Hip To Be Square But Anarchy != Order

22 Apr, 2026

...at least not yet, because the scheme (wait for it!) proposed by Gemini Pro 3.1 Deep Research for the problem I presented it with has this major caveat: it seriously still needs it's Bluff - Catching Committee, enter hierachical authority. Otherwise participants could all too easily simply a) pretend things are more important to them than they actually are or b) pretend a greater willingness to walk away than is real, or a combination of a) and b), which provides unacceptable amount of 'gaming the system' - leverage. But anyway it gave me something to think about and reflect upon, hopefully for you too!

My initial prompt:

Assume the role of a practically and holistically inclined advisor / teacher who sees the forest from the trees and keeps things at the level of their irreducible complexity, no more, no less.

Just how did John Nash "solve cooperative bargaining" (a claim by the founder of mediator.ai on YCHN)? Don't use the example at mediator.ai front page. Instead teach the simple idea behind it. Then clarify it's relation to these things 1) constraint solver - type problem solving 2) category theory, I mean using category theory as a kind of meta - scema to both Nash and constraint solving.

Focus solely on how this all applies to a hypothetical group formed for the purpose of mutual aid and whose members want to produce a real synergic win - win situation for it's members.

The output format should be like a first draft for the founding charter of such an organisation and introduction to it's underlying theoretical foundation.

https://mediator.ai/ https://news.ycombinator.com/item?id=47835411

It's response:

Founding Charter and Theoretical Architecture for Synergic Mutual Aid Organizations

Introduction: The Holistic View of Human Cooperation

The architecture of sustained human cooperation requires moving beyond mere aspirations of goodwill. Historically, informal cooperative endeavors, including mutual aid networks and community resource pools, have frequently succumbed to the frictions of unspoken grievances, the combinatorial explosion of complex decision-making, and the ultimate exhaustion of their most dedicated members. When individuals attempt to organize solely on the basis of altruism, they often encounter a scaling limit; everyday forms of collectivism burn out when they lack a structural mechanism to process complex disputes and scale equitable decisions. To establish a mutual aid organization capable of delivering a genuine, persistent, and synergistic win-win situation for all its members, the institutional design must be grounded in mathematical rigor. It must operate at the level of irreducible complexity: capturing the essential dynamics of human preference, power, and physical constraints—no more, and no less. This document serves as both the theoretical foundation and the inaugural charter for a new paradigm of synergic mutual aid. It establishes a structural framework based on three interdependent mathematical paradigms: the Nash Cooperative Bargaining Solution, Constraint Satisfaction Problem (CSP) architecture, and Category Theory. Together, these frameworks provide a rigorous, holistic mechanism for translating subjective human needs into fair, enforceable, and scalable cooperative agreements. The goal of this organization is not charity, which implies a unidirectional transfer of energy, but synergy. As observed in the optimization of multi-microgrid energy systems, true mutual aid occurs when the coordinated sharing of resources unlocks efficiencies that reduce total system costs, eliminate waste, and generate a surplus that no single entity could produce in isolation. We seek to apply this exact principle of networked, synergic optimization to human labor, capital, and time.

Part I: The Mechanics of Cooperative Bargaining

The fundamental, irreducible challenge of any mutual aid group is the division of jointly created surplus. When individuals pool resources, time, or labor, they generate a total value greater than the sum of their isolated efforts. This surplus is the lifeblood of the cooperative. However, the exact distribution of this surplus presents a profound operational challenge. If the distribution is perceived as unfair, or if it systematically exploits one member's patience or resources, the cooperative structure inevitably fractures.

