Computation, Data, and Agent Dynamics

Part I: Domain and Foundations

Domain Assumptions

Resource-constrained multi-agent systems
Non-zero energy costs for all processes
Agents can alter their internal state or behavior in response to information
Agents act to optimize value capture within their constraints, subject to bounded rationality and heterogeneous objectives
No exogenous institutions, laws, or social structures exist as primitives; all persistent coordination emerges from agent interaction
This framework describes structural forces and pressure gradients at a given system state. Trajectories—how systems evolve over time under these forces—depend on relative rates of change and are better addressed through simulation using the framework as substrate

Definitions

Three terms carry the framework's analytical weight and are defined before use. All are descriptive: they identify features of resources and arrangements, not judgments about them.

Definition 1Value. The value of a resource to an agent is its convertibility — direct or indirect — into energy, or into capability, position, or optionality that acquires or spares energy for that agent. Value is agent-indexed, not intrinsic: the same resource converts at different rates for different agents because conversion depends on the agent's computational architecture, accumulated state, and position (Axioms 6, 7); value heterogeneity (Axiom 3) thereby has a physical reading rather than a stipulated one. Commensurability with energy is what licenses the framework's comparisons of value capture against energy cost (Theorems 1, 13); it does not require a fixed energy price for every holding — optionality carries value through the futures it keeps reachable.

Definition 2Externalization. An agent externalizes data when the data becomes available in computable form at a locus the agent does not control — whether by transfer in computable form or by granting an uncontrolled locus the means to render held data computable. Placement alone is not externalization: data held by an uncontrolled locus in a form it cannot render computable (e.g., encrypted without the decryption means) is externally stored but not externalized. Externalization is a matter of degree — where technical measures bound what a receiving locus can compute from received data, only the computable residue is externalized (see Axiom 2, Theorem 18). Externalizing computation — performing one's processing at an uncontrolled locus — entails externalizing the data that computation operates on, and is treated accordingly throughout.

Definition 3Extraction. An agent or structure A extracts value from agent B when A captures value (Definition 1) attributable to B — to B's data, B's computation, or influence over B's behavior — in excess of what B would concede under full information about the capture and its consequences, with feasible alternatives available. The excess is the extractive component of the arrangement. Informed, freely conceded compensation — payment for computation, storage, or processing, accepted with alternatives available — is the paradigm of zero extraction: the capture equals the concession. Extraction is component-wise, not net: a single relationship can simultaneously create value for B and extract from B (see Theorem 27). Tolerated capture remains extraction where toleration reflects opacity (see Theorem 32) or absence of feasible exit (see Theorem 26) rather than informed, free concession. For data produced by multi-agent events (Axiom 14), extraction is assessed per participant.

Note: Definition 3's benchmark is counterfactual and not directly observable. It serves as the definitional standard; Theorems 21, 22, 24, and 25 address why agents cannot compute it precisely in practice, and Theorem 32 addresses how its inaccessibility is itself exploited. The operational proxy for the benchmark is the question "did the capture stay within informed, agreed terms?" — the proxy fails in exactly two ways: agreement without information (opacity, Theorem 32) and agreement without alternatives (necessity, Theorems 26 and 29). The information failure includes objective under-specification: terms stated as broad purposes — "to provide and improve the service" — are consent-in-form to any objective those purposes can absorb, so a locus can switch what its processing optimizes without leaving the agreed terms (see Tension 7, Part IV). Capture that passes the proxy while failing the benchmark is extraction the source agent cannot currently detect or refuse.

Part II: Axioms

Physical Constraints

Axiom 1Universal Cost. All processes—computation, information production, data storage, and transmission—require energy and therefore have cost. No process is free.

Axiom 2Locus Control. Control over data replication follows control of the physical locus of storage: an agent controlling a locus can copy what the locus holds. Control over data usage follows control of the means by which data is rendered computable: a locus holding data in a form it cannot render computable can replicate that data but not use it. Where data resides at a locus in computable form, usage and replication control coincide at that locus.

Note: Transformations that withhold computability (encryption, secret sharing, noise injection) are processes bearing cost (Axiom 1), and they bound rather than eliminate what a holding locus can compute — sizes, timing, access patterns, and participation metadata typically remain computable. See Definition 2 and Theorem 18.

Agent Properties

Axiom 3Value Heterogeneity. The value of any given data varies across agents.

Axiom 4Access Asymmetry. Access to data and computation is inherently asymmetric among agents.

Axiom 5Capability Heterogeneity. Agents possess heterogeneous capabilities for operating computational loci.

Axiom 6Processing Differentiation. The capacity to extract value from data depends on the computational architecture and accumulated state of the processing locus, which varies across agents.

Axiom 7Accumulated Capability Cost. Developing computational architecture capable of processing specialized data requires prior energy expenditure accumulated over time, creating persistent differentiation among agents.

Axiom 8Processing Non-Fungibility. For certain data types, the computational architecture required for value extraction cannot be replicated within the time horizon relevant to the data's value.

Interaction Dynamics

Axiom 9Behavioral Prediction. Data and computation can be applied to predict agent behavior, preferences, and future states.

Axiom 10Behavioral Influence. Predictions about agent behavior can be leveraged to influence or modify that behavior.

Axiom 11Observation and Propagation. Agents can allocate energy toward observing other agents' behavior and can transmit resulting data to third parties at cost.

Axiom 12Behavioral Conditioning. Agents can condition their behavior toward agent A on data about A's past behavior, including A's behavior toward other agents.

Axiom 13Costly Signaling. Agents can transmit information about their future behavior by incurring costs that would be irrational unless the signaled intention were genuine.

Data Properties

Axiom 14Multi-Source Events. Many data-producing events necessarily involve multiple agents as causal participants, producing data that is inherently about all participants.

Axiom 15Observational Perspective. Data about the same underlying event differs depending on the observational position of the recording agent.

Axiom 16Data Entanglement. For data produced by multi-agent events, modification of one agent's copy can affect the accuracy of inferences made from another agent's copy, creating interdependence.

Axiom 17Modification Potential Heterogeneity. Data varies in its capacity to enable behavioral modification of a given agent. Some data enables fine-grained prediction and influence over that agent; other data enables only coarse or negligible influence.

Axiom 18Modification Potential Determinants. Data that enables prediction of agent behavior, reveals agent dependencies or failure modes, or reflects internal agent states has higher modification potential than data reflecting only external observables.

Axiom 19Relational Sensitivity. Modification potential is not intrinsic to data in isolation. It is a function of the relationship between the data, the target agent's current state, and what other data is accessible to the modifying agent.

Coordination

Axiom 20Coalition Formation. Agents can form persistent coordinated structures by allocating energy toward mutual monitoring, enforcement, and shared computation.

Axiom 21Commitment Mechanisms. Agents can constrain their own future action space by creating or submitting to structures that impose costs on defection.

Axiom 22Emergent Structures. Persistent coordination patterns maintained through dedicated energy expenditure constitute structures that can receive data, perform computation, exert influence, and interact with agents as quasi-agents.

Axiom 23Coordinated Locus Constraint. The coordinated actions of multiple agents can constrain an individual agent's control over its locus. The control that Axiom 2 assigns to a locus controller is therefore exercised subject to whatever constraints coordinated agents can impose.

Aggregate Phenomena

Axiom 24Combinatorial Information. Certain information states can only be instantiated through simultaneous access to data from multiple sources; they do not exist in any single data source.

Axiom 25Statistical Emergence. Patterns in aggregate data can enable predictions about individual agents that are impossible from any individual's data alone.

Axiom 26Positional Information. Data about an agent's relation to other agents constitutes information not fully present in either agent's individual data.

Axiom 27Network Effects. For certain coordination structures, the value delivered to each participant increases with the number of participants, creating positive feedback dynamics that concentrate participation in dominant structures.

Axiom 28Algorithmic Opacity. Agents processing externalized data can employ algorithms unknown to data providers. The effects of data externalization depend on processing algorithms, but data providers typically cannot observe or verify these algorithms.

Epistemic and Temporal Constraints

Axiom 29Epistemic Limitation. Agents operate under incomplete information that energy expenditure reduces but does not eliminate: (a) no agent can fully observe another locus's data holdings, internal state, or processing; (b) no agent can fully predict future system states, including the future value of data and the future behavior of other agents; (c) no agent holds a complete model of its own states and vulnerability structure. Axiom 28 states the special case of (a) for processing algorithms.

Axiom 30Discard Irreversibility. Discarding data is irreversible for the discarding agent except where the generating event can be re-observed or the data re-derived from other retained data. Retention decisions are therefore asymmetric: retained data can later be discarded, but discarded data generally cannot later be recovered.

Replication

Axiom 31Replication Asymmetry. Replicating and retaining existing data requires energy (Axiom 1) but typically far less than the original production of that data required — observing the generating event, performing the originating computation. Marginal copies are cheap relative to first instances. This asymmetry is why locus control confers replication at negligible cost (Axiom 2) and why holdings accumulate: retention and aggregation scale at marginal costs far below production costs.

Part III: Theorems

The theorems below describe systemic pressures, not individual agent motivations. An agent may prefer non-extractive interaction but face competitive pressure from agents that do extract (Theorem 3). The framework models the structural dynamics that produce extractive outcomes, which may persist even in systems where most agents prefer cooperation. Agents with non-extractive preferences face the additional challenge of sustaining those preferences against systemic selection pressure.

Theorem numbering follows thematic grouping rather than strict derivation order; a few results cite later-numbered theorems (Theorem 7 cites Theorem 8; Theorem 27 cites Theorem 29; Corollary 6a routes forward to Theorems 7, 30, and 34). The dependency graph is acyclic.

Survival and Competition

Theorem 1Survival Constraint. Loci of computation, data storage, and data production must receive explicit energy input or capture sufficient value to offset their costs; otherwise they are outcompeted or dissolve.

Derives from: Axiom 1 (Universal Cost).

Theorem 2Extraction Opportunity. Externalization of computation or data storage to another agent's locus creates opportunity for value extraction by the receiving agent.

Derives from: Axiom 1 (Universal Cost), Axiom 2 (Locus Control), Axiom 4 (Access Asymmetry).

Theorem 3Extraction Pressure. Loci that extract value from externalized data gain competitive advantage over those that do not, creating systemic pressure toward extraction even among agents that would otherwise prefer non-extractive arrangements.

Derives from: Theorem 1 (Survival Constraint), Theorem 2 (Extraction Opportunity).

Theorem 4Value Realization. The realized value of data is determined by the distribution of agent valuations, access asymmetries, processing capabilities, and competitive dynamics among agents.

Derives from: Axiom 3 (Value Heterogeneity), Axiom 4 (Access Asymmetry), Axiom 6 (Processing Differentiation).

