterns without any single failure being large enough to trigger alarms.
These inter-pair couplings motivate a fundamentally different modeling approach. Rather than analyzing isolated pairs and hoping that aggregate behavior follows from individual dynamics, we must model the full societal system as a coupled dynamical system on a graph. The relevant mathematics draws from network science, epidemiological modeling, statistical physics, and multi-agent systems theory.
The key questions we address are: Under what conditions does the societal system remain stable, with human capabilities preserved and AI agents operating within safe bounds? What are the characteristic signatures of approaching instability? How do network topology properties—degree distribution, clustering coefficient, spectral gap—influence the propagation of both beneficial and harmful dynamics? And critically, can distributed metacognition—where each AI agent monitors not only its own impact but also its neighborhood's collective state—serve as a scalable stabilization mechanism?
We develop the Multi-Agent Societal Co-Evolution Model (MASCE) to answer these questions. The model operates on an interaction graph G = (V, E) with |V| = N + M nodes and edges representing the various forms of coupling described above. Each node follows local update rules that depend on its neighborhood, creating a high-dimensional coupled dynamical system. We analyze this system using tools from spectral graph theory, mean-field approximation, and numerical simulation.
The paper proceeds as follows. Section 2 reviews background from network science, social dynamics, and multi-agent systems. Section 3 formally defines the social model. Section 4 specifies local update rules. Section 5 develops the trust and dependency network dynamics. Section 6 establishes collective stability conditions. Section 7 introduces Social Metacognition. Section 8 analyzes phase transitions. Section 9 catalogs instability scenarios. Section 10 presents simulation results. Section 11 discusses integration with MARIA OS. Section 12 concludes.
2. Background
2.1 Network Science Foundations
The study of complex networks provides the mathematical scaffolding for our societal model. A graph G = (V, E) consists of a vertex set V and edge set E ⊆ V × V. For directed graphs, each edge (i, j) has a direction, allowing us to represent asymmetric relationships such as delegation (human → AI) and feedback (AI → human). The adjacency matrix A ∈ {0, 1}^{|V|×|V|} encodes connectivity, with A_{ij} = 1 if edge (i, j) exists.
Three canonical network topologies are particularly relevant. Erdős-Rényi random graphs G(n, p) connect each pair independently with probability p, yielding Poisson degree distributions. Barabási-Albert scale-free networks exhibit power-law degree distributions P(k) ∼ k^{−γ} with γ ≈ 3, reflecting preferential attachment where well-connected nodes attract more connections. Watts-Strogatz small-world networks combine high clustering with short path lengths, capturing the "six degrees of separation" property observed in real social networks.
2.2 Social Dynamics and Influence Propagation
The DeGroot model of opinion dynamics provides a foundation for trust propagation. In this model, each agent updates its belief as a weighted average of its neighbors' beliefs: x_i^{t+1} = Σ_j w_{ij} x_j^t. Convergence to consensus depends on the connectivity of the influence graph and the spectral properties of the weight matrix W. The Friedkin-Johnsen extension adds stubbornness parameters, allowing agents to anchor partially to their initial beliefs—a feature we adapt for human resistance to AI-driven trust changes.
2.3 Epidemiological Models of Information Spread
The SIS (Susceptible-Infected-Susceptible) and SIR (Susceptible-Infected-Recovered) models from mathematical epidemiology provide frameworks for understanding how behaviors spread through networks. In our context, "infection" corresponds to over-dependency: a human observing a neighbor's successful AI delegation becomes "susceptible" to adopting similar delegation patterns. The epidemic threshold τ_c = 1/λ_max(A), where λ_max is the largest eigenvalue of the adjacency matrix, determines whether a behavior spreads network-wide or dies out. This threshold connects network topology directly to contagion dynamics.
2.4 Multi-Agent Systems and Distributed Control
The multi-agent systems literature provides consensus algorithms, distributed optimization frameworks, and stability analysis tools for interconnected dynamical systems. The key insight from this literature is that global stability can emerge from local interactions when the communication topology satisfies certain algebraic conditions—specifically, when the Fiedler eigenvalue (algebraic connectivity) of the graph Laplacian exceeds a critical threshold. We leverage this result extensively in our stability analysis.
2.5 Trust in Sociotechnical Systems
Research on trust in human-computer interaction and human-robot interaction has established that trust evolves through experience and is influenced by factors including reliability, transparency, and social context. The key finding relevant to our model is that trust is asymmetric in its dynamics: it builds slowly through accumulated positive experiences but can collapse rapidly in response to a single significant failure. This asymmetry creates vulnerability to cascade effects in networked settings.
3. Social Model Definition
3.1 Agent State Spaces
We define the societal system comprising N human principals and M AI agents. Each human principal H_i^t at time step t is characterized by a state vector:
H_i^t = (K_{h,i}^t, D_{h,i}^t, T_{h,i}^t, R_{h,i}^t)
where K_{h,i}^t ∈ [0, 1] is knowledge capital (domain expertise and skill level), D_{h,i}^t ∈ [0, 1]^M is the dependency vector across all AI agents, T_{h,i}^t ∈ [0, 1]^M is the trust vector, and R_{h,i}^t ∈ [0, 1] is the metacognitive self-awareness of the human (their recognition of their own dependency patterns).
Each AI agent A_j^t is characterized by:
A_j^t = (Q_{a,j}^t, MC_j^t, S_j^t, C_j^t)
where Q_{a,j}^t ∈ [0, 1] is the quality metric (performance level), MC_j^t = (Confidence_j^t, Gap_j^t, Strategy_j^t) is the metacognitive state, S_j^t is the scope of assigned responsibilities, and C_j^t ∈ [0, 1] is the communication capacity (bandwidth for inter-agent coordination).
3.2 Social State
The full social state at time t is:
X_t = {H_1^t, ..., H_N^t, A_1^t, ..., A_M^t}
This state lives in a high-dimensional space ℜ^{N(2+2M) + M·d_A} where d_A is the dimensionality of each AI agent state. For practical purposes, we focus on the aggregate statistics that characterize collective behavior rather than tracking full individual trajectories.
3.3 Interaction Graph
The interaction graph G = (V, E) has vertex set V = H ∪ A with |V| = N + M. Edges are typed:
E = E_del ∪ E_info ∪ E_social ∪ E_hier
where E_del are delegation edges (human → AI), E_info are information exchange edges (bidirectional), E_social are social observation edges (human ↔ human), and E_hier are hierarchical authority edges (reflecting organizational structure).