Teaching the Simple Idea: Maximizing the Product

In 1950, mathematician John Nash formalized a solution to the cooperative bargaining problem that avoided the pitfalls of arbitrary human mediation, emotional manipulation, or rigid top-down authority. The simple yet profound idea underlying Nash's solution is the mathematical maximization of fairness through the multiplication of individual gains. To understand the elegance of this, one must first understand the baseline. The mechanism assumes that every participant has a "disagreement point" or "fallback" position, often referred to in modern negotiation theory as the Best Alternative to a Negotiated Agreement (BATNA). This point, denoted mathematically as d_i for an individual i, represents the utility, wealth, or well-being a person retains if no cooperative agreement is reached and they simply walk away. For a mutual aid organization, the baseline is the condition of isolation. The absolute minimum requirement for an agreement is that it selects a set of outcomes (a payoff vector) that leaves every single participant strictly better off than their disagreement point. While traditional utilitarian philosophy attempts to maximize the total sum of utility across all participants (\sum (u_i - d_i)), this method frequently results in highly skewed distributions. Consider a scenario where a mutual aid cooperative generates a surplus valued at 10 units. If the system attempts to maximize the sum, any combination (9 + 1, 7 + 3, or 5 + 5) yields the exact same total sum of 10. A sum-maximizing algorithm possesses no internal mechanism to differentiate between deep exploitation and perfect equity; if allocating all resources to the most efficient member generates a slightly higher total sum (e.g., 10.1 + 0), the mathematics will demand exactly that, leaving the other member with nothing but their baseline. This violates the psychological and functional requirements of mutual aid. John Nash solved this by proving that the only uniquely fair division of surplus is the one that maximizes the product of the participants' utility gains. The Nash product is mathematically expressed as: Where n is the number of participants, u_i is the utility achieved by participant i under the proposed agreement, and d_i is their disagreement baseline.

The Geometric Intuition of Fairness

The intuition behind maximizing the product rather than the sum is deeply geometric and foundational to holistic systems thinking. If you are tasked with creating a rectangle with a fixed perimeter (a metaphor for a fixed amount of surplus to distribute), the rectangle that yields the maximum possible area (the product of its sides) is always a perfect square. In the realm of bargaining, the product of 9 and 1 is merely 9. The product of 7 and 3 is 21. But the product of 5 and 5 is 25. The mathematical nature of multiplication heavily penalizes extreme inequalities. By maximizing the Nash product, the system intrinsically seeks out the most balanced distribution of value, automatically gravitating toward the "square" of perfect equity. Crucially, this mechanism adjusts seamlessly to differing needs, baselines, and leverage. Game-theoretic fairness does not pretend that disparities do not exist; rather, it acknowledges power—defined as the ability to inflict disutility on a counterparty by walking away—and neutralizes it through proportional gains. If one member is risking significantly more capital or time (resulting in a higher baseline d_i that they forfeit upon failure), the Nash product cannot be maximized unless that member receives a proportionately larger share of the surplus. It ensures that absolutely no "value is left on the table" and that the benefits of the cooperative deal are divided proportionately to the relative gains each side achieves compared to their walk-away point.

The Axiomatic Foundations of Equity

The Nash bargaining solution is not an arbitrary heuristic; it is the mathematically inevitable result of four irreducible axioms of fairness. Any mutual aid system that wishes to remain holistically stable must structurally uphold these four axioms in every interaction :

While alternative axiomatic solutions exist—most notably Kalai's proportional solution (the Kalai-Smorodinsky model), which replaces the scale invariance axiom with a strict monotonicity axiom to ensure proportionality based on maximum possible gains—the Nash solution remains the most robust for decentralized cooperative organizations. The Nash model's reliance on scale invariance allows for a vastly more decentralized evaluation of utility, which is vital when members of a mutual aid group are trading fundamentally different forms of value (e.g., childcare hours for carpentry work) where establishing a unified, monotonic scale of utility is impossible.

Risk Aversion and Asymmetry

A holistic view of bargaining must account for the psychological realities of the participants. Game theory demonstrates that in bargaining scenarios, the more risk-averse player inherently captures a smaller share of the surplus. If Player A is terrified of the negotiation breaking down (a high risk of breakdown) and Player B is comfortable walking away, Player B will naturally secure a larger portion of the Nash product. In a traditional capitalist market, this is viewed as a feature of leverage. In a mutual aid organization, however, unmitigated risk aversion can lead to the slow exploitation of the most vulnerable members—those who rely most heavily on the cooperative. By abstracting the negotiation process into a mathematical algorithm that optimizes the Nash product independently of the real-time emotional panic of the participants, the system protects risk-averse members from being bullied into suboptimal deals. The math calculates what is fair based on objective inputs, insulating the vulnerable from the adversarial brinkmanship of traditional bargaining.