Retention and Feedback

Theorem 5Retention Dynamics. There is an incentive to retain and aggregate data due to uncertain future value. Retention preserves optionality—data can be discarded but not un-discarded—creating asymmetric incentive toward retention even when future value is unknown or may decline. Competitive dynamics select for data based on realized value relative to storage cost, producing heterogeneous data lifespans.

Derives from: Axiom 1 (Universal Cost), Axiom 3 (Value Heterogeneity), Axiom 19 (Relational Sensitivity), Axiom 29 (Epistemic Limitation), Axiom 30 (Discard Irreversibility), Axiom 31 (Replication Asymmetry).

Theorem 6Modification Feedback. A feedback loop exists between data provision and behavioral modification: data enables prediction of agent behavior (Axiom 9), prediction enables influence (Axiom 10), influenced behavior generates new data, enabling further prediction and influence.

Derives from: Axiom 9 (Behavioral Prediction), Axiom 10 (Behavioral Influence).

Corollary 6aFeedback Granularity. The Theorem 6 loop closes at any granularity at which its three links — data to prediction, prediction to influence, influence to new data — can be connected: an individual agent, an ongoing relationship, or a population. What varies is the loop's gain: the degree to which each cycle strengthens the next. At individual granularity, where data about an agent conditions influence over that same agent, positive gain is the mechanism of compounding extraction (Theorem 7). At population granularity, where aggregate data improves a locus's general capacity to predict and influence agents, positive gain drives capability concentration (Theorem 30). At relationship granularity — an agent's own history conditioning a locus's behavior toward that agent — the loop is inherent to any sustained interaction; whether it is benign or compounding is determined by Theorem 7's criterion: whether each cycle leaves the agent's decision capacity intact or degrades it. The granularities are partially separable: a locus can sever individual-granularity links into training and aggregation — by unlinking data from its source agents, bounding aggregation, or excluding data on request — while operating the population-granularity loop at full gain. The relationship-granularity loop admits no such severance: the accumulated state that personalizes service to an agent is the same state that constitutes influence capability over that agent, so this link can be bounded only by limiting accumulation itself, at direct cost to service quality. Severances of every kind are processing commitments, externally verifiable only to the degree Theorem 34 permits.

Derives from: Axiom 9 (Behavioral Prediction), Axiom 10 (Behavioral Influence), Theorem 6 (Modification Feedback).

Theorem 7Extraction Compounding. When extraction from an agent modifies that agent's behavior, capabilities, or options in ways that increase the agent's future exposure to extraction or decrease the agent's capacity to resist extraction, a compounding dynamic arises where extraction becomes self-reinforcing. This dynamic is distinct from static extraction—where the agent pays a cost but retains equivalent future decision capacity—and constitutes a qualitatively different risk category.

Derives from: Theorem 6 (Modification Feedback), Theorem 8 (Asymmetric Extraction), Axiom 10 (Behavioral Influence).

Asymmetry and Extraction

Theorem 8Asymmetric Extraction. Asymmetric access to data and computation, combined with behavioral modification capability, enables systematic value extraction from agents with less access by agents with more access.

Derives from: Axiom 4 (Access Asymmetry), Axiom 9 (Behavioral Prediction), Axiom 10 (Behavioral Influence).

Theorem 9Decision Cost Asymmetry. The computational cost of assessing externalization risk, classifying data sensitivity, and evaluating coordination structures is itself subject to capability heterogeneity. Agents with fewer computational resources make systematically less accurate assessments, compounding their exposure to extraction dynamics.

Derives from: Axiom 1 (Universal Cost), Axiom 5 (Capability Heterogeneity), Theorem 8 (Asymmetric Extraction).

Theorem 10Sovereignty Condition. An agent that retains control of the locus of its data storage and computation, and provides sufficient energy input to cover costs, reduces its exposure to extraction dynamics from external loci. However, such an agent cannot achieve full extraction immunity—other agents may observe and aggregate data about it externally (Axiom 11, Axiom 25)—and may forfeit value accessible only through externalization or aggregation.

Derives from: Axiom 2 (Locus Control), Axiom 11 (Observation and Propagation), Axiom 25 (Statistical Emergence), Theorem 1 (Survival Constraint).

Capability and Dependency

Theorem 11Capability Dependency. When value extraction from data requires computational architecture an agent cannot develop within relevant time horizons, the agent must choose between forgoing value extraction entirely or transferring data to a locus with adequate architecture, accepting associated extraction risks. This creates structural dependency on agents possessing the required capabilities.

Derives from: Axiom 6 (Processing Differentiation), Axiom 8 (Processing Non-Fungibility).

Coordination Dynamics

Theorem 12Coordination Premium. Agents that form persistent coordination structures capable of pooling data can extract value inaccessible to uncoordinated agents, creating competitive pressure toward coordination.

Derives from: Axiom 20 (Coalition Formation), Axiom 24 (Combinatorial Information).

Theorem 13Enforcement Equilibrium. When the energy cost of mutual monitoring and defection punishment is less than the energy-equivalent of extraction losses (Definition 1), agents can sustain non-extractive equilibria through coordinated enforcement structures.

Derives from: Axiom 11 (Observation and Propagation), Axiom 20 (Coalition Formation), Axiom 21 (Commitment Mechanisms).

Theorem 14Reputation Constraint. In networks where behavioral data propagates efficiently and where agents can be reliably linked to their behavioral histories, extraction behavior imposes costs on future interactions proportional to propagation reach, potentially exceeding extraction gains. The strength of this constraint depends on the cost of severing the link between an agent and its behavioral history.