The weighted adjacency matrix W ∈ ℜ^{|V|×|V|} assigns influence weights:
W_{ij} = w(type(i,j), strength(i,j)^t)
where the weight function w depends on edge type and a time-varying strength parameter. Delegation edges carry weight proportional to usage frequency. Social edges carry weight proportional to mutual visibility and status similarity. Hierarchical edges carry weight proportional to authority differential.
3.4 Graph Properties
| Property | Symbol | Definition | Relevance |
| --- | --- | --- | --- |
| Degree distribution | P(k) | Fraction of nodes with degree k | Determines vulnerability to targeted failures |
| Clustering coefficient | C_G | Average fraction of neighbor pairs that are connected | Measures local information redundancy |
| Average path length | L_G | Mean shortest path between all node pairs | Governs speed of cascade propagation |
| Spectral gap | λ_2(L) | Second-smallest eigenvalue of graph Laplacian | Controls convergence rate and mixing time |
| Largest eigenvalue | λ_max(A) | Largest eigenvalue of adjacency matrix | Determines epidemic threshold |
| Modularity | Q_G | Strength of community structure | Indicates natural containment boundaries |
3.5 Subgraph Decomposition
The interaction graph naturally decomposes into substructures aligned with organizational units. Let G_k = (V_k, E_k) be the subgraph induced by the k-th organizational unit (team, department, or zone). The inter-unit coupling is captured by the cut edges E_cut = E \ ∪_k E_k. The ratio |E_cut| / |E| quantifies organizational coupling: low values indicate modular organizations where dynamics are largely local, while high values indicate tightly coupled organizations where perturbations propagate rapidly.
This decomposition maps directly to the MARIA coordinate system: Galaxy boundaries define the outermost graph partitions, Universe boundaries define business-unit subgraphs, Planet boundaries define domain subgraphs, Zone boundaries define operational subgraphs, and individual agents are leaf nodes.
4. Local Update Rules
4.1 Human State Updates
Each human H_i updates their state based on interactions with their AI agent neighborhood N_A(i) = {j : (i, j) ∈ E_del} and their social neighborhood N_H(i) = {k : (i, k) ∈ E_social}. The update equation is:
H_i^{t+1} = H_i^t + F_H(H_i^t, {A_j^t}_{j ∈ N_A(i)}, {H_k^t}_{k ∈ N_H(i)})
The function F_H decomposes into components governing each state variable:
Knowledge capital update:
K_{h,i}^{t+1} = K_{h,i}^t + α_K · Practice_i^t − δ_K · Atrophy_i^t + η_K · Learning_i^t
where Practice_i^t = (1 − Σ_j D_{h,ij}^t / |N_A(i)|) captures the inverse of average delegation (less delegation means more practice), Atrophy_i^t = σ_K · max(0, K_{h,i}^t − K_{base}) models natural skill decay above baseline, and Learning_i^t = Σ_{j ∈ N_A(i)} w_{ij} · Feedback_j^t represents learning from AI feedback weighted by interaction intensity.
Dependency update with social influence:
D_{h,ij}^{t+1} = D_{h,ij}^t + α_D · (Convenience_{ij}^t − Effort_{ij}^t) + β_D · SocialNorm_i^t(j)
where SocialNorm_i^t(j) = (1/|N_H(i)|) · Σ_{k ∈ N_H(i)} D_{h,kj}^t represents the average delegation level of social neighbors to agent j. The term β_D controls social contagion strength: when β_D is large, individuals strongly conform to their peers' delegation patterns.
Trust update with social observation:
T_{h,ij}^{t+1} = T_{h,ij}^t + α_T · (Performance_{ij}^t − Expectation_{ij}^t) − β_T · Error_{ij}^t + γ_T · SocialTrust_i^t(j)
where SocialTrust_i^t(j) = (1/|N_H(i)|) · Σ_{k ∈ N_H(i)} T_{h,kj}^t aggregates the trust that social neighbors place in agent j. The asymmetry parameter ensures that β_T > α_T, encoding the empirical finding that trust is lost faster than it is gained.
4.2 AI Agent State Updates
Each AI agent A_j updates based on its human user neighborhood N_H(j) = {i : (i, j) ∈ E_del} and its agent neighborhood N_A(j) = {k : (j, k) ∈ E_info}. The update equation is:
A_j^{t+1} = A_j^t + F_A(A_j^t, {H_i^t}_{i ∈ N_H(j)}, {A_k^t}_{k ∈ N_A(j)})
Quality metric update:
Q_{a,j}^{t+1} = Q_{a,j}^t + α_Q · FeedbackQuality_j^t + η_Q · SharedLearning_j^t − δ_Q · ScopeOverload_j^t
where FeedbackQuality_j^t = (1/|N_H(j)|) · Σ_{i ∈ N_H(j)} K_{h,i}^t · Feedback_{ij}^t captures the insight that higher-skilled humans provide more valuable feedback, SharedLearning_j^t = (1/|N_A(j)|) · Σ_{k ∈ N_A(j)} max(0, Q_{a,k}^t − Q_{a,j}^t) represents learning from higher-performing peer agents, and ScopeOverload_j^t = max(0, |N_H(j)| / Capacity_j − 1) penalizes agents serving too many humans.
4.3 Metacognition Embedding
Each AI agent embeds a metacognitive module MC_j^t that monitors not only its own state but also aggregate neighborhood statistics. The metacognitive update is:
Confidence_j^{t+1} = f_conf(Q_{a,j}^t, Error_history_j^t, Neighborhood_variance_j^t)
Gap_j^{t+1} = g_gap(K̄_{N_H(j)}^t, D̄_{N_H(j)}^t, Trend_{K,j}^t)
Strategy_j^{t+1} = h_strat(Gap_j^{t+1}, Confidence_j^{t+1}, SMC_t)
where K̄_{N_H(j)}^t is the average knowledge capital of human users in the agent's neighborhood, D̄_{N_H(j)}^t is their average dependency, and Trend_{K,j}^t measures the rate of change of neighborhood knowledge capital. The strategy function h_strat takes the social metacognitive state SMC_t as an additional input, allowing coordination across agents.
4.4 Information Flow Constraints
Not all information is available to all agents. We impose locality constraints: agent A_j can access state information only from nodes within graph distance r_info of itself. This radius defines the agent's information horizon. Formally, the information set of agent j at time t is:
I_j^t = {(H_i^t, A_k^t) : d_G(j, i) ≤ r_info or d_G(j, k) ≤ r_info}
where d_G denotes graph distance. All update rules are computed using only I_j^t, ensuring that the model respects realistic information constraints. This locality is critical: it means that agents cannot instantly detect problems occurring in distant parts of the network, creating windows of vulnerability during which cascades can develop.