Part II: Constraint Satisfaction: The Topography of Reality

While Nash bargaining provides the mechanism for selecting the optimal point of agreement, it requires a defined space of possibilities from which to choose. The universe of possible agreements is termed the "feasibility set". In reality, human cooperation is strictly bounded by physical, temporal, and cognitive limitations. Before a mutual aid group can divide a surplus, it must first calculate what is mathematically and physically possible. This is the domain of the Constraint Satisfaction Problem (CSP) paradigm, and understanding its relation to Nash bargaining is the key to preventing organizational burnout.

Defining the Feasible Space

A constraint satisfaction problem is defined mathematically by three interdependent components :

1. Variables (V): A set of elements {v_1, v_2,..., v_n} representing the decisions the mutual aid group must make. These could represent who performs a specific task, what time a shared vehicle is utilized, or how much capital is drawn from a shared fund.
2. Domains (D): A set of discrete or continuous values {d_1, d_2,..., d_n} that those variables can assume. For instance, the domain for a labor variable might be the available hours in a week; the domain for a financial variable might be the total integers between 0 and the cooperative's bank balance.
3. Constraints ©: A set of strict mathematical relations {c_1, c_2,..., c_m} that restrict the allowable combinations of variable values. In the context of a synergic win-win organization, constraints are not punitive restrictions; they are the bedrock of psychological safety and operational realism. Constraints may include participation thresholds (e.g., no member may be asked to contribute more than 10 hours of manual labor a week), resource limits (e.g., the shared server can only process 100 terabytes a month), or liquidity bounds (e.g., the emergency financial pool cannot drop below a $5,000 reserve threshold).

The Symbiosis of CSP and Nash Bargaining

The relationship between constraint solving and cooperative bargaining is foundational to our institutional design. They are two halves of the same holistic cognitive process. CSP algorithms—whether utilizing backtracking, heuristic search, or constraint propagation—serve to carve out the boundary of reality. They sift through millions of combinatorial possibilities to establish what economists call the "upper contour" of the gains from trade function: the strict frontier of feasible agreements where the participation constraints of every individual are satisfied. If constraint solving is the cartography of the possible, Nash bargaining is the compass pointing to the optimal destination within that map. The integration of these two frameworks operates as follows:

1. Phase 1 (Constraint Solving): The mutual aid infrastructure maps the resources, hard limits, and time capacities of its members. It establishes strong k-consistency, ensuring that any localized agreement between a subset of members does not violate the global constraints of the broader network. This filters out any physical impossibilities, contradictory commitments, or agreements that breach individual BATNAs (fallback points). This phase produces a multi-dimensional geometry of valid, feasible agreements—the "unblocked set".
2. Phase 2 (Nash Optimization): Operating exclusively within this strictly mapped feasibility set, the system then searches for the single coordinate that maximizes the Nash product, thereby locating the optimal point of synergy and fairness. This interplay fundamentally resolves a vulnerability in traditional, informal mutual aid groups, which often burn out due to "scope creep" and guilt-driven overcommitment. By systematically defining constraints before engaging in surplus negotiation, the organization ensures that it never formulates a "fair" distribution of an impossible workload. The CSP defines the structural limits of human empathy and physical reality; the Nash solution ensures maximum equity within those limits.

Part III: Category Theory as the Meta-Schema of Scale

A profound operational limitation emerges when mutual aid organizations attempt to scale. The Nash bargaining solution and CSPs are computationally and cognitively straightforward when applied to isolated, two-person interactions (e.g., two members dividing the labor of a shared garden). However, as a mutual aid group grows to encompass dozens or hundreds of members, engaging in dynamic, overlapping, multi-party agreements, the mathematical complexity undergoes a combinatorial explosion. To maintain an environment of irreducible complexity at scale—seeing the forest from the trees without losing the integrity of the individual leaves—the underlying architecture must transition from analyzing isolated games and constraints to analyzing their universal structural relationships. This requires Category Theory.

The Mathematics of Compositionality

Category theory is a highly abstract branch of mathematics that focuses on structures and the relationships (morphisms) between them, rather than the specific, granular details of the objects themselves. It provides a universal "meta-schema" that allows vastly different mathematical concepts to be translated into a common operational language. In recent years, "Applied Category Theory" has emerged to solve complex coordination problems in economics, physics, and social sciences. For our mutual aid organization, category theory serves as the grammar of reality. Under this schema, smaller games and constraint problems act as primitive components—akin to building blocks or logic gates. Recently, theorists have introduced "Compositional Game Theory," utilizing symmetric monoidal categories to construct "open games". Traditional game theory treats a strategic interaction as a closed system: a definitive, inescapable matrix of players, actions, and payoffs. An open game, by contrast, is a game played relative to an arbitrary environment, where information and utility flow into and out of the game's boundaries via "string diagrams". This introduces the concept of coutility—which is the utility generated by an open game and returned to its environment (the broader mutual aid network). These open games (our mutual aid agreements) can be combined using two fundamental algebraic operations :

• Sequential Composition: Linking the output of one mutual aid agreement to the input of another via categorical composition. For example, the synergic surplus yield of an agricultural open game feeds directly into the constraint domain of a communal kitchen open game.
• Parallel Composition (Monoidal Products): Executing independent agreements simultaneously without interference, while accurately tracking their combined state through monoidal products.

Unifying Nash, Constraints, and Categories

Category theory reveals the deep structural unity between constraint satisfaction and cooperative bargaining. In advanced computational mathematics, the algebraic structure of constraint polymorphisms can be explicitly described as set-functors defined as right Kan extensions. Similarly, Nash equilibria, bargaining solutions, and best-response dynamics are modeled as functors mapping from a category of games to a category of sets. By treating both the CSP feasibility boundaries and the Nash bargaining optimization as morphisms within a symmetric monoidal category, the mutual aid organization can achieve true, frictionless modularity. This implies a radical reimagining of organizational governance. A sub-group of three members can formulate an internally coherent, Nash-optimized, constraint-satisfied agreement. Through categorical composition, this sub-agreement can dynamically interact with another sub-agreement formed by five other members across the city. The organization does not need to recalculate a massive, monolithic global Nash product from scratch for all eight people, which would be computationally prohibitive. Because the components are categorically robust and equilibria-preserving, the systemic composition of fair micro-agreements reliably and automatically scales into a macro-institution of fairness. Category theory provides the architectural blueprint that allows the mutual aid group to function as a complex, decentralized organism. It transforms rigid bureaucracy into fluid, string-diagrammatic workflows, allowing the organization to process shifting constraints and preferences seamlessly across various nodes of cooperation. It is the ultimate holistic tool: ensuring that the interconnectedness of the forest never violates the specific constraints of the trees.

Part IV: The Technological Engine of the Cooperative

The theoretical elegance of Nash bargaining and CSPs has historically faced a massive practical roadblock: human cognition. John Nash's solution requires each party to provide a precise "utility function"—a mathematical equation that takes a set of deal terms and produces a specific utility number. Even trained economists find it nearly impossible to accurately map their own complex, multi-dimensional preferences into an absolute score for non-trivial negotiations. If a mutual aid organization relies on its members to manually draft their utility functions and calculate Nash products, the organization will fail instantly. Therefore, the cooperative must employ a technological engine to bridge the gap between human subjectivity and mathematical optimization.

Preference Elicitation via Pairwise Comparison

Instead of demanding absolute scores (e.g., "Rate your desire for the community van on Tuesday on a scale of 1 to 100"), the organization's technological infrastructure utilizes iterative, pairwise comparisons. Humans are notoriously bad at absolute valuation, but we are exceptionally good at comparative valuation. Members interact with an automated elicitation system (potentially powered by Large Language Models or similar conversational agents) that captures their individual preferences. The system asks hundreds of constrained, head-to-head questions: “Given your priorities, would you prefer outcome A or outcome B?”. From this matrix of pairwise rankings, the system mathematically infers an approximate utility function that allows it to rank any new potential agreement on behalf of the user. Crucially, this conversational elicitation is designed to "tease out unstated preferences". Mediation and mutual aid involve deep human and emotional components; often, a member's primary desire is not just resource allocation, but an acknowledgment of past labor, a need for rest, or an apology for a previous friction. By capturing these soft, hidden interests and mapping them into the utility inference, the system ensures that the eventual Nash calculation honors the whole human, not just the financial or temporal transaction.

Genetic Search within the Feasible Space

Once the utility functions are inferred and the constraint solver has mapped the boundaries of the possible, the system must find the agreement that maximizes the Nash product. Because the feasible space of a multi-variable mutual aid agreement is vast, the organization employs a genetic algorithm to search for the optimal outcome.