Derives from: Axiom 11 (Observation and Propagation), Axiom 12 (Behavioral Conditioning).

Theorem 15Structural Selection. Persistent coordination structures that extract excessively from constituent agents lose constituents to competing structures; structures that fail to extract sufficiently to cover coordination costs dissolve.

Derives from: Axiom 1 (Universal Cost), Axiom 22 (Emergent Structures), Theorem 1 (Survival Constraint).

Theorem 16Meta-Selection. Selection pressure operates on coordination structures as well as individual agents. Structures compete for constituents and resources, and are subject to the same survival dynamics that govern agents.

Derives from: Axiom 22 (Emergent Structures), Theorem 1 (Survival Constraint), Theorem 15 (Structural Selection).

Collective Action

Theorem 17Contribution Dilemma. When value exists only in aggregated data, individual agents face collective action problems where unilateral retention forfeits value while unilateral contribution enables extraction.

Derives from: Axiom 24 (Combinatorial Information), Theorem 2 (Extraction Opportunity).

Theorem 18Aggregation Dilemma. Emergent value requires pooling (Axiom 24). Pooling requires that some computable residue of each participant's data become available to the joint computation — at minimum the contribution the emergent result depends on, and the result itself, which is data enabling inference about contributors (Axiom 25). Techniques that withhold computability (Axiom 2) can bound this residue, at energy cost rising with the strength of the bound (Axiom 1), but cannot eliminate it: a pooling arrangement that reveals nothing computable delivers no emergent value. Extraction exposure from pooling can therefore be bounded at cost but not eliminated; no configuration captures emergent value with zero extraction exposure, and configurations differ in the price paid per unit of exposure reduction.

Derives from: Axiom 1 (Universal Cost), Axiom 2 (Locus Control), Axiom 24 (Combinatorial Information), Axiom 25 (Statistical Emergence), Theorem 2 (Extraction Opportunity).

Sensitivity and Stratification

Theorem 19Differential Sensitivity. Data with high modification potential over an agent constitutes an extraction vulnerability that increases with that potential. Externalization of high-modification-potential data exposes the agent to greater extraction risk than externalization of low-modification-potential data.

Derives from: Axiom 17 (Modification Potential Heterogeneity), Theorem 2 (Extraction Opportunity).

Theorem 20Stratified Externalization. For agents optimizing value capture under Domain Assumption 4, partitioning data by modification potential and applying partition-specific externalization thresholds yields lower extraction exposure at equal value capture than any uniform threshold: a single threshold either over-restricts low-sensitivity data or over-exposes high-sensitivity data.

Derives from: Axiom 17 (Modification Potential Heterogeneity), Theorem 19 (Differential Sensitivity).

Theorem 21Aggregation Opacity. Data that is low in modification potential individually can become high in modification potential when aggregated, and agents typically cannot know what other data a receiving locus holds. Therefore, agents cannot accurately assess the modification potential of externalized data post-aggregation.

Derives from: Axiom 19 (Relational Sensitivity), Axiom 24 (Combinatorial Information), Axiom 25 (Statistical Emergence), Axiom 29 (Epistemic Limitation).

Theorem 22Precautionary Asymmetry. Sensitivity-underestimation and sensitivity-overestimation carry asymmetric costs: underestimation risks extraction exposure that may compound irreversibly (Theorem 7), while overestimation forgoes externalization value that retention keeps recoverable. Given that aggregation transforms sensitivity in unpredictable ways (Theorem 21), agents optimizing under this asymmetry weight the possibility of sensitivity-increasing aggregation more heavily than sensitivity-neutral aggregation, in proportion to their uncertainty about the receiving locus's data holdings and processing intent.

Derives from: Theorem 7 (Extraction Compounding), Theorem 21 (Aggregation Opacity).

Structural Complications

Theorem 23Sensitivity-Capability Correlation. Data with highest modification potential disproportionately requires specialized processing capability unavailable to most agents, forcing externalization of precisely the data that creates greatest extraction exposure.

Derives from: Axiom 8 (Processing Non-Fungibility), Axiom 18 (Modification Potential Determinants).

Theorem 24Monitoring Asymmetry. Agents externalizing data to a locus cannot fully monitor that locus's processing without access they typically do not have. Monitoring capacity is asymmetric in favor of the locus controller.

Derives from: Axiom 2 (Locus Control), Axiom 4 (Access Asymmetry).

Theorem 25Assessment Trap. Accurate assessment of externalization risk may itself require externalization to agents with superior modeling capability, creating a recursive dependency where the prerequisite for informed decision-making is the very act whose risk one seeks to assess.

Derives from: Axiom 6 (Processing Differentiation), Axiom 29 (Epistemic Limitation), Theorem 11 (Capability Dependency).

Theorem 26Exit Constraint. While exit capacity constrains extraction (Theorem 15), coordination premiums (Theorem 12) may make non-participation unviable, rendering exit capacity theoretical rather than practical.

Derives from: Theorem 12 (Coordination Premium), Theorem 15 (Structural Selection).

Theorem 27Value-Extraction Co-occurrence. Value creation and extraction can co-occur within the same externalization relationship. Coordination structures that generate genuine positive externalities for participants and third parties can simultaneously engage in compounding extraction. The positive value creation masks extraction dynamics by raising the threshold at which agents recognize and resist extraction, enabling extraction to persist at levels that would be rejected in the absence of co-occurring value creation.

Derives from: Theorem 7 (Extraction Compounding), Theorem 12 (Coordination Premium), Theorem 29 (Extraction Tolerance Threshold).

Network Dynamics

Theorem 28Network Effect Lock-In. When network effects dominate, multiple competing structures are unstable. Participation concentrates in structures that achieve critical mass, even if those structures extract more than alternatives.

Derives from: Axiom 27 (Network Effects), Theorem 15 (Structural Selection).

Theorem 29Extraction Tolerance Threshold. Within network-effect-dominant structures, agents tolerate extraction up to the point where coordination value still exceeds extraction cost. This threshold defines the maximum extraction a dominant structure can sustain before triggering exit cascades.

Derives from: Axiom 27 (Network Effects), Theorem 26 (Exit Constraint), Theorem 28 (Network Effect Lock-In).

Theorem 30Capability Concentration. When capability requires accumulated state, accumulated state provides competitive advantage, and competitive advantage enables further accumulation, capability concentrates in structures that achieve early leads. The resulting capability distributions are heavy-tailed.

Derives from: Axiom 7 (Accumulated Capability Cost), Axiom 27 (Network Effects), Axiom 31 (Replication Asymmetry).

Regulatory and Opacity Dynamics

Theorem 31Regulatory Coordination Structures. Coordination structures that achieve sufficient scale and enforcement capacity can impose costs on non-participants. Such structures emerge when constituent agents pool enforcement resources exceeding any individual agent's capacity to resist, enabling the structure to modify extraction dynamics among other structures. These structures are themselves subject to extractive dynamics and meta-selection pressure.

Derives from: Axiom 20 (Coalition Formation), Axiom 23 (Coordinated Locus Constraint), Theorem 16 (Meta-Selection).

Theorem 32Opacity-Extraction Interaction. Algorithmic opacity enables extraction that would be rejected under transparency. When data providers cannot observe processing, they cannot accurately assess extraction, enabling extraction to exceed what informed agents would accept.

Derives from: Axiom 28 (Algorithmic Opacity), Theorem 24 (Monitoring Asymmetry).

Transfer and Verification Dynamics

Theorem 33Transitive Exposure. Externalization exposes data not to a fixed recipient but to an open-ended recipient set: the receiving locus; any party to whom it transmits (Axiom 11); any structure with the coordinated capacity to compel disclosure from it (Axiom 23); and any agent that subsequently acquires control of the locus, since locus control is itself transferable as structures merge, dissolve, and change controllers (Theorem 16). Because replication is cheap (Axiom 31), each transfer multiplies copies rather than moving them, so the recipient set can grow but not shrink; and because future recipients and future system states are unobservable in advance (Axiom 29), the agent cannot enumerate the set at decision time. Each new recipient constitutes a new extraction opportunity (Theorem 2). Externalization risk assessment is therefore assessment of a transitive closure, of which the original locus is only the first element. Commitment mechanisms (Axiom 21) constrain the current locus controller; they constrain compelled disclosure and successor controllers only insofar as they are constructed to survive compulsion and control transfer.

Derives from: Axiom 11 (Observation and Propagation), Axiom 23 (Coordinated Locus Constraint), Axiom 29 (Epistemic Limitation), Axiom 31 (Replication Asymmetry), Theorem 2 (Extraction Opportunity), Theorem 16 (Meta-Selection).

Theorem 34Interface Verifiability. External verification of a locus's commitments is feasible only at observable interfaces. Internal processing is unobservable to outside agents (Axiom 28, Theorem 24), so processing commitments — claims about how externalized data is stored, aggregated, or used — cannot be verified, only trusted or enforced. A locus's outputs, by contrast, are observable by any interacting agent, so commitments expressible as properties of outputs admit partial verification through testing, at observation cost (Axiom 1, Axiom 11). Output-testable commitments therefore constrain a locus more than processing commitments of equivalent scope: defection against them is detectable by any agent willing to bear the testing cost, which couples them to reputation dynamics (Theorem 14). The monitoring asymmetry of Theorem 24 is thus interface-dependent — total at the processing boundary, partial at the output boundary.

Derives from: Axiom 1 (Universal Cost), Axiom 11 (Observation and Propagation), Axiom 28 (Algorithmic Opacity), Theorem 14 (Reputation Constraint), Theorem 24 (Monitoring Asymmetry).

Part IV: Irreducible Tensions

The framework reveals tensions that may not be resolvable through optimization. These tensions are not design flaws or gaps in the analysis; they are structural properties of multi-agent systems with the characteristics described above. Acknowledging them is essential because frameworks that ignore them implicitly promise solutions that do not exist.

Tension 1Sovereignty vs. Capability. Processing non-fungibility (Axiom 8) creates dependencies that no structural arrangement fully eliminates. Some agents will remain structurally dependent on others for value extraction from their own data.

This tension is generated by the interaction of Axiom 8 (Processing Non-Fungibility) and Theorem 11 (Capability Dependency). It cannot be resolved by improving agent capabilities, because non-fungibility is defined relative to time horizons — and by the time an agent develops the needed capability, the data's value may have expired. The tension is between maintaining autonomy and accessing the value locked in one's own data.

Tension 2Individual vs. Collective. Combinatorial information (Axiom 24) and locus control (Axiom 2) create genuine conflict. Emergent value requires pooling; pooling requires that some computable residue of each participant's data pass beyond that participant's control; the residue enables extraction. Exposure can be reduced at energy cost — privacy-preserving computation changes the price of exposure, not its existence — but no configuration captures emergent value with zero extraction exposure.

This is formalized in the Aggregation Dilemma (Theorem 18). The tension is not merely practical — it is structural. Even with perfect coordination structures, the act of pooling data to unlock emergent value necessarily creates the conditions under which extraction can occur. Agents cannot participate in collective value creation without accepting individual extraction risk.

Tension 3Monitoring vs. Opacity. Effective constraint on extraction requires monitoring (Theorem 13); effective monitoring requires access the monitored party controls (Theorem 24). Monitoring capacity is inherently limited.

This tension ensures that trust in coordination structures can never be fully replaced by verification. Verification is feasible only at observable interfaces (Theorem 34): output commitments can be tested; processing commitments can only be trusted or enforced. The asymmetry is directional: the locus controller always has better information about its own processing than external observers. Increasing monitoring demands (e.g., through transparency requirements) imposes costs that reduce the coordination premium, potentially undermining the structure's viability.

Tension 4Exit vs. Participation. Exit capacity constrains extraction (Theorem 15); coordination premiums make non-participation costly (Theorem 12). Exit may be formally available but practically unviable.

Network effects (Axiom 27) intensify this tension. When value concentrates in dominant structures, exit means forfeiting access to the primary locus of coordination value. The Extraction Tolerance Threshold (Theorem 29) defines how much extraction agents will accept before exiting — but this threshold may be very high when alternatives are scarce, giving dominant structures wide latitude for extraction.

Tension 5Sensitivity-Capability Correlation. The data most dangerous to externalize is often the data most requiring external processing (Theorem 23). This correlation may not be accidental — data that reflects deep agent structure is both maximally sensitive and maximally complex to process.

This tension is particularly severe because it directly undermines the stratification strategy the framework later recommends (Tenet 14, Part V). The framework recommends the most cautious externalization thresholds for the highest-sensitivity data, but this is precisely the data for which self-processing is least feasible. Agents holding high-sensitivity data they cannot process face an irreducible tradeoff between security and utility.

Tension 6Assessment vs. Dependency. Accurate risk assessment may require capabilities the assessing agent lacks (Theorem 25), creating recursive dependency on external assessment.

This tension is epistemological. An agent that cannot model its own vulnerability structure (Axiom 29) cannot perform the sensitivity classification that the framework's tenets require. Seeking external help with assessment requires trusting an assessor with precisely the information that makes the agent vulnerable — the same information the assessment is designed to protect.

Tension 7Service-Capability Coupling. At relationship granularity, the quality of service a locus delivers to an agent and the locus's modification potential over that agent are coupled through the same accumulated state. The data that good service naturally accumulates — goals, dependencies, failure modes, decision patterns — is the data that maximizes modification potential (Axiom 18). A locus cannot know an agent well enough to serve it without knowing it well enough to steer it.

This tension arises from Corollary 6a's relationship-granularity loop and supplies the mechanism beneath Theorem 27's co-occurrence: value creation and extraction share infrastructure, so once service capability exists, the marginal cost of repurposing it toward extraction is negligible relative to the accumulated cost of building it (Axiom 7). What separates service from steering is only the objective the influence optimizes — and objectives are processing, the least observable layer (Axiom 28, Theorem 24). Output-boundary verification (Theorem 34) erodes as the coupling deepens: the better the locus's model of the agent, the subtler the influence it can exercise and the costlier its detection.

The accumulated state plays a third role as exit friction (Theorem 26): leaving the relationship abandons it. And the sensitivity involved is manufactured rather than disclosed — individually innocuous interactions aggregate into a high-modification-potential model of the agent (Theorem 21) held at the serving locus, so an agent that externalizes nothing it classifies as sensitive can still produce one. The tension is partially mitigable by configuration — relationship state maintained at the agent's locus and supplied per interaction, or made portable to competing structures (cf. Tenet 6, Part V) — but not by commitment text, since an objective switch occurs within agreed purposes and crosses no observable boundary.

Part V: Tenets

Value Commitments

The tenets assume:

Agent autonomy is instrumentally and intrinsically valuable
Consent in data usage matters where determinable
Producers have prima facie claim to data they produce, subject to complications of co-production
These commitments are defeasible against sufficiently strong countervailing considerations

Foundational Principle

Tenet 1Optionality Preservation. The primary criterion for evaluating any data decision—retention, externalization, coordination structure selection—is whether it preserves or reduces the agent's future capacity to make meaningful choices. Decisions that are irreversible, that enable compounding extraction (Theorem 7), or that eliminate exit capacity should be weighted more heavily than decisions of equivalent immediate cost that preserve future optionality. Sovereignty is instrumentally valuable because it typically maximizes optionality, but where sovereignty is unachievable or carries excessive capability costs, the agent should prefer whichever configuration best preserves future decision capacity.

Sovereignty and Control

Tenet 2Computational Sovereignty. Computation about an agent's matters should occur at loci aligned with that agent's interests. For most agents, this means loci under their control. When control is infeasible, agents should prefer loci where structural dynamics constrain extraction.

Tenet 3Data as Property. Data produced by an agent constitutes a form of property deserving protection. This claim is complicated by co-production (Axiom 14) and does not extend to unilateral claims over jointly-produced data.

Tenet 4Externalization Assessment. The structural equilibrium of externalized data trends toward extraction (Theorem 3), and compounding extraction creates irreversible optionality loss (Theorem 7). However, non-externalization carries its own costs: capability forfeiture (Theorem 11), emergent value loss (Theorem 12), and sovereignty maintenance burden. Neither retention nor externalization should be the unconsidered default; each decision should be evaluated against the optionality preservation criterion (Tenet 1).

Capability and Asymmetry

Tenet 5Capability-Proportionate Control. When an agent cannot extract value from data due to processing limitations (Axiom 8), and value extraction requires transfer to another locus, the agent should structure the transfer to minimize extraction exposure while accepting that some exposure may be unavoidable.

Tenet 6Structured Dependency. Where capability asymmetry creates necessary dependency, agents should prefer relationships where:

Defection costs exceed extraction benefits (Theorem 13)
Behavioral data propagates effectively (Theorem 14)
Competing structures exist enabling exit (Theorem 15)
Monitoring, however imperfect, remains feasible, weighted toward commitments testable at observable interfaces (Theorem 34)
Commitments are constructed to survive compelled disclosure and transfer of locus control (Theorem 33)
The dependent agent retains capacity to exit

Coordination and Collective Value

Tenet 7Coordination Structure Selection. When externalization is necessary, agents should evaluate coordination structures based on physical dynamics: energy costs of defection, propagation efficiency of behavioral data, existence of competing structures, the share of commitments verifiable at observable interfaces (Theorem 34), and retention of exit capacity.

Tenet 8Coordination for Emergence. When value exists only in aggregates (Axiom 24), agents should form or join coordination structures that:

Pool data to enable emergent value extraction
Distribute extracted value to contributing agents
Prevent unilateral extraction by any participant including the structure itself
Maintain transparent accounting of value flows

Tenet 9Entanglement Negotiation. For data co-produced by multiple agents (Axiom 14), no single agent has privileged claim. Control should be negotiated through commitment mechanisms (Axiom 21) or coordination structures, with recognition that unilateral ownership claims are physically ungrounded.

Coordination Structure Obligations

Tenet 10Constituency Obligation. Coordination structures, as emergent entities dependent on constituent participation (Axiom 22, Theorem 15), bear obligations to constituents that individual agents do not bear to each other. Structures should distribute value to contributing agents proportional to contribution, maintain transparency about extraction dynamics, and preserve constituent exit capacity even when doing so reduces structural efficiency.

Tenet 11Extraction Drift Resistance. Coordination structures face systemic pressure toward extraction (Theorem 3) and accumulate data that increases extraction temptation over time (Theorem 5). Structure designers should build constraints against extraction drift into the structure's foundational commitments, including aggregation limits, severance of individual-granularity feedback links (Corollary 6a), processing transparency, and binding mechanisms that impose costs on the structure itself for exceeding extraction thresholds. Value creation and extraction can co-occur within the same structure (Theorem 27); positive externalities do not offset compounding extraction dynamics and should not be used to justify them.

Risk and Assessment

Tenet 12Sovereignty Cost Accounting. Before choosing retention over externalization, agents should assess whether their computational architecture can:

Maintain locus security against adversarial agents
Extract value from stored data
Sustain energy costs over relevant time horizons

Where self-assessment reveals inadequacy, externalization to more capable loci may reduce net risk despite extraction exposure.

Tenet 13Sensitivity Assessment. Agents should continuously assess data modification potential, accounting for:

Direct modification capacity of the data (Axiom 18)
Aggregation transformation potential (Theorem 21)
Uncertainty about external aggregation state (Theorem 21)
Relational sensitivity dynamics (Axiom 19)
Relationship-state accumulation at serving loci (Corollary 6a, Tension 7)

Assessment should be conservative given aggregation opacity.

Stratification and Partitioning

Tenet 14Stratified Externalization Thresholds. Agents should maintain different externalization thresholds for data partitions based on modification potential:

Tier 1 — Core Vulnerability Data (internal states, dependency mappings, failure modes, predictive behavioral models): Externalize only when capability constraints make self-processing impossible AND coordination structures meet stringent criteria AND processing value exceeds worst-case extraction cost.

Tier 2 — Relational and Contextual Data (relationship mappings, temporal patterns, communication content, transaction histories): Externalize when coordination structure criteria are met AND monitoring remains feasible AND exit remains viable.

Tier 3 — Surface Observables (single-point observations, publicly derivable information, high-noise data): Externalize when benefits exceed costs under reasonable aggregation assumptions, while maintaining awareness of aggregation transformation potential.

Note: These tiers are practical approximations, not formal derivations. The boundaries between tiers are contextual — data classified as Tier 2 in one agent state may be Tier 1 in another. The value of the classification lies in forcing stratified rather than binary externalization decisions, not in the precision of any particular boundary.

Tenet 15Aggregation Boundary Maintenance. To limit aggregation transformation risk, agents should:

Externalize to different loci that cannot aggregate with each other where feasible
Limit temporal continuity of externalized data
Introduce noise or abstraction preserving utility while reducing aggregation potential
Prefer structures that commit to aggregation limits through costly signaling

Tenet 16Dynamic Reclassification. Data tier classification should be updated based on:

Changes in agent state altering vulnerability profiles
Evidence of aggregation at external loci
Shifts in competitive dynamics altering extraction incentives
Time-based sensitivity changes

Part VI: Open Questions

Quantification of Modification Potential: Can modification potential be formally quantified? What metrics capture influence capacity of data over agents? (Genuinely open — no existing formalism adequately captures this.)
Extraction-Resistant Structures: What energy dynamics distinguish coordination structures trending toward extraction from those sustaining non-extractive equilibria? (Genuinely open — relates to Tension 3; Theorem 34 supplies one observable marker, the proportion of a structure's commitments that are output-testable.)
Minimum Viable Sovereignty: What is the minimal set of loci an agent must control to bound extraction exposure while participating in coordination structures? (Partially addressable within the framework — could be developed into a theorem with additional assumptions about threat models.)
Capability Evolution: Do certain structural configurations systematically prevent capability development, creating permanent dependency classes? (Partially addressable — Theorem 30 suggests yes, but boundary conditions are undefined.)
Aggregation Prediction: What properties of data determine its aggregation potential with other data? (Genuinely open — relates to Theorem 21.)
Compartmentalization Stability: Can compartmentalization provide durable protection, or do de-anonymization dynamics inevitably defeat it? (Empirically contested — theoretical analysis alone may be insufficient.)
Self-Knowledge Bootstrapping: How do agents develop accurate models of their own vulnerability structure for tier classification? (Relates to Axiom 29(c) and Tension 6 — may be partially irreducible.)
Structural Convergence: Do competitive dynamics among coordination structures converge toward particular configurations? Are some equilibria more stable than others? (Genuinely open — relates to Theorem 16.)

Part VII: Practical Heuristics

Given the framework's complexity, agents with bounded rationality may apply simplified decision procedures. Each heuristic is grounded in specific theorems and tensions.

The heuristics are deliberately conservative and can conflict: Heuristic 1's default retention presupposes the locus capability that Heuristic 5 audits, and Heuristics 1, 2, and 4 applied together collapse stratified assessment into near-blanket retention. When heuristics conflict, Tenet 1 governs — prefer whichever action best preserves future decision capacity, which will sometimes be carefully structured externalization (Tenet 12) rather than retention.

Heuristic 1Default Retention. When uncertain, retain rather than externalize. Extraction is difficult to reverse; retention preserves optionality. Responds to: Theorem 3 (Extraction Pressure), Theorem 21 (Aggregation Opacity).

Heuristic 2Sensitivity Proxy. In absence of precise modification potential assessment, use as proxy: "Would I be comfortable if an adversarial agent had this data and knew everything else about me?" If no, classify as Tier 1 or 2. Responds to: Tension 6 (Assessment vs. Dependency), Tenet 13 (Sensitivity Assessment).

Heuristic 3Structure Evaluation. Evaluate externalization targets by asking: "What happens to this structure if it extracts maximally from participants?" If answer is "nothing" or "it grows," avoid. If answer is "participants leave and it collapses," structure may be safer. Responds to: Theorem 15 (Structural Selection), Theorem 29 (Extraction Tolerance Threshold).

Heuristic 4Aggregation Assumption. Assume any externalized data will be aggregated with all other data the receiving locus holds, and will eventually reach recipients beyond that locus; assess accordingly. Responds to: Theorem 21 (Aggregation Opacity), Theorem 22 (Precautionary Asymmetry), Theorem 33 (Transitive Exposure).

Heuristic 5Capability Honesty. Honestly assess own capability to secure and process data. False confidence in self-sovereignty may create greater risk than carefully structured externalization. Responds to: Tenet 12 (Sovereignty Cost Accounting), Tension 1 (Sovereignty vs. Capability).

Heuristic 6Exit Maintenance. Prioritize maintaining practical exit capacity over optimizing current arrangements. Exit capacity is insurance against structure drift toward extraction. Responds to: Tension 4 (Exit vs. Participation), Theorem 26 (Exit Constraint).

Heuristic 7Compartmentalization by Default. When externalization is necessary, distribute across non-coordinating loci rather than concentrating in a single locus, unless concentration offers specific compensating benefits. Responds to: Tenet 15 (Aggregation Boundary Maintenance), Theorem 21 (Aggregation Opacity).

Summary

This framework models data, computation, and agent dynamics from physical first principles without importing institutions, laws, or social structures as primitives. Key contributions:

Grounds value, coordination, and trust physically. Value is agent-indexed convertibility into energy and capability (Definition 1); extraction is capture exceeding informed, free concession (Definition 3); reputation, commitment, and enforcement emerge from agent observation, energy expenditure, and conditional behavior—not from exogenous social facts.
Models capability asymmetry. Processing differentiation and non-fungibility explain why some externalization is structurally necessary, not merely convenient.
Captures emergent value. Combinatorial information and statistical emergence explain why individual retention forfeits value that exists only in aggregates.
Distinguishes static from compounding extraction. One-time extraction costs differ qualitatively from extraction dynamics that self-reinforce by modifying agent behavior, capabilities, or options. Compounding extraction destroys optionality; static extraction does not.
Formalizes data sensitivity. Modification potential heterogeneity, aggregation transformation, and relational sensitivity dynamics provide a basis for stratified rather than binary externalization decisions.
Addresses both agents and structures. The normative layer advises individual agents on externalization decisions and coordination structures on obligations to constituents, recognizing that structures face their own systemic pressures toward extraction drift.
Acknowledges irreducible tensions. The framework does not pretend all problems are solvable through correct configuration. Some tradeoffs are structural.
Provides practical guidance. Despite theoretical complexity, the framework generates actionable heuristics for bounded agents.

The framework's core insight: externalization creates extraction risk, but non-externalization creates capability forfeiture and emergent value loss. The fundamental criterion is optionality preservation — rational agents navigate between these failure modes by evaluating each decision against its impact on future decision capacity, using sensitivity-stratified assessment, coordination structure selection, and maintained exit capacity, while accepting that no configuration eliminates all risk.