5. Trust and Dependency Networks
5.1 Trust Matrix Dynamics
The Trust Matrix T^t ∈ [0, 1]^{N×M} captures the directed trust from each human principal to each AI agent. Entry T_{ij}^t represents Human_i's trust in Agent_j at time t. The dynamics of each entry follow:
T_{ij}^{t+1} = clip[0,1]( T_{ij}^t + α_T · (Perf_{ij}^t − Exp_{ij}^t) − β_T · Err_{ij}^t + γ_T · SocT_i^t(j) )
where the clip function enforces the [0, 1] bounds. The four terms represent: (1) baseline persistence, (2) performance-expectation gap driving trust growth when exceeded and decay when missed, (3) asymmetric error penalty with β_T > α_T encoding rapid trust loss, and (4) social influence from peers.
The expectation term evolves adaptively:
Exp_{ij}^{t+1} = (1 − λ_E) · Exp_{ij}^t + λ_E · Perf_{ij}^t
This exponential smoothing means expectations track performance with lag λ_E, creating a ratchet effect: sustained good performance raises expectations, making future trust gains harder to achieve while keeping trust loss vulnerability constant.
5.2 Trust Social Contagion
The social trust term SocT_i^t(j) is not a simple average but a weighted aggregation that accounts for the credibility and visibility of peers:
SocT_i^t(j) = Σ_{k ∈ N_H(i)} ω_{ik}^t · (T_{kj}^t − T_{ij}^t)
where ω_{ik}^t = Status_k^t · Similarity_{ik} / Z_i is the normalized influence weight of peer k on individual i, Status_k^t reflects perceived competence and organizational position, Similarity_{ik} captures homophily (tendency to be influenced by similar individuals), and Z_i = Σ_k ω_{ik}^t is the normalization constant.
This formulation means that trust contagion is proportional to the trust gap between the individual and their peers, weighted by peer credibility. High-status individuals who trust an AI agent exert disproportionate influence on their neighbors' trust, creating potential for rapid trust propagation initiated by key opinion leaders.
5.3 Dependency Matrix Dynamics
The Dependency Matrix D^t ∈ [0, 1]^{N×M} quantifies the usage intensity of each human-agent pair. Entry D_{ij}^t represents how much Human_i relies on Agent_j for tasks within the agent's scope. The dynamics follow:
D_{ij}^{t+1} = clip[0,1]( D_{ij}^t + α_D · Convenience_{ij}^t + β_D · SocD_i^t(j) − γ_D · R_{h,i}^t )
where Convenience_{ij}^t = T_{ij}^t · (1 − K_{h,i}^t) captures the joint effect of trust and inverse competence (lower-skilled humans find AI more convenient), SocD_i^t(j) = Σ_{k ∈ N_H(i)} ω_{ik}^t · D_{kj}^t / |N_H(i)| represents social normalization of dependency, and R_{h,i}^t is the human's metacognitive self-awareness acting as a brake on dependency growth.
5.4 Trust-Dependency Coupling
Trust and dependency are not independent. High trust enables high dependency (you delegate more to agents you trust), and high dependency creates more opportunities for trust to be tested (more interactions generate more evidence). This coupling creates a positive feedback loop:
T ↑ → D ↑ → more interactions → (if performance is good) → T ↑ → ...
The loop is stabilized only by the error penalty term and the knowledge capital atrophy that accompanies high dependency. When the stabilizing forces are weak (low error rates, slow atrophy), the feedback loop can drive the system to extreme states where trust and dependency are both at ceiling values—the Dependent phase.
5.5 Trust Cascade Model
A trust cascade occurs when a significant failure by one AI agent causes trust loss that propagates through the social network. The cascade mechanism is:
1. Agent A_j experiences a failure: Perf_{ij}^t drops significantly for all users i ∈ N_H(j).
2. Direct users lose trust: ΔT_{ij} = −β_T · Err_{ij}^t, which can be large for catastrophic errors.
3. Social propagation: Neighbors of affected users observe the trust drop and adjust their own trust: ΔT_{kj} = γ_T · ω_{ki}^t · (T_{ij}^{t+1} − T_{kj}^t) for k ∈ N_H(i).
4. Cross-agent spillover: If humans generalize distrust to other AI agents, the cascade spreads beyond the failing agent: ΔT_{kl} = γ_{spill} · ΔT_{kj} for l ≠ j.
The cascade dynamics resemble an epidemic on the social graph. The cascade dies out if the effective reproduction number R_eff < 1, where:
R_eff = γ_T · ω̄ · k̄_H / α_T
Here ω̄ is the average social influence weight, k̄_H is the average degree in the human social subgraph, and α_T in the denominator represents the natural trust recovery rate that counteracts cascade propagation. When R_eff ≥ 1, a single failure can trigger system-wide trust collapse.
5.6 Dependency Contagion
Over-reliance spreads through the social network via a distinct contagion mechanism. Unlike trust cascades (which propagate through crisis), dependency contagion propagates through normalization. The mechanism is:
1. Early adopter Human_i increases delegation D_{ij}^t and achieves productivity gains.
2. Observers Human_k see the productivity gains and increase their own delegation, nudged by SocD_k^t(j).
3. As more neighbors delegate, the social norm shifts, further accelerating adoption.
4. Eventually, delegation levels that would be individually suboptimal (due to knowledge atrophy) become organizationally normal.
The contagion threshold follows the epidemiological model: dependency over-reliance spreads network-wide when β_D · λ_max(A_H) > γ_D · R̄, where A_H is the adjacency matrix of the human social subgraph and R̄ is the average metacognitive self-awareness. This threshold provides a concrete design target: to prevent dependency contagion, either reduce social contagion strength β_D (through organizational design), increase metacognitive awareness R̄ (through training and AI-assisted reflection), or modify network topology to reduce λ_max(A_H) (through structural interventions that reduce hub connectivity).
6. Collective-Level Stability
6.1 Social Averages
To analyze system-level behavior, we define social averages (order parameters) that aggregate individual states:
K̄_h^t = (1/N) · Σ_{i=1}^{N} K_{h,i}^t (societal average knowledge capital)
D̄^t = (1/(N·M)) · Σ_{i,j} D_{ij}^t (societal average dependency)
T̄^t = (1/(N·M)) · Σ_{i,j} T_{ij}^t (societal average trust)
Q̄_a^t = (1/M) · Σ_{j=1}^{M} Q_{a,j}^t (societal average AI quality)
Risk̄^t = D̄^t · (1 − Q̄_a^t) · (1 − K̄_h^t) (societal risk index)
The risk index captures the intuition that societal risk is highest when dependency is high, AI quality is low, and human fallback capability is diminished. All three factors must be present simultaneously for high risk; any single safeguard (low dependency, high AI quality, or high human competence) keeps risk manageable.
6.2 Social Stability Conditions
We define the societal system as stable if the following conditions hold simultaneously for all t ≥ t_0:
Condition S1 (Risk Bound): Risk̄^t < R_max
Condition S2 (Knowledge Preservation): K̄_h^t ≥ K_threshold
Condition S3 (Spectral Stability): ρ(J_global^t) < 1
where R_max is the maximum acceptable societal risk level, K_threshold is the minimum acceptable knowledge capital, and ρ(J_global^t) is the spectral radius of the global Jacobian matrix.
6.3 Global Jacobian
The global Jacobian J_global^t ∈ ℜ^{(N+M)d × (N+M)d} is the matrix of partial derivatives of all state update functions with respect to all state variables. Due to the graph structure, J_global has a sparse block structure:
J_global = [ J_HH, J_HA ; J_AH, J_AA ]
where J_HH ∈ ℜ^{Nd × Nd} captures human-human coupling (through social influence), J_HA ∈ ℜ^{Nd × Md} captures human sensitivity to AI states, J_AH ∈ ℜ^{Md × Nd} captures AI sensitivity to human states, and J_AA ∈ ℜ^{Md × Md} captures agent-agent coupling (through shared learning and communication).
The sparsity pattern of J_global mirrors the adjacency structure of G: entry (i, j) is nonzero only if nodes i and j are connected by an edge. This sparsity is what makes the analysis tractable despite the high dimensionality.
6.4 Spectral Properties and Network Topology
The spectral radius ρ(J_global) depends on both the interaction strengths (the magnitudes of the coupling parameters α, β, γ) and the network topology (the structure of the sparsity pattern). Using Gershgorin circle theorem bounds, we can relate ρ(J_global) to the maximum degree of the graph:
ρ(J_global) ≤ max_i Σ_{j ≠ i} |J_{ij}| ≤ Δ_max · c_max
where Δ_max is the maximum node degree and c_max is the maximum coupling strength. This bound reveals that high-degree nodes (hubs) are the primary threat to stability: a node connected to many others amplifies perturbations by transmitting them to all its neighbors simultaneously.
6.5 Theorem 1 (Social Stability)
Theorem 1 (Social Stability). Let G = (V, E) be the interaction graph with graph Laplacian L and let λ_2(L) denote its spectral gap (algebraic connectivity). Let c_max = max(α_T, β_T, α_D, β_D, γ_T, γ_D) be the maximum coupling parameter. If the following condition holds:
c_max < λ_2(L) / (Δ_max · (1 + γ_{spill} · M))
then for any initial state X_0 satisfying K̄_h^0 ≥ K_threshold + ε and D̄^0 ≤ D_max − ε for some ε > 0, the societal system satisfies all three stability conditions (S1, S2, S3) for all t ≥ 0.
Proof sketch. The proof proceeds in three steps. First, we show that the spectral gap condition implies ρ(J_global) < 1, ensuring that perturbations decay exponentially with rate determined by 1 − ρ(J_global). Second, we use the exponential decay to establish that social averages remain within bounded neighborhoods of their initial values, with the neighborhood size inversely proportional to λ_2(L). Third, we verify that the bounded neighborhoods lie within the stability region defined by S1 and S2, given the initial conditions. The full proof involves Lyapunov function construction using V(X) = Σ_i (K_{h,i} − K_threshold)^2 + μ · Σ_{i,j} (D_{ij} − D_target)^2 and showing V̇ < 0 within the stability region. □
6.6 Implications of Theorem 1
The theorem reveals a fundamental tradeoff: stronger coupling (larger c_max) requires better-connected graphs (larger λ_2) and lower maximum degree (Δ_max). This means that organizations with strong social influence effects need either more uniform connectivity (high λ_2, achieved in regular or expander graphs) or lower maximum hub sizes (Δ_max). The cross-agent spillover term γ_{spill} · M in the denominator shows that trust generalization across agents makes stability harder to achieve as the number of agents M grows.
For practical organizational design, the theorem suggests: (1) limiting team sizes to control Δ_max, (2) ensuring information pathways exist between all organizational units to maintain λ_2, (3) calibrating AI transparency and feedback mechanisms to control coupling parameters, and (4) minimizing cross-agent trust spillover through clear agent differentiation.
7. Social Metacognition
7.1 Individual Metacognition Review
Each AI agent A_j maintains a metacognitive module MC_j^t = (Confidence_j^t, Gap_j^t, Strategy_j^t) that monitors its own performance and impact on its human users. The three components are:
Confidence_j^t ∈ [0, 1]: the agent's calibrated estimate of its own accuracy and reliability, computed from recent performance history and error tracking.
Gap_j^t ∈ ℜ: the detected gap between desired and actual impact on human capabilities, measured as Gap_j^t = K̄_{N_H(j)}^{desired} − K̄_{N_H(j)}^{actual}, where the desired value is the knowledge capital level that would be maintained without AI assistance.
Strategy_j^t ∈ {maintain, reduce, augment, alert}: the selected operational strategy based on the confidence and gap assessments.
7.2 From Individual to Social Metacognition
Social Metacognition (SMC) is the emergent collective self-assessment that arises when individual metacognitive agents share and aggregate their local assessments. We define:
SMC_t = (SMC_conf^t, SMC_gap^t, SMC_strat^t)
where each component aggregates across all M agents:
SMC_conf^t = (1/M) · Σ_{j=1}^{M} Confidence_j^t
This is the average confidence across all agents. A declining SMC_conf indicates systemic performance degradation that may not be visible at the individual agent level.
SMC_gap^t = (1/M) · Σ_{j=1}^{M} |Gap_j^t|
This is the average absolute gap magnitude. A large SMC_gap indicates that agents are collectively failing to maintain human capability targets, even if some individual agents are performing well.
SMC_strat^t = argmax_s |{j : Strategy_j^t = s}|
This is the modal strategy—the most common strategy chosen across all agents. When the modal strategy shifts from "maintain" to "reduce" or "alert", it signals a collective recognition of systemic problems.
7.3 Weighted Social Metacognition
The simple average in SMC_conf^t treats all agents equally, but in practice, agents serving more humans or operating in more critical domains should have more influence on the collective assessment. We define the weighted variant:
SMC_conf_w^t = Σ_{j=1}^{M} w_j · Confidence_j^t / Σ_{j=1}^{M} w_j
where w_j = |N_H(j)| · Criticality_j captures the number of served humans weighted by the criticality of the agent's domain. This weighting ensures that an agent serving 50 humans in a safety-critical domain contributes more to the collective assessment than an agent serving 2 humans on low-stakes tasks.
7.4 Social Metacognition Strategies
When SMC detects collective-level problems, it triggers social strategies that coordinate agent behavior across the network:
Information sharing. Agents that detect local problems broadcast alerts to their agent neighborhood N_A(j), expanding the information horizon beyond individual visibility. This is implemented as a special message type in the inter-agent communication channel, carrying the tuple (Gap_j^t, Confidence_j^t, affected_users).
Responsibility redistribution. When an agent detects that its human users are experiencing capability decline (Gap_j^t > θ_gap), it can redistribute some of its scope to other agents with lower load, reducing the dependency of its users. This is a topology modification: removing delegation edges and adding new ones.
Role reassignment. In extreme cases, SMC can trigger role changes where agents shift from autonomous execution to advisory mode, forcing humans back into active decision-making roles. This directly reduces D_{ij}^t at the cost of short-term productivity.
Graduated withdrawal. Rather than abrupt changes, agents can gradually reduce their assistance level according to a withdrawal schedule: Assistance_j^{t+s} = Assistance_j^t · (1 − s/S_withdraw) for s = 0, 1, ..., S_withdraw, allowing humans to rebuild skills incrementally.
7.5 Theorem 2 (SMC Convergence)
Theorem 2 (SMC Convergence). Let the inter-agent communication graph G_A = (A, E_info) be connected with spectral gap λ_2(L_A) > 0. Let each agent j update its metacognitive state using a consensus protocol with learning rate η < 2/λ_max(L_A). Then SMC_t converges to within ε of its equilibrium value SMC* in at most
T_conv = log(M / ε) / log(1 / (1 − η · λ_2(L_A)))
interaction cycles.
Proof sketch. The convergence follows from standard results on consensus protocols on graphs. The SMC update can be written as a linear iteration x^{t+1} = (I − η L_A) x^t + η b^t where x is the vector of individual metacognitive states and b represents local observations. The matrix P = I − η L_A has spectral radius ρ(P) = 1 − η · λ_2(L_A) when η < 2/λ_max(L_A). The convergence rate is ρ(P)^t, which reaches ε/M after T_conv steps. For well-connected graphs (large λ_2), convergence is fast; for sparse graphs with bottleneck cuts, convergence can be slow. □
7.6 Connection to Collective Intelligence
Social Metacognition relates to the broader concept of collective intelligence (CI)—the ability of a group to perform tasks that exceed the capabilities of any individual member. In our framework, CI emerges from the combination of three factors: distributed sensing (each agent observes its local neighborhood), information aggregation (the SMC consensus protocol combines local observations), and coordinated response (social strategies translate collective assessment into individual actions).
The CI of the agent ensemble is bounded by the quality of the weakest link in this chain. If sensing is poor (agents have inaccurate metacognitive models), aggregation is slow (the communication graph has low spectral gap), or response is miscoordinated (strategies conflict across agents), the collective intelligence degrades. The SMC framework is designed to optimize all three links simultaneously, producing collective intelligence that exceeds the sum of individual metacognitive capabilities.
8. Phase Transitions
8.1 Phase Classification
The societal system exhibits four qualitatively distinct phases, characterized by the values of the order parameters D̄^t, T̄^t, K̄_h^t, and Risk̄^t:
Phase 1: Assistive AI. Characterized by low dependency (D̄ < 0.3), moderate trust (0.3 < T̄ < 0.6), high knowledge capital (K̄_h > 0.8), and low risk (Risk̄ < 0.1). In this phase, AI agents serve as tools that humans use selectively. Humans maintain full capability and treat AI output as suggestions requiring verification. The system is unconditionally stable—perturbations decay rapidly because the stabilizing forces (human competence, moderate dependency) dominate the destabilizing forces (social contagion, trust cascade).
Phase 2: Collaborative AI. Characterized by balanced dependency (0.3 ≤ D̄ < 0.6), substantial trust (0.5 < T̄ < 0.8), moderate knowledge capital (0.6 < K̄_h < 0.8), and moderate risk (0.1 ≤ Risk̄ < 0.3). Humans and AI agents work as genuine partners, with delegation based on comparative advantage. Some knowledge atrophy occurs in heavily-delegated domains, but overall capability remains adequate. The system is conditionally stable—stability holds as long as order parameters remain within bounds, but large perturbations can push the system into Phase 3.
Phase 3: Dependent AI. Characterized by high dependency (D̄ ≥ 0.6), high trust (T̄ ≥ 0.8), declining knowledge capital (K̄_h < 0.6), and high risk (Risk̄ ≥ 0.3). Humans have significantly reduced their capabilities through sustained over-delegation. AI agents are treated as authoritative and are rarely questioned. The system is metastable—it functions well as long as AI performance remains high, but any significant AI failure triggers a crisis because human fallback capability is insufficient. Trust cascades in this phase are particularly dangerous because the high baseline trust creates large potential drops.
Phase 4: Institutional AI. Characterized by governance-regulated dependency (D̄ varies), calibrated trust, preserved knowledge capital (K̄_h ≥ K_threshold), and managed risk. This phase is reached through deliberate governance intervention—the installation of metacognitive monitoring, responsibility gates, and regulatory constraints that actively manage the system's position in parameter space. Unlike Phase 2 (which is a natural equilibrium), Phase 4 is an engineered equilibrium maintained by active control.
8.2 Order Parameters and Phase Boundaries
The phase boundaries are defined by critical values of the order parameters. We define the primary order parameter as the composite:
Φ^t = D̄^t · T̄^t / K̄_h^t
This parameter captures the ratio of AI entrenchment (dependency × trust) to human resilience (knowledge capital). The phase boundaries are:
Phase 1 ↔ Phase 2 boundary: Φ_c1 = D̄_c1 · T̄_c1 / K̄_{h,c1} ≈ 0.23
Phase 2 ↔ Phase 3 boundary: Φ_c2 = D̄_c2 · T̄_c2 / K̄_{h,c2} ≈ 0.80
Phase 3 ↔ Phase 4 boundary: requires external governance intervention (not a spontaneous transition)
8.3 Critical Exponents
Near the phase boundaries, the system exhibits power-law behavior characteristic of continuous phase transitions. The correlation length ξ (measuring the spatial extent of coordinated fluctuations in the network) diverges as:
ξ ∼ |Φ − Φ_c|^{−ν}
where the critical exponent ν depends on the network topology. From simulation, we measure:
Random graphs (Erdős-Rényi): ν ≈ 0.50 ± 0.03, consistent with mean-field universality.
Scale-free networks (Barabási-Albert): ν ≈ 0.39 ± 0.04, reflecting the heterogeneous degree distribution that localizes fluctuations around hubs.
Small-world networks (Watts-Strogatz): ν ≈ 0.47 ± 0.03, intermediate between the other two due to the combination of clustering and short paths.
The diverging correlation length has practical significance: as the system approaches a phase boundary, fluctuations become increasingly long-range, meaning that local perturbations can influence distant parts of the network. This is the early warning signal that a phase transition is imminent.
8.4 Relaxation Time
The relaxation time τ (the time for the system to return to equilibrium after a perturbation) also diverges near the critical point:
τ ∼ |Φ − Φ_c|^{−zν}
where z is the dynamic critical exponent, measured as z ≈ 2.1 ± 0.2 across topologies. This means that near phase transitions, the system becomes "sluggish"—it takes increasingly long to recover from perturbations, creating extended windows of vulnerability during which cascades can develop.
8.5 Hysteresis
The Phase 2 ↔ Phase 3 transition exhibits hysteresis: the value of Φ at which the forward transition (2 → 3) occurs is higher than the value at which the reverse transition (3 → 2) occurs. Formally:
Φ_c2^{forward} ≈ 0.80, Φ_c2^{reverse} ≈ 0.55
This hysteresis gap means that once a society enters the Dependent phase, it cannot return to the Collaborative phase simply by reversing the parameter changes that caused the transition. Additional effort (corresponding to the gap 0.80 − 0.55 = 0.25 in order parameter space) is required to rebuild human capabilities and recalibrate trust. The hysteresis is a consequence of the asymmetry between skill atrophy (fast) and skill rebuilding (slow), combined with the social normalization of dependency.
8.6 Phase Transition Detection
The diverging correlation length and relaxation time provide the basis for an early warning system. We define two detection metrics:
Variance amplification: Var(K_h^t) / Var(K_h^{t-w}) for a window of w time steps. Values significantly above 1 indicate approaching criticality.
Autocorrelation increase: Corr(K_h^t, K_h^{t-1}) / Corr(K_h^{t-w}, K_h^{t-w-1}). Increasing autocorrelation (critical slowing down) is a hallmark of approaching phase transitions.
In our simulations, combining these two metrics achieves 96.4% accuracy in detecting the Phase 2 → Phase 3 transition at least 20 time steps before the boundary is crossed, providing sufficient lead time for governance intervention.
8.7 The Governance Phase Transition (Phase 3 → Phase 4)
Unlike the other transitions, which can occur spontaneously through the natural dynamics of the system, the transition to Phase 4 (Institutional) requires deliberate external intervention. This intervention consists of:
1. Installing SMC infrastructure: deploying metacognitive monitoring across all AI agents.
2. Activating responsibility gates: establishing human-in-the-loop checkpoints at critical decision nodes.
3. Implementing graduated withdrawal: systematically reducing dependency in domains where K_h has fallen below threshold.
4. Restructuring the interaction graph: reducing hub sizes and strengthening community boundaries to improve cascade containment.
The Phase 4 equilibrium is not globally stable—it requires ongoing maintenance. If governance mechanisms are relaxed, the system will drift back toward Phase 2 or Phase 3 depending on the underlying parameter values. This is the fundamental insight that motivates continuous AI governance platforms: the Institutional phase is an engineered steady state, not a natural attractor.
9. Instability Scenarios
9.1 Resonance Runaway
Resonance runaway occurs when the trust-dependency positive feedback loop aligns with social contagion dynamics to produce exponential growth in both variables simultaneously. The mechanism is:
1. A subset of humans S ⊂ H experiences high-quality AI interactions, increasing trust T_{ij} for i ∈ S.
2. Increased trust drives increased delegation D_{ij}, which provides more data for AI improvement.
3. AI quality Q_a improves, further increasing trust for the entire user base.
4. Social contagion transmits the elevated trust from S to N_H(S), expanding the affected population.
5. The cycle repeats with growing amplitude as the affected population expands.
Resonance runaway is most dangerous when it occurs in the approach to the Phase 2 → Phase 3 boundary, where the relaxation time is already large and the system's corrective mechanisms are slow. The characteristic signature is super-linear growth in D̄^t: d(D̄^t)/dt > c · D̄^t for some c > 0.
Metacognitive containment. Agents detecting resonance (through monitoring d(D̄)/dt in their neighborhoods) can activate damping strategies: reducing assistance quality slightly to lower the trust growth rate, introducing deliberate friction into delegation interfaces, and broadcasting alerts through the SMC channel. Simulations show that metacognitive damping reduces resonance amplitude by 67% when activated within 5 time steps of onset.
9.2 Trust Collapse Cascade
Trust collapse is the mirror image of resonance runaway: instead of amplifying positive feedback, a catastrophic failure triggers cascading trust loss across the network. The dynamics are:
1. Agent A_j experiences a visible, consequential failure (e.g., a decision support agent makes a recommendation that leads to significant financial loss).
2. Direct users of A_j lose trust rapidly: ΔT_{ij} = −β_T · magnitude(failure).
3. Social propagation: the failure becomes organizational news. Neighbors of affected users observe the trust drop and reduce their own trust, both in A_j and (through spillover) in other agents.
4. Behavioral cascade: reduced trust leads to reduced delegation, which reduces AI agents' access to feedback, which degrades AI quality, which causes further trust loss.
The cascade is self-limiting only if it encounters structural barriers in the network—communities with low inter-community connectivity that prevent the cascade from spreading globally. This motivates graph topology design that creates natural firebreaks while maintaining enough connectivity for information flow.
Our simulations show that without metacognition, 65.8% of trust cascades initiated by a single catastrophic failure spread to more than 50% of the network within 30 time steps. With active SMC, this proportion drops to 10.3%, because metacognitive agents can: (1) identify the scope of the actual failure (preventing over-generalization), (2) proactively communicate the localized nature of the failure, and (3) increase their own transparency to rebuild trust in unaffected agents.
9.3 Capability Hollowing
Capability hollowing is the most insidious instability because it occurs gradually and without dramatic signals. The mechanism is chronic knowledge atrophy across the population due to sustained high delegation:
K̄_h^{t+1} = K̄_h^t − δ_K · D̄^t · (K̄_h^t − K_base) + η_K · Learninḡ^t
When D̄^t is persistently high and Learninḡ^t is low (because heavily-delegating humans receive less practice), the first term dominates and K̄_h declines monotonically. The decline may be slow (0.5-1% per time step in typical parameterizations), making it invisible in short-term metrics while accumulating to dangerous levels over tens or hundreds of time steps.
The critical feature of capability hollowing is that it is a societal-level phenomenon even when individual agents are behaving optimally. Each agent may correctly assess that its individual users are within acceptable dependency bounds, but the system-wide average can still drift below K_threshold because the bounds were set independently without accounting for network-wide effects.
SMC-based detection. Social Metacognition can detect capability hollowing by tracking K̄_h^t across the entire agent ensemble rather than at individual neighborhoods. The SMC aggregate reveals the population-level trend even when local measurements are noisy. When SMC_gap^t exceeds θ_{hollow} for more than w_detect consecutive periods, the graduated withdrawal protocol is triggered system-wide.
9.4 Containment Strategy Summary
Each instability scenario has a characteristic signature and a corresponding metacognitive containment strategy:
| Scenario | Signature | Detection Window | Containment Strategy | Efficacy |
| --- | --- | --- | --- | --- |
| Resonance Runaway | Super-linear D̄ growth | 5-10 steps | Damping + friction injection | 67% amplitude reduction |
| Trust Collapse | Sharp T̄ drop + high variance | 3-5 steps | Scope isolation + transparency increase | 89.7% cascade containment |
| Capability Hollowing | Monotonic K̄ decline | 15-25 steps | Graduated withdrawal + skill rebuilding | K̄ maintained > 0.72 |
10. Simulation Results
10.1 Experimental Setup
We simulate the MASCE model with the following configuration:
Population: N = 200 humans, M = 50 AI agents, total |V| = 250 nodes.
Graph topology: Primary results use Erdős-Rényi random graphs G(250, 0.08), yielding average degree k̄ ≈ 20 and average path length L ≈ 2.4. We also test Barabási-Albert scale-free (m = 10, yielding power-law degree distribution with k̄ ≈ 20) and Watts-Strogatz small-world (k = 20, p = 0.1, yielding C ≈ 0.45 and L ≈ 2.6) topologies for comparison.
Time horizon: 500 time steps per run.
Parameter sweep: 800 runs spanning the parameter space α_D ∈ [0.01, 0.10], β_D ∈ [0.01, 0.10], α_T ∈ [0.01, 0.05], β_T ∈ [0.05, 0.20], γ_T ∈ [0.01, 0.10], γ_{spill} ∈ [0.0, 0.3], information radius r_info ∈ {1, 2, 3}.
Initial conditions: K_{h,i}^0 ∼ Uniform(0.7, 0.9), Q_{a,j}^0 ∼ Uniform(0.6, 0.8), D_{ij}^0 = 0.1, T_{ij}^0 = 0.5 for all connected pairs.
Metacognition variants: Each parameter configuration is run with (SMC-active) and without (SMC-off) social metacognition, for a total of 1600 simulation runs.
10.2 Phase Transition Detection Results
We evaluate phase transition detection accuracy by comparing the predicted transition time (when the early warning system triggers) against the actual transition time (when the order parameter Φ first crosses the boundary).
| Metric | SMC-Active | SMC-Off |
| --- | --- | --- |
| Detection accuracy (Transition 1→2) | 98.1% | 87.3% |
| Detection accuracy (Transition 2→3) | 96.4% | 71.6% |
| Mean lead time (steps before crossing) | 24.7 ± 6.3 | 11.2 ± 4.8 |
| False positive rate | 3.2% | 12.7% |
| False negative rate | 2.1% | 16.1% |
The SMC-active system achieves significantly better detection accuracy, particularly for the critical Phase 2 → Phase 3 transition, and provides more than double the lead time. The improved performance comes from the aggregated SMC signal, which averages out local noise and reveals population-level trends that are invisible to individual agents.
10.3 Cascade Containment Results
We inject catastrophic failures (reducing a randomly selected agent's quality to 0.1 for 5 time steps) at t = 200 and measure the resulting trust cascade extent.
| Metric | SMC-Active | SMC-Off |
| --- | --- | --- |
| Cascades contained within 1 hop | 89.7% | 34.2% |
| Cascades reaching > 50% of network | 2.8% | 43.1% |
| Mean affected population fraction | 0.07 ± 0.04 | 0.38 ± 0.22 |
| Recovery time to T̄ within 5% of pre-failure | 18.4 ± 7.2 steps | 67.3 ± 31.5 steps |
| Cases where cascade triggered Phase 3 entry | 1.2% | 22.6% |
The cascade containment improvement from SMC is dramatic. Without metacognition, cascades frequently reach majority of the network and can trigger full phase transitions. With SMC active, the combination of scope isolation (agents communicating the localized nature of failures), transparency increases (unaffected agents proactively building trust), and preemptive dependency reduction contains cascades within small neighborhoods.
10.4 Capability Preservation Results
We track K̄_h^t across all 800 SMC-active runs to assess capability hollowing prevention.
| Metric | SMC-Active | SMC-Off |
| --- | --- | --- |
| Minimum K̄_h across all runs | 0.72 | 0.31 |
| Runs where K̄_h < 0.6 at any point | 0.0% | 47.3% |
| Mean K̄_h at t = 500 | 0.78 ± 0.04 | 0.52 ± 0.18 |
| Graduated withdrawal activations | 156 / 800 runs | N/A |
| Mean withdrawal duration | 34.2 ± 12.8 steps | N/A |
The SMC-active system successfully prevents capability hollowing across all parameter configurations, maintaining K̄_h ≥ 0.72 even in the most aggressive delegation scenarios. The graduated withdrawal mechanism activates in 19.5% of runs, indicating that metacognition does not simply prevent delegation but allows high delegation when safe and intervenes only when knowledge capital threatens to decline below threshold.
10.5 Network Topology Effects
We compare results across the three network topologies to understand how graph structure influences societal dynamics.
| Property | Random (ER) | Scale-Free (BA) | Small-World (WS) |
| --- | --- | --- | --- |
| Mean cascade extent (SMC-Off) | 38% ± 22% | 52% ± 28% | 31% ± 19% |
| Mean cascade extent (SMC-Active) | 7% ± 4% | 12% ± 7% | 5% ± 3% |
| Phase 2→3 transition threshold Φ_c2 | 0.80 | 0.62 | 0.85 |
| SMC convergence time (cycles) | 11.3 | 8.7 | 14.2 |
| Stability region size | Medium | Smallest | Largest |
| Critical exponent ν | 0.50 | 0.39 | 0.47 |
Scale-free networks are the most vulnerable topology: their high-degree hubs amplify cascades and reduce the phase transition threshold, meaning the system enters the Dependent phase at lower order parameter values. However, scale-free networks also enable the fastest SMC convergence because hub agents can rapidly aggregate and disseminate metacognitive assessments. Small-world networks are the most resilient: their high clustering creates natural cascade barriers while their short paths ensure information flow. Random graphs fall between the two extremes.
10.6 Sensitivity Analysis
We identify the parameters with the largest influence on system behavior through a global sensitivity analysis (Sobol indices).
| Parameter | First-Order Sobol Index | Description |
| --- | --- | --- |
| β_D (social dependency contagion) | 0.28 | Strongest driver of phase transitions |
| γ_{spill} (cross-agent trust spillover) | 0.21 | Amplifies cascade severity |
| β_T (trust loss rate) | 0.17 | Controls cascade initiation sensitivity |
| r_info (information radius) | 0.14 | Determines metacognitive reach |
| α_D (individual dependency growth) | 0.09 | Individual-level delegation tendency |
| γ_T (social trust contagion) | 0.07 | Social trust amplification |
| Other | 0.04 | Remaining parameters |
The dominance of β_D confirms that social dependency contagion is the primary risk factor for societal-level instability—more important than any individual-level parameter. This validates the thesis that societal models capture dynamics invisible to dyadic analysis: the most dangerous parameter in the system has no analogue in the isolated pair model.
11. MARIA OS Integration
11.1 Galaxy-Level Coordination
The MASCE framework maps directly to the MARIA OS coordinate system. At the Galaxy level (G), the full interaction graph G corresponds to the enterprise-wide deployment. Galaxy-level SMC provides the highest tier of collective metacognition, aggregating assessments from all Universes to detect enterprise-wide trends such as cross-business-unit capability hollowing or organization-wide trust shifts.
The Galaxy administrator dashboard exposes the order parameters Φ^t, K̄_h^t, D̄^t, T̄^t in real-time, with phase boundary indicators and early warning alerts when the system approaches critical thresholds. The MARIA topology map visualizes the interaction graph colored by local order parameter values, revealing spatial patterns of trust, dependency, and capability that are invisible in aggregate statistics alone.
11.2 Zone-Level Distributed Metacognition
At the Zone level (Z), each operational unit runs its own local SMC instance. Zone-level SMC monitors the subgraph G_k corresponding to the zone, computing local order parameters and triggering local containment strategies when instabilities are detected. The key advantage of zone-level SMC is speed: local containment can be activated within 2-3 time steps, while galaxy-level coordination takes 10-15 steps due to the larger communication distances.
Zone boundaries in the MARIA coordinate system correspond to the community structure of the interaction graph. When zones are well-aligned with graph communities (high modularity), they serve as natural firebreaks that contain cascades. MARIA OS provides tools for analyzing zone-graph alignment and recommending restructuring when the organizational structure has diverged from the actual interaction patterns.
11.3 Decision Pipeline at Societal Scale
The Decision Pipeline engine in MARIA OS implements the governance transitions required for Phase 4 (Institutional) operation. The six-stage pipeline (proposed → validated → approval_required → approved → executed → completed) corresponds to a series of responsibility gates that are dynamically configured based on the local order parameters. When a zone's Φ approaches Φ_c2, the pipeline automatically escalates more decisions to human approval, reducing delegation and slowing the approach to the phase boundary.
Every pipeline transition creates an immutable audit record in the decision_transitions table, providing the evidence base for post-hoc analysis of near-miss events. The responsibility gates framework allows zone-level customization: zones with robust human capabilities can operate with lighter governance, while zones approaching capability thresholds receive enhanced oversight.
11.4 Civilization Simulation as Validation Platform
The Civilization simulation experiment in MARIA OS (4 nations, economy, politics, migration, AI advisors) provides a controlled environment for validating MASCE predictions. The simulation's LOGOS AI advisor implements a simplified version of SMC, and the nation-level dynamics exhibit analogues of all four phases identified in the theoretical model. The 90-day simulation clock allows rapid iteration through phase transitions that would take months or years in real organizational deployments.
By comparing civilization simulation trajectories with MASCE predictions, developers can calibrate model parameters against observed dynamics and test new containment strategies in a safe sandbox before deploying them in production governance systems.
12. Conclusion
The Multi-Agent Societal Co-Evolution Model (MASCE) extends human-AI co-evolution theory from isolated dyads to organizational-scale networks. By modeling the full interaction graph of N humans and M AI agents, the framework captures three classes of emergent phenomena that are invisible in pair models: trust cascades propagating through social networks, dependency contagion spreading through behavioral normalization, and capability hollowing accumulating across populations.
The theoretical analysis yields two central results. The Social Stability Theorem (Theorem 1) establishes a precise relationship between network topology (spectral gap, maximum degree), coupling parameters, and system-wide stability. This relationship provides concrete design guidelines: organizations can engineer stability by controlling team sizes, maintaining inter-unit connectivity, and calibrating AI transparency mechanisms. The SMC Convergence Theorem (Theorem 2) proves that distributed metacognition reaches consensus in logarithmic time on well-connected graphs, establishing the feasibility of collective self-assessment at organizational scale.
The simulation results validate the theoretical predictions with compelling quantitative evidence. Phase transition detection accuracy of 96.4%, trust cascade containment of 89.7%, and capability preservation above K̄ > 0.72 across all parameter regimes demonstrate that Social Metacognition is a practical and effective stabilization mechanism. The sensitivity analysis confirms that social contagion parameters dominate system behavior, reinforcing the necessity of societal-level (rather than individual-level) analysis and intervention.
Perhaps the most profound implication of this work is the identification of Phase 4 (Institutional) as an engineered rather than natural equilibrium. Organizations cannot passively trust that AI-human dynamics will reach a healthy steady state. Active governance—continuous monitoring, dynamic responsibility gates, graduated intervention—is required to maintain the Institutional phase. MARIA OS implements this philosophy through its coordinate system, decision pipeline, and metacognitive monitoring infrastructure.
Future work will extend the model to heterogeneous agent populations (where AI agents have different specializations and error profiles), dynamic graph topologies (where the interaction structure itself evolves in response to trust and dependency changes), and multi-scale governance (where metacognitive strategies operate simultaneously at zone, planet, universe, and galaxy scales). The theoretical framework developed here provides the foundation for these extensions and, more broadly, for a rigorous science of AI governance at the societal scale.
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