Through this evolutionary search process, the algorithm inevitably gravitates toward agreements that both parties prefer over their BATNA, identifying mutual improvements and synergic win-wins that the human participants could never have manually calculated. The AI drafts the terms, acting purely as a facilitation layer. It does not arbitrate or enforce; it merely presents the mathematically optimal synthesis of the members' stated desires, which the members are then free to formally adopt.

Part V: The Founding Charter of the Mutual Aid Organization

The following articles serve as the constitutional scaffolding for the mutual aid organization. They are designed to operationalize the theories of Nash Bargaining, Constraint Satisfaction, and Categorical Composition into an actionable, binding framework for synergic human cooperation.

Preamble

We, the founding members of this mutual aid organization, recognize that genuine, sustained cooperation cannot rely solely on the volatility of altruism, nor can it thrive under the zero-sum mechanics of unbridled self-interest. We exist to synthesize an environment where the collective whole consistently produces more value than the sum of its individual parts. To protect the integrity of our members and the stability of our community, we reject arbitrary mediation, emotional coercion, and power-based hierarchies. Instead, we establish this organization upon the bedrock of rigorous mathematical fairness, structural feasibility, and modular scalability. This Charter outlines the irreducible mechanics of our cooperation, guaranteeing that every interaction generates a true, synergistic win-win outcome.

Article I: The Axiom of Synergy and Mutual Benefit

Section 1.01: The Purpose of Association The sole operational objective of this organization is the generation and equitable distribution of synergic surplus. Synergy is defined as the tangible or intangible value created when members combine resources, labor, or cognitive capacity, exceeding what those members could have achieved in isolation. Section 1.02: Rejection of Zero-Sum Engagements No organizational mechanism shall be utilized to facilitate zero-sum transfers, where one member's gain is strictly predicated on another member's loss. All formal agreements registered under this organization must mathematically demonstrate the existence of a cooperative surplus prior to execution.

Article II: Individual Sovereignty and the Disagreement Point

Section 2.01: The Recognition of BATNA The organization recognizes that cooperative strength derives from voluntary association. Every member possesses a baseline state, defined as their Best Alternative to a Negotiated Agreement (BATNA), or their "disagreement point". This represents the resources, time, and well-being a member retains if they choose not to enter a specific mutual aid agreement. Section 2.02: Absolute Protection of Baselines No agreement within this organization shall be deemed valid if it requires a member to accept an outcome inferior to their disagreement point. Individual rationality is a strict prerequisite for participation. The organization views the BATNA not as a threat, but as an essential, structurally vital boundary that ensures psychological safety and prevents exploitative dynamics. Section 2.03: Mitigation of Leverage-Seeking and Bluffing While the BATNA is protected, the system operates on the assumption that parties desire a fair deal. Members are prohibited from utilizing the preference elicitation process maliciously to gather data for adversarial leverage-seeking. Because mathematical algorithms cannot easily distinguish between a genuine willingness to walk away and a strategic bluff, chronic manipulation of BATNA parameters to artificially skew the Nash product violates the social contract of the cooperative and is grounds for peer review.

Article III: The Rule of Constraint Feasibility

Section 3.01: Definition of the Feasible Space Prior to any allocation of surplus or formulation of obligation, all agreements must map the strict boundaries of physical, temporal, and psychological reality. This process constitutes the organization's internal Constraint Satisfaction Protocol. Section 3.02: Declaration of Limitations Members entering an agreement must transparently declare their constraints. These include, but are not limited to:

• Maximum allowable time contributions.
• Hard limits on capital or physical resource expenditure.
• Dependencies on other ongoing organizational agreements. Section 3.03: Algorithmic Veto and the Upper Contour Any proposed agreement that violates the declared constraints of any participant, or violates the thermodynamic limits of the organization's shared resources, is deemed mathematically unfeasible. Such proposals fall outside the "upper contour" of feasible agreements and shall be immediately rejected or reformulated by the constraint solver before any negotiation of terms begins, ensuring the organization never attempts to divide an impossible outcome.

Article IV: The Mechanism of Nash Value Allocation

Section 4.01: The Standard of Fairness When a feasible space of cooperation has been established, and a synergic surplus is identified, the distribution of that surplus shall not be determined by majoritarian voting, hierarchical authority, or the raw sum of generalized utility. The distribution shall exclusively utilize the logic of the Nash Cooperative Bargaining Solution. Section 4.02: Product Optimization Over Sum Optimization The organization formally rejects the utilitarian maximization of the sum of benefits, which permits deep, localized inequalities in the name of total systemic efficiency. All agreements shall aim to maximize the product of the individual gains over their respective disagreement points. This mathematical rule structurally mandates equity, heavily penalizing unequal distributions and naturally allocating value proportionately to those who sacrifice the most relative to their baseline. Section 4.03: Enforcement of the Four Axioms Every agreement brokered by the organization's technological engine must withstand audit against the four foundational axioms of John Nash :

1. Efficiency: No surplus is wasted or left on the table.
2. Symmetry: Identical contributions and constraints yield identical rewards, blind to external social status.
3. Scale Invariance: Members are permitted to value their time and resources subjectively; the system balances relative, not absolute, subjective values.
4. Independence of Irrelevant Alternatives: The introduction or retraction of hypothetical solutions does not destabilize existing fair agreements.

Article V: Categorical Scaling and Modularity

Section 5.01: The Architecture of Composition The organization recognizes that enforcing constraints and Nash optimality across a large population simultaneously is computationally and socially intractable, leading to the collapse of traditional collectivism. Therefore, the organization structures its macro-governance according to the principles of Compositional Game Theory and Category Theory. Section 5.02: Modularity of Agreements (Open Games) Agreements between small subsets of members shall be treated formally as "open games" or categorical morphisms. An agreement between three people regarding a local tool-library is an autonomous, self-contained module. It generates a specific coutility (output) based on specific constraints (inputs). Section 5.03: Sequential and Parallel Integration The organization expands not by creating monolithic, centralized treaties, but by diagrammatically wiring together local agreements.

• Modules may run in parallel (e.g., a child-care cooperative module operates independently alongside a community garden module).
• Modules may compose sequentially (e.g., the output of the garden module serves directly as the constraint input for a neighborhood kitchen module). By utilizing symmetric monoidal architectures to compose these micro-agreements, the organization guarantees that the macro-structure remains inherently fair and stable, proving that the complexity of the whole does not compromise the mathematical fairness of the parts.

Article VI: Dispute Resolution and Human Primacy

Section 6.01: Facilitation, Not Arbitration While the organizational architecture utilizes computation, genetic algorithms, and constraint solvers to generate candidate agreements, the system acts strictly as a facilitator. The AI drafts the terms and maps the Nash products, but it cannot make them legally or socially binding on its own. Section 6.02: The Ultimate Human Veto The ultimate authority to accept, modify, or reject an agreement rests solely with the human participants. Every member retains the unalienable right to exercise their BATNA and reject any proposed synthesis if it feels "brittle" or fundamentally flawed in a way the algorithms failed to capture. Section 6.03: Resolution of Infeasibility If the constraint solver identifies an empty feasibility set—meaning no agreement can be reached without violating someone's baseline limitations—the organization shall not use social pressure, guilt, or majority rule to force an agreement. Instead, the involved members must either:

1. Temporarily dissolve the cooperative effort in that specific domain, resting in their BATNA.
2. Broaden the systemic boundaries by importing surplus from a sequentially composed module elsewhere in the categorical network.

Conclusion: The Horizon of Synergic Win-Win

The failure of historical mutual aid initiatives frequently stems from a reliance on an unsustainable cognitive and emotional load. Members are asked to continuously navigate the treacherous waters of resource scarcity, implicit expectations, and guilt, leading inevitably to friction, power disparities, and dissolution. By offloading the architecture of fairness to the mathematical rigors of the Nash Cooperative Bargaining Solution, mapping the strict boundaries of reality via Constraint Satisfaction algorithms, and scaling these interactions seamlessly through the topological logic of Category Theory, this organization achieves a fundamental paradigm shift. It treats human capacity not as an infinite resource to be exploited by a collective, but as a bounded, sacred constraint. It treats mutual benefit not as an aspirational slogan, but as a geometric optimization problem to be systematically solved. This Charter ensures that the organization remains a continuous, frictionless engine for synergy. By keeping the mechanisms at the level of their irreducible complexity, the mutual aid network becomes an anti-fragile institution: one where the self-interest of the individual and the prosperity of the collective are mathematically and inextricably linked, securing a persistent, verifiable win-win reality for all members.

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