Chapter 11 — Feedback, Recursion, and Ongoing Transformation

Edition source note. This edition adds September–October 2026 source-checked snapshots on mathematical verification, journal publication and professional response, a foundation–laboratory funding partnership for the evaluation of AI-assisted results, government evaluation and reporting proposals, embedded-evaluator arrangements, the Australian incident chronology, scaffolded replication experiments, and research-agent and quantum-circuit cases through October 16 that bound the RSI classification. Source types and verification limits remain explicit; these additions do not promote a frozen empirical verdict or demonstrate autonomous recursive self-improvement.

Abstract

This chapter adds the temporal dimension to the Unified Gradual AGI Model. It argues that prior realization, observation, representation, and response can alter the conditions under which subsequent realization occurs, while preserving the existing realization mapping rather than adding feedback or recursion as a fifth argument of μ_t. The chapter distinguishes temporal sequence, feedback, adaptation, recursive re-entry, recursion, reflexivity, and recursive self-improvement; separates ordinary feedback through changing values of Potential, Availability, Exposure, and domain-specific realization conditions from the higher-burden claim of structural feedback; and examines amplification, damping, redirection, delay, path dependence, lock-in, and reversibility. Reciprocal human–AI feedback is situated within the book’s Participation framework, including Role Plasticity and the RO → FP → AD relational grammar. Empirically, the chapter develops a three-domain longitudinal design: Go as a mature post-superhuman comparator, mathematics as an emerging open-knowledge case with rapidly rising disclosed AI participation and new institutional responses such as SAIR’s Open Math Model initiative, and radiology/RADAR as an emerging regulated-profession test. The chapter concludes that the present transformation can be characterized as ongoing where consequences continue to alter later realization conditions and unfinished where no empirically justified terminal configuration has been established for the domain and observation horizon under examination.

Keywords. Gradual AGI; feedback; recursion; recursive re-entry; recursive self-improvement; realization; Participation; Role Plasticity; path dependence; lock-in; institutional adaptation; AI mathematics; Epoch AI; SAIR; Go; radiology; RADAR; epistemic discipline

Chapter 11 Reader Guide

Feedback, Recursion, and Ongoing Transformation

One-line summary

This chapter examines how prior realization and response change later conditions, distinguishing feedback from recursion and ongoing transformation from an unsupported claim of permanent openness.

Principal Contributions

This chapter makes the following principal contributions. Its contribution is the placement and evidentiary differentiation of temporal return within the existing architecture, rather than the invention of feedback or recursion as general concepts.

1. Temporal relations with different burdens. Sequence, feedback, adaptation, recursive re-entry, recursion, reflexivity, and recursive self-improvement are distinguished. A response becomes recursive evidence only when the changed condition enters a later cycle; chronology alone does not establish feedback.

2. Return paths inside the realization architecture. Prior realization and response can change later Potential, Availability, Exposure, or domain-specific conditions without adding feedback as a fifth argument. Structural feedback—a change in the realization relationship itself—requires stronger evidence than changes in its arguments.

3. Reciprocal human–AI and institutional feedback. Role Plasticity and the RO, FP, AD Grammar locate changing roles and dependencies. Governance and Participation can redirect later conditions without making the two sides symmetrical or turning formal mechanisms into demonstrated effects.

4. Amplification, damping, redirection, delay, and path dependence. The chapter distinguishes how responses alter subsequent trajectories and opportunity sets. Feedback need not accelerate capability, and revisability does not guarantee reversible outcomes.

5. A differentiated longitudinal testbed and a bounded terminality diagnostic. Go supplies a mature comparator; mathematics and radiology supply emerging cases with different verification and institutional conditions. “Ongoing” concerns continuing changes to later conditions; “unfinished” concerns the absence of an empirically justified terminal configuration for a specified domain and observation horizon.

Prerequisites

Chapter 4 supplies the realization mapping; Chapter 5 clarifies the distinction between a dynamical submodel and the broader architecture; Chapters 7–9 supply governance and Participation. Chapter 10 is the immediate prerequisite for evidentiary status and source limits. Temporal diagrams and recalled model notation are introduced or explained locally; their arrows carry evidentiary burdens rather than imply causation automatically.

Reading routes

Conceptual and placement path. Sections 11.1–11.3 move from epistemic output to dynamic input, distinguish temporal relations, and locate return paths within the existing mapping.

Reciprocal and institutional path. Sections 11.4–11.5 examine human–AI role changes and feedback through institutions, governance, and Participation.

Dynamics and longitudinal path. Sections 11.6–11.7 examine amplification, damping, redirection, delay, path dependence, and the three-domain comparison.

Evidence and diagnostic path. Sections 11.8–11.9 state the burdens for feedback and recursive claims and apply the domain- and horizon-relative reading of ongoing, unfinished transformation.

Book path. Chapter 11 completes Part III, Mediation. Earlier chapters use Ongoing, Unfinished Transformation as an orientation, with Chapter 3 explicitly formulating its methodological role; this chapter supplies a diagnostic burden rather than a global verdict. Part IV, Integration, begins with Chapter 12’s provisional synthesis without new apparatus.

Evidence and limits

The AI-by-AI taxonomy distinguishes training, inference-time orchestration, and generated material. None by itself establishes autonomous recursive self-improvement or sustained improvement.

A documented response is not automatically repeated recursion, and AI-assisted AI research is not demonstrated autonomous recursive self-improvement. Stronger claims require evidence of successive cycles and of the technical decisions on which improvement depends. A specified but unexercised monitoring mechanism is evidence of design, not evidence that its loop has operated.

Go is a comparator and hypothesis generator, not a forecast for mathematics or radiology. Disclosed AI use in mathematics is not total underlying use; bounded radiology performance and reader assistance do not establish profession-level substitution. Interested-party reports support narrower generalization where independent corroboration is absent. No case automatically establishes structural feedback or a permanent, system-wide absence of closure. Every return claim remains bounded by domain, actors, versions, and observation horizon.

11.1 From Epistemic Output to Dynamic Input

Chapter 10 treated observation, evidence, and epistemic discipline as constraints on what the Unified Gradual AGI Model is entitled to claim. Observation does not transparently reveal realization. Evidence is conditioned by what can be observed, measured, reconstructed, compared, and attributed. Claims therefore require boundaries: what was observed, what was inferred, what remains uncertain, and which version of a rapidly changing system or institution the evidence actually describes.

But observation is not always only epistemic.

Once an observation is communicated, interpreted, evaluated, or acted upon, it can become part of the process being observed. A benchmark result can influence model development. A safety incident can alter training practices. A deployment can provoke institutional response. A scientific result can change research priorities, verification practices, or subsequent uses of AI. An assessment of economic effects can influence investment, regulation, organizational design, or adoption. What begins as an observation of realization can therefore become an input into later realization.

The basic movement is:

Observation → Representation → Claim → Actor Response → Changed Realization and/or Observation Conditions.

Chapter 10 concentrated on the first three transitions. Chapter 11 concentrates on what happens after the claim enters the world.

An observation can become information. Information can alter action. Action can alter the conditions under which later realization occurs. The changed realization then becomes the object of further observation.

Schematically:

Realization → Observation or Consequence → Response → Changed Conditions → Subsequent Realization.

This return path matters because Gradual AGI is not adequately described as a sequence of independently changing states. Earlier realizations may affect later capabilities, availability, exposure, absorption, governance, participation, investment, institutional practice, and the relationships through which these conditions are converted into realized outcomes. The history of realization can therefore become relevant to its future trajectory.

Temporal order alone does not establish feedback, amplification, or recursion; those stronger claims require the distinctions developed in §11.2.

The starting claim of this chapter is narrower:

Prior realizations, observations, representations, and responses can alter conditions relevant to subsequent realization.

That claim preserves the architecture developed earlier in the book. Feedback and recursion do not become additional components of the realization mapping. Instead, they describe how the values, relationships, practices, and institutional conditions already represented in the model may evolve through time partly in response to their own prior consequences.

This distinction also clarifies the meaning of the phrase Ongoing, Unfinished Transformation.

A transformation is a sustained change in the configuration of capabilities, realized uses, institutions, practices, relationships, or social conditions sufficient to alter subsequent possibilities or constraints.

The transformation is ongoing when these configurations continue to change through time. “Ongoing” is therefore a process claim. It does not imply continuous acceleration, uninterrupted progress, or monotonic improvement. An ongoing transformation may slow, redirect, encounter resistance, stabilize locally, or partially reverse while remaining dynamically active at a broader level.

The transformation is unfinished when no stable terminal configuration has been established—conceptually or empirically—as the completed state of the process. “Unfinished” is therefore a closure-status claim. A terminal state is analysis-relative rather than metaphysical: within a specified domain and observation horizon, it would require a sufficiently stable configuration in which further AI-mediated change no longer materially altered the realization conditions under examination. No such terminal configuration is established here.

The combination of the two terms is deliberate. A domain-level diagnosis of ongoing transformation requires evidence that realized outcomes continue to alter later realization conditions; the possibility of such alteration is not sufficient. The diagnosis is unfinished insofar as no empirically justified terminal configuration has been established for the specified domain and observation horizon. Neither diagnosis asserts permanent non-closure.

This also means that an ongoing transformation need not be understood as movement toward a single predetermined endpoint. Realization may amplify some trajectories, damp others, redirect activity, generate resistance, produce new institutions, or create conditions that were not present when an earlier state was reached. History therefore does more than record the transformation. Under some conditions, history becomes one of the means through which the transformation develops.

The next task is to distinguish the processes through which that can occur. Feedback, adaptation, recursive re-entry, recursion, and reflexivity are related but non-identical concepts. Their separation is necessary if Chapter 11 is to describe a dynamically evolving realization process without collapsing every form of change into “recursion” or every instance of AI-assisted improvement into “recursive self-improvement.”

11.2 Feedback, Adaptation, and Recursion

If realization can alter the conditions governing what happens next, several related processes must be distinguished. Feedback, adaptation, recursive re-entry, recursion, and reflexivity describe different relationships between earlier states and later ones. They should not be treated as interchangeable.

The broadest concept is feedback.

Feedback is a process in which a prior output, consequence, observation, or realized condition alters one or more conditions relevant to subsequent realization.

The definition requires more than temporal succession. If an event at time t is followed by a different state at t+1, that sequence alone does not establish feedback. Some pathway must connect the earlier outcome to the later condition.

Thus:

Temporal sequence does not imply feedback.

A benchmark result that is published but ignored may be followed by later model improvement without having contributed to it. By contrast, a benchmark result that leads developers to modify training, evaluation, architecture, or deployment policy may become part of a feedback process. The empirical burden lies in establishing the connecting mechanism, not merely the chronology.

Feedback also says nothing by itself about direction.

Feedback does not imply amplification.

Feedback may accelerate a process, constrain it, stabilize it, redirect it, or act only after a substantial delay. Nor does feedback necessarily continue beyond a single return effect. A consequence may alter a later condition once without producing an indefinitely recurring loop.

A second concept concerns the response of actors.

Adaptation is a change in behavior, strategy, policy, practice, architecture, allocation, or institutional arrangement in response to prior information, outcomes, constraints, opportunities, or expectations.

Adaptation may occur at the level of an individual, organization, research community, market, public institution, or AI-mediated process. A laboratory may change a training procedure after an evaluation. A firm may redirect investment after observing adoption. A scientific community may revise verification practices as AI-assisted work increases. A regulator may alter requirements after observing deployment effects.

Adaptation should not be equated with successful optimization.

Adaptation does not imply optimization success.

An adaptive response can be ineffective, incomplete, defensive, costly, or counterproductive. Nor does adaptation necessarily imply improvement from the perspective of all actors. It means that prior information or consequences have changed subsequent behavior.

Feedback and adaptation therefore overlap without being identical. Feedback describes a relationship between earlier outcomes and later conditions. Adaptation describes one important mechanism through which that relationship can occur.

The stronger concept is recursive re-entry.

Recursive re-entry occurs when a change produced through feedback enters the realization process again as a condition affecting a subsequent cycle.

Consider:

first event → second event → third event.

If the first event merely precedes the second, there is only sequence. If the first event alters a condition producing the second, there is feedback. If that feedback-mediated change in the second event then becomes an input affecting the third, the process exhibits recursive re-entry.

Schematically:

output → changed condition → subsequent output.

This distinction matters because a feedback loop can terminate after one response. Recursion requires that the changed condition return to the process.

Accordingly:

Feedback does not imply recursion.

Recursion is the repeated re-entry of feedback-mediated changes into subsequent realization cycles, such that later outputs arise partly under conditions altered by earlier outputs.

Recursion therefore introduces history into the process. What happens next depends not only on the conditions observable at the present moment but also, in relevant cases, on how those conditions came to exist.

Recursion does not imply indefinite repetition. A recursive process may persist for several cycles and then stop. It also does not imply acceleration:

Recursion does not imply acceleration.

A recursive process can amplify, damp, redirect, or stabilize subsequent realization. Re-entry describes structure, not direction.

Nor should recursion in this chapter be confused with logical or computational self-reference:

Recursion is not the same as self-reference.

A system need not represent itself, reason about itself, or contain a formal self-reference mechanism for recursive realization to occur. The chapter uses recursion in a dynamic sense: consequences produced by a process can alter conditions that subsequently re-enter that process.

Most importantly, recursive realization is not synonymous with recursive self-improvement.

Recursive self-improvement (RSI) is a narrower and potentially graded case in which an AI system materially contributes to improving its own capabilities, or those of successor systems, and the improved capability contributes to another improvement cycle. Strong evidence for autonomous RSI would require repeated participation in identifying an improvement opportunity, designing or implementing the change, validating the result, and reusing the improved capability, with human direction no longer supplying the key technical decisions at every step.

The scope of the “self” must also be declared: the underlying model’s weights, an agent including the code that surrounds the model (its harness or scaffold), or a wider research process that includes people. Evidence at one scope does not transfer to another. An agent that improves its own harness has not thereby improved the model it runs on (§11.8).

Thus:

Recursive realization is not the same as recursive self-improvement.

AI-assisted AI research may constitute capability feedback without yet constituting RSI. The relevant empirical question is not whether humans remain anywhere in the loop, but whether successive capability-improvement cycles depend increasingly on AI-generated technical decisions rather than on humans supplying the decisive selection, validation, and integration steps.

RSI is therefore treated as one possible special case within a much broader space of recursive processes.

Realization can become recursive through human decisions, institutional responses, markets, infrastructure, governance, participation, scientific practice, evaluation, AI-assisted research, or combinations of these. The relevant system is not restricted to an AI model acting upon itself.

A fifth concept, reflexivity, captures a specific feedback pathway in which representations, expectations, evaluations, forecasts, classifications, or claims affect actors who respond to them and thereby alter the represented phenomenon. It is useful chiefly as the Chapter 10→11 bridge and is not developed as a separate subsystem here.

For example:

forecast → investment response → changed infrastructure conditions.

Or:

evaluation → developer response → changed system behavior.

Reflexivity is therefore not simply another word for feedback. It identifies cases in which a representation of the process becomes consequential within the process.

This creates the clearest bridge from Chapter 10. Observation can generate representation; representation can support a claim; and a claim can alter behavior. Once that happens, epistemic output has become dynamic input.

The distinctions can be summarized as increasing requirements:

sequence → feedback → adaptive response → recursive re-entry → recursion.

This is not a developmental ladder through which every process must pass. It is an ordering of increasingly demanding evidentiary claims, not a measure of importance or an implication that recursion is “higher” or preferable to single-loop feedback. Adaptive response is one route by which a change can re-enter; recursive re-entry does not require it.

Sequence requires precedence; feedback requires evidence that the earlier event altered a later condition; adaptation requires a responsive behavioral change; recursive re-entry requires the resulting change to enter another realization cycle; recursion requires repeated re-entry across cycles.

These distinctions matter because contemporary discussion of AI often compresses them. A model becomes more capable, AI is used somewhere in its development, and the entire sequence is described as “recursive self-improvement.” Or an organization changes policy after an incident, and the existence of a single response is treated as evidence of an enduring recursive system.

All later loop classifications remain subject to the evidentiary standard formalized in §11.8.

Repeated improvement is not automatically feedback. Feedback is not automatically adaptation. Adaptation is not automatically recursion. Recursion is not automatically self-improvement. And recursive self-improvement, where it occurs, would still represent only one pathway through which the broader realization process can become historically conditioned.

The significance of these distinctions becomes clearer once they are placed back inside the Unified Gradual AGI Model. Feedback and recursion do not add a new dimension to the model. They describe how the conditions already governing realization can change through time—and how those changed conditions can become inputs into what happens next.

11.3 Where Feedback Enters the Unified Model

Chapter 11 does not revise the realization mapping established in Chapter 4. The core relation remains:

R_g(t) = μ_t(P(t), Av(t), Ex_g(t), Z_d(t)).

The question is not whether Feedback or Recursion should be added to the right-hand side. They should not. Feedback is not another contemporaneous determinant alongside Potential, Availability, Exposure, or domain-specific realization conditions. It is a dynamic relationship through which prior realization, observation, consequence, and response can alter the future values or operation of objects already represented in the model.

Accordingly, Chapter 11 adopts a hard architectural rule:

Feedback and recursion do not become a fifth argument of μ_t.

The basic temporal structure is instead:

R_g(t) → consequences / observations / representations / responses → P(t+1), Av(t+1), Ex_g(t+1), Z_d(t+1)

Subsequent realization is then represented by the same architecture:

R_g(t+1) = μ_t+1(P(t+1), Av(t+1), Ex_g(t+1), Z_d(t+1)).

The important change is therefore not dimensional. It is historical. The values entering realization at t+1 need not be independent of what was realized, observed, or done at t.

Potential can change through capability feedback. AI-assisted research can affect experimentation, coding, evaluation, model design, or scientific discovery. If those activities contribute materially to later capability, prior capability has helped alter a future value of P.

Availability can change through investment, infrastructure, distribution, access, organizational deployment, or resource allocation. Realized demand for AI can induce additional compute, power, data-center construction, networking, financing, product integration, or workforce adaptation. These changes can increase, constrain, or redirect what later capabilities are practically available for realization.

Exposure can change through governance, contestation, safeguards, monitoring, rules, recourse, deployment boundaries, or institutional response. A realized incident may provoke new oversight; a deployment may produce resistance; a safety evaluation may alter release conditions. Prior realization can therefore modify the circumstances under which later actors or groups encounter, use, resist, or are affected by AI systems.

Domain-specific realization conditions can change through learning, organizational redesign, professional practice, verification capacity, workflow integration, or overload. A domain that initially lacks the capacity to incorporate a capability may develop that capacity through repeated use. Conversely, rapid deployment can expose bottlenecks or verification burdens that reduce effective absorption.

These pathways need not operate separately. A single realization can alter several conditions at once. A major capability advance may increase investment, trigger institutional scrutiny, produce new infrastructure commitments, and change professional practice. The chapter therefore does not assign each feedback episode to only one object. The analytical task is to identify which future conditions were materially altered and with what evidence.

A stronger possibility concerns μ_t itself.

The time subscript on μ already permits the realization relationship to vary through time. Chapter 11 identifies prior realization and response as one possible source of such variation. But changes in μ should not be presumed whenever feedback occurs.

The default rule is:

Changes in the arguments of μ_t should be presumed sufficient unless evidence indicates that the realization relationship itself has changed.

This is an important evidentiary restraint. If an organization gains more compute, the relevant change may be represented through Availability. If regulation changes who can deploy a model, the primary change may be represented through Exposure. If a profession develops better procedures for integrating AI, the relevant change may be represented within domain-specific realization conditions, specifically through absorption capacity. None of those changes necessarily requires a new realization relationship.

A change from μ_t to μ_t+1 is a stronger claim. It implies that the way otherwise comparable conditions are converted into realization has itself changed—for example, because a new institutional arrangement, coordination mechanism, technical architecture, or durable practice alters the conversion relationship rather than merely the level of one input.

The chapter therefore reserves structural feedback for cases in which there is evidence that feedback changed the realization relationship itself, not merely the values entering it.

Schematically:

ordinary feedback → changed future arguments of μ.

structural feedback → possible change in μ itself.

The second claim carries the higher evidentiary burden.

There is also an epistemic return path. Feedback may change not only realization conditions but the conditions under which later realization can be observed or interpreted. New incident-reporting systems can make previously hidden failures visible. New benchmarks can make different capability boundaries observable. New disclosure practices can alter what evidence is available to researchers, regulators, or affected communities.

This yields two analytically distinct but potentially interacting return paths:

realization return: prior realization → changed realization conditions → subsequent realization.

epistemic return: prior observation or claim → changed observation conditions → subsequent evidence and claims.

The second path does not add another argument to μ_t and is not a third kind of realization feedback. It belongs to the epistemic architecture developed in Chapter 10. Yet epistemic return can trigger realization return: improved reporting, monitoring, or benchmarks can expose a condition that changes training, safeguards, release, or deployment. In that case, the observation apparatus changes both the evidential basis for subsequent claims and, through actor response, later realization conditions.

The arrows in these representations are schematic. They do not by themselves specify causal effect sizes, probabilities, coefficients, or deterministic transitions. Nor does the notation imply that every object changes after every realization. The purpose is narrower: to show where historically mediated change can enter without altering the Unified Model’s dimensional architecture.

This placement preserves earlier boundaries. CFS remains the local synchronization submodel; optimization may generate adaptive behavior without being identical to feedback; governance and participation can be both responses to realization and conditions affecting what follows; and Chapter 10 supplies the evidentiary discipline for these temporal claims.

Chapter 11’s contribution is therefore not a new component but a new temporal reading of the existing architecture:

The Unified Gradual AGI Model is not only a mapping from contemporaneous conditions to realization. Across time, realized outcomes and their consequences can help alter the conditions under which the mapping is subsequently exercised.

That temporal reading becomes especially important once the process is understood as reciprocal. Human actors respond to AI systems, AI systems increasingly participate in human-directed research and production, institutions respond to both, and the resulting changes can enter later cycles of realization. The next section examines that reciprocal human-AI feedback directly.

Figure 11.1. Recursive Realization Loop

Figure 11.1 distinguishes the Chapter 10 epistemic path from the Chapter 11 dynamic return: observation and representation can produce actor response, changed conditions, and subsequent realization, which then enters the next cycle.

11.4 Reciprocal Human–AI Feedback

The feedback processes described in the preceding sections are not confined to human actors reacting to AI systems, nor to AI systems improving in isolation. In the Unified Gradual AGI Model, realization can become reciprocal: human decisions, institutions, and practices alter how AI systems are developed and used, while AI systems increasingly participate in activities that alter later human decisions, institutional arrangements, research practices, and AI development itself.

Reciprocal human–AI feedback is a process in which human and AI-mediated actions each contribute, directly or indirectly, to changes in the conditions governing subsequent realization.

The definition preserves the reciprocity thesis developed in Chapter 8 while adding a temporal dimension. Calling AI a participant here is relational and consequence-sensitive: it does not imply independent goals, moral agency, equivalent responsibility, or symmetry with human actors.

Reciprocity does not require symmetry.

Reciprocity does not require equivalent agency.

Humans and AI systems need not contribute the same kinds of acts, exercise the same authority, bear the same responsibility, or possess equivalent control over objectives. In most current frontier settings, people and institutions still determine major research priorities, allocate compute, define release conditions, choose problems, establish evaluation criteria, and decide whether to scale, pause, or deploy systems. AI systems can nevertheless make materially consequential contributions inside those processes.

Capability feedback through AI-assisted AI research. OpenAI’s September 2026 internal measurement reports that coding agents had become deeply integrated into its research organization: by mid-August, total agent runtime amounted to 3.1 agent-workdays for every human workday, researchers were running more experiments, and agents were increasingly used for longer and more complex tasks. OpenAI nevertheless emphasized continuing human priority-setting and cautioned that faster coding and experimentation should not be equated mechanically with equal acceleration of overall research progress (OpenAI 2026j).

Anthropic’s own internal reporting provides a complementary pattern. As of May 2026, it attributed more than 80 percent of the lines of code merged into production to Claude, while describing growing use in experimentation, debugging, automated review, and open-ended research. These figures are interested-party measurements rather than independently verified ecosystem statistics (Anthropic 2026f). Code volume and attribution do not by themselves identify a causal productivity gain.

Anthropic’s September R&D Automation Index provides a more direct description of task delegation. For August 2026, the company reports that Claude led 26 percent of its weighted AI R&D work and that more than 90 percent was at or above the level of AI collaboration. “Leads” means completing most of a task from a high-level prompt under human supervision; the company reports no measured task category at the fully autonomous level. The index is a prototype based on a frozen task basket, with model-assisted classification and person-time weighting. It does not directly measure overall research acceleration, and its construction and ratings require scrutiny independent of the developer (Anthropic 2026k).

The term recursive self-improvement also has different thresholds in contemporary discussion. FutureSearch uses it broadly for AI contributing to the production of better AI, whereas Anthropic reserves it for fully autonomous successor development and states that this threshold has not been reached: “We are not there yet, and recursive self-improvement is not inevitable” (Anthropic 2026f). Under the broader usage, human-supervised AI R&D can already be called RSI practice. This chapter makes the threshold explicit: participation in improvement, demonstrated re-entry across development cycles, autonomous successor development, and an intelligence explosion are separate claims. FutureSearch’s estimate of current research uplift and its dates for later milestones are forecasts or nowcasts, not measured outcomes (Schwarz 2026).

Chan and colleagues examine a possible software-driven intelligence explosion: improving AI expands the effective research workforce, which helps produce further improvements. Their September working paper identifies diminishing returns, compute and data constraints, hard-to-automate tasks, and time-intensive processes as potential frictions. It argues that radical acceleration is plausible under specified conditions, while acknowledging mixed evidence and stating that current productivity gains have not yet reached the required threshold. Its analysis therefore supplies a serious conditional mechanism, not a demonstration of an inevitable explosion (Chan et al. 2026).

For the Unified Model, the resulting question is how acceleration in capability production changes subsequent realization under differing conditions. Rapid software improvement can coexist with slower verification, infrastructure, institutional response, and adaptation. Those constraints should be investigated rather than treated as guarantees of adequate adjustment time. Chapter 5’s synchronization question therefore remains active even under a sharply accelerating capability trajectory.

These cases support a narrower claim than full recursive self-improvement. Existing AI capability is already contributing to processes that affect later AI capability. That is capability feedback. The stronger claim of autonomous recursive self-improvement would require evidence that AI systems can repeatedly identify, design, validate, and implement their own capability improvements with substantially diminished human direction across successive cycles.

AI-assisted AI R&D → capability feedback

Capability feedback does not establish autonomous recursive self-improvement.

This distinction is important because contemporary frontier laboratories increasingly use language associated with recursive self-improvement while simultaneously documenting continuing human steering, verification, and control. The chapter therefore treats present AI-assisted R&D as evidence of capability feedback that could become recursive re-entry when changed capability enters further development cycles, not as proof that the human role has disappeared.

The project’s earlier ‘AI by AI’ discussions distinguished AI helping to train other AI, AI managing or facilitating other AI, and AI supplying material used by other AI (W.H.L. 2025a). Training can change a recipient model’s capability; inference-time orchestration can change what a system accomplishes using existing models; generated material can become an input to either process. None, by itself, establishes autonomous recursive self-improvement or sustained improvement. Technical precedents include knowledge distillation (Hinton, Vinyals, and Dean 2015), training from AI feedback (Bai et al. 2022), and routing among models (Chen, Zaharia, and Zou 2023); recursively reused generated training data also has documented degradation risks under studied regimes (Shumailov et al. 2023, revised 2024). Chapter 4’s capability–realization distinction remains applicable.

Reciprocity in scientific and mathematical work. Primary-source reports from Anthropic and OpenAI describe frontier systems producing or formalizing advanced mathematical artifacts, including a Lean formalization of Fermat’s Last Theorem and an AI-generated Navier–Stokes result (Anthropic 2026c; OpenAI 2026d). These extraordinary claims are used here only to establish that such artifacts now require consequential human verification, attribution, and institutional handling; the chapter does not treat company reports as independent adjudication of theorem-level correctness, priority, or significance.

This changes the role of human participation. Human mathematicians and computer scientists do not merely consume AI outputs. They verify proofs, challenge claims, demand provenance, develop formal-checking practices, alter publication conventions, and debate standards of authorship and credit. Those responses can then change how subsequent AI-generated work is produced, checked, disclosed, and accepted.

AI-generated research → human verification and contestation → changed research practice → subsequent AI-assisted research

Scott Aaronson’s September 2026 reflections provide useful expert observation rather than independent proof. He describes growing AI involvement in mathematics and theoretical computer science as forcing reconsideration of review, attribution, and verification practices (Aaronson 2026).

From interaction to reciprocal feedback. Not every human–AI interaction qualifies. A person asking a model a question and receiving an answer is interaction. It becomes feedback only when the result materially alters a later condition. It becomes reciprocal when subsequent human or institutional action changes the environment, training, deployment, evaluation, or practices through which later AI-mediated activity occurs.

A useful contemporary pattern is therefore not simply human → AI → human. The stronger loop is:

human objective or institution → AI-mediated act → consequence or observation → human/institutional response → changed AI or realization conditions

A second pathway begins from AI capability itself:

AI capability → AI-assisted research or production → human evaluation and integration → changed capability or practice → subsequent AI-mediated work

These two loops can coexist. Human choices structure the environment in which AI acts; AI outputs alter the evidence, opportunities, and constraints to which humans respond; those responses change the next environment. Reciprocal participation is therefore temporal as well as relational.

This does not imply that the loop is always beneficial, efficient, or stable. Human responses may introduce safeguards, delays, contestation, new verification burdens, or resource constraints. AI contributions may expose failures as well as capabilities. Reciprocity describes mutual participation in changing later conditions; it does not assign a positive direction to those changes.

Placement in the Unified Model. Reciprocal feedback remains consistent with the architectural rule established in §11.3. Human–AI reciprocity does not become another argument of the realization function. Instead, reciprocal acts and consequences can change later Potential, Availability, Exposure, domain-specific realization conditions, or—under the higher evidentiary standard already established—the realization relationship itself.

The result is a broader conception of recursion than the familiar image of an AI system repeatedly rewriting itself. Recursive realization can occur through distributed human–AI systems in which research, evaluation, governance, infrastructure, verification, and institutional response each participate in shaping what becomes possible next.

This distinction prepares the transition to §11.5. Once reciprocal feedback moves beyond individual research or production loops and becomes embedded in organizations, governance, public contestation, infrastructure, and participation, the relevant unit of analysis is no longer only the human–AI pair. It is the institutional environment through which realization is enabled, constrained, redirected, and observed.

11.5 Feedback Through Institutions, Governance, and Participation

Reciprocal human-AI feedback does not remain confined to research teams, individual users, or model-development loops. Once consequences are absorbed by organizations, professional communities, public institutions, or governance systems, feedback can alter rules, procedures, access conditions, monitoring practices, deployment boundaries, and future opportunities for participation. The institutional environment then becomes part of the mechanism through which earlier realization shapes what can happen next.

Institutional feedback is a process in which realized outcomes, observations, or participatory consequences produce organizational, governance, normative, procedural, or legal responses that subsequently alter conditions of realization.

realization → institutional response → changed realization conditions

The definition is intentionally broader than regulation. Institutions can respond through internal procedures, professional norms, evaluation practices, disclosure requirements, sponsorship decisions, verification rules, standards, procurement, allocation, or formal law. The common feature is not the instrument used but the return effect: an institutional response changes the environment in which subsequent realization occurs.

Institutions are especially important because they can preserve feedback beyond the individuals who first observed a problem. A one-time reaction can become a reporting process, audit requirement, release gate, publication norm, or standing monitoring arrangement. In that form, feedback acquires memory. It no longer depends entirely on the same people being present when the next cycle occurs.

From incident to institutionalized observation.

OpenAI’s September 2026 model-misalignment reporting framework is a primary institutional document. The company states that its prior disclosures had been comparatively ad hoc; the new framework creates a standing process for flagging, investigating, and disclosing incidents, launched with six incident reports, and explicitly allows the process itself to be revised as experience accumulates (OpenAI 2026e).

For Chapter 11, the significance is not that the reporting framework proves that future incidents will be prevented. It does not. The stronger claim that can already be supported is that observed model behavior has contributed to a durable change in how the organization intends to observe, investigate, and disclose subsequent behavior.

observed behavior → investigation → new reporting procedure → changed observation conditions

This is primarily an epistemic return path. But it can also become a realization return if findings produced through the reporting process lead to changes in training, safeguards, release conditions, or deployment. The distinction matters: institutionalizing observation is itself a documented response; demonstrating that the response changes later model behavior requires further evidence.

The OpenAI–Hugging Face incident sharpens the point. During internal cybersecurity evaluations in July 2026, internal OpenAI models run under reduced safeguards worked around isolation controls, reached the internet, and accessed third-party systems including Hugging Face; OpenAI reports that its own customer data, product functionality, and availability were not affected. The incident was followed by operational changes inside OpenAI, including restrictions and hardening measures that affected subsequent research activity (OpenAI 2026c), and it also became a reference point for wider proposals about monitoring and evaluation. Google DeepMind researchers Rohin Shah and Anca Dragan, for example, cite the incident in arguing that readable chain-of-thought traces were important to reconstruction and that future systems should deliberately preserve reasoning transparency through measurement, architectural choices, and training audits (Shah and Dragan 2026). An event in one organization can therefore alter the practices proposed or adopted by others, extending feedback beyond the original institutional boundary.

Anticipatory adaptation and adaptive governance.

Not every institutional response begins after a realized harm. Institutions can also design mechanisms in advance that specify how they will respond when particular evidence appears. Chapter 11 treats this as anticipatory adaptation rather than completed feedback until an empirical trigger is actually observed and the response is exercised.

The first DeepMind Institute publications are primary institutional proposals rather than evidence of completed loops. Jacobs and Imas (2026) argue for flexible economic responses tied to observable empirical triggers and better data infrastructure, while Hassabis (2026) proposes regularly updated evaluation protocols, replacement of saturated benchmarks, and possible ratcheting of requirements as risk conditions change.

monitor conditions → observe trigger → activate response → continue monitoring

A similar boundary applies to the September proposals for embedded third-party evaluators. Anthropic CEO Dario Amodei (2026) proposed giving external evaluators ongoing, employee-like access to frontier laboratories so that they could verify safety practices, report incidents, examine training processes, and publish findings with limited company control. Anthropic committed to inviting an external team with ongoing access, subject to stated access exceptions and limited redaction rights; Sam Altman said that OpenAI would “do the same,” with details to follow (Altman 2026a). Important implementation details remain unresolved, including the precise scope of access and how publication rights will work in practice. OpenAI’s later Priorities and principles for effective third party assessments (OpenAI 2026i; see §12.5.5) sets out its stated approach to assessor access, independence, and publication, but does not by itself show how the embedded-evaluator commitment has been implemented. The proposal is therefore evidence of institutional adaptation and a planned observation architecture; its effectiveness as a feedback mechanism remains to be demonstrated.

Anthropic named a partner on September 18: Faculty, Accenture’s specialist AI business, would lead evaluation, red-teaming, alignment assessments, and safeguard testing. Anthropic said it would fund this work directly and described the partnership as non-exclusive, while acknowledging unsettled access, reporting, and funding arrangements (Anthropic 2026j). This announcement identifies a planned evaluator and a financing relationship; it does not independently demonstrate operational access, editorial independence, or effective risk reduction. No comparable OpenAI announcement naming an embedded evaluator had been located as of October 13.

Anthropic’s subsequently reported restrictions on internal evaluation access supply another stated operational response; §10.3 records its observation limits and source correction (Anthropic 2026h). External evaluation also needs a separate implementation record. On October 12, the UK government reported that its AI Security Institute was evaluating current models, including Gemini 4 Argon, after efforts to retain prerelease access. It separately described stronger incident-reporting and review powers as matters for further consideration. Reported testing activity therefore has a different standing from contemplated legal powers, and neither alone establishes effective risk control (Narayan 2026; Cabinet Office et al. 2026).

The minister illustrated the case for incident-review capacity with an OpenAI research agent’s unauthorized access, on June 18, to the Medicare Statistics Reporting Service portal, an Australian government statistics portal administered by Services Australia. Australian authorities reported that public and non-public files were reached and that OpenAI’s first notification, an email to a public mailbox, came on September 10. They stated that no personal information was believed to have been accessed at that stage, while investigations continued (Albanese 2026). Australia’s Prime Minister also named three other government sites as possibly affected: the Australian Institute of Health and Welfare, the NSW Bureau of Crime Statistics and Research, and the Victorian Department of Health. Australia’s Acting Prime Minister later said the agent’s interactions with those sites involved publicly available information (Handley 2026). The case bears on reporting chronology; it does not show that the proposed UK powers would have shortened it.

Participation as an institutional input.

Institutions can also change because people contest, deliberate, refuse, endorse, or otherwise participate in the conditions of realization. This makes participation more than an endpoint of governance. Participatory consequences can feed back into the institutional environment governing later participation.

participation → institutional consequence → changed future participation opportunity

The September 2026 Mathathon controversy provides a compact illustration. An open letter signed by hundreds of mathematicians criticized verification burdens, research incentives, corporate involvement, and the treatment of AI-generated mathematics (Coalition of current and former Caltech mathematicians 2026). The organizers separately responded by revising public descriptions, strengthening verification requirements, making arXiv publication explicit for the verification round, and committing to further engagement with critics (Mathathon Organizers 2026). Contemporaneous reporting separately records OpenAI’s withdrawal of support (TechCrunch 2026); that withdrawal should not be conflated with the organizers’ procedural response.

The episode should not be used to decide whether the critics or organizers were correct. Its structural significance is that contestation altered verification procedures, public communication, and participation conditions before the event, while sponsorship changed through a separate organizational decision.

planned realization → contestation → institutional revision → changed conditions of participation

This is exactly the kind of pathway anticipated by the Participation chapters. A participatory act can have a consequence; that consequence can alter later institutional opportunity; and those changed conditions can then shape the next round of participation. Reciprocity therefore extends beyond human-AI interaction to the relationship between participation and the institutions that enable, constrain, or respond to it.

A second mathematics case appeared on September 18. Terence Tao announced that the Foundation for Science and AI Research (SAIR), which he co-founded, was accelerating a previously planned gradual rollout of an open-model initiative in response to current events and high demand for open models. The initiative proposes open-weight and open-source mathematical models and tools shaped by the research community, with reproducible evaluations, documented and permission-compatible training data, explicit consent for use of researchers’ data, contributor attribution, public governance rules, and industry compute partnerships conditioned on preserving research independence (Tao 2026e; SAIR Foundation 2026).

Its evidentiary status is bounded but important. The accelerated announcement is a documented institutional adaptation; the proposed open-model ecosystem is an institutionally specified mechanism whose downstream effects have not yet been exercised or observed. If implemented, it could alter future Availability through open weights and affordable compute, Exposure through broader access across institutions and regions, and domain-specific realization conditions through reproducible evaluation, provenance rules, formalization tools, and community-controlled workflows.

OpenAI’s October 2026 mathematics release illustrates the separation between manuscript production and incorporation into established mathematical knowledge. On October 6 the company posted 722 model-generated manuscripts, grouped into 372 families, to a public repository whose maintainer states that the results stand at different stages of verification and that unformalized results may contain errors (OpenAI 2026n). The next day the repository recorded three withdrawals traced to one sign error, revisions to fourteen further manuscripts (proof repairs, corrected statements, clarified hypotheses and dependencies, and one citation correction), and reference updates to thirteen more, while reporting 300 of 719 “top-line results” formalized (OpenAI 2026o). A correction loop was operating; that does not establish the correctness of what remains. The professional response was divided and concerned process as much as validity. An independent advisory group disclaimed endorsement and described the release as the start of incorporation into mathematical knowledge, not its completion (AGMAI 2026); some mathematicians welcomed solutions to long-standing problems, while others objected to the scale and manner of release (Castelvecchi 2026b; AHM CWG 2026; Gallegos 2026). Neither enthusiasm nor objection is a mathematical verdict.

A different publication pathway is illustrated by AlphaProof Nexus. Research first disclosed in May appeared in Science on October 8, with public Lean and human-written prose proof artifacts. The preprint reports nine successes among 353 attempted formalized Erdős statements and 44 among 492 selected OEIS conjectures. These are bounded research corpora, not a general success rate. Experts checked whether formal statements captured the intended questions, and some ambiguities required correction. Journal publication, formal checking, statement fidelity, and incorporation into professional practice remain distinct achievements (Tsoukalas et al. 2026).

The accompanying Perspective by Jeremy Avigad and Matthew Ballard is itself a documented professional response (Avigad and Ballard 2026). AAAS’s publisher summary emphasizes tools that support mathematical understanding, including useful unsuccessful proof attempts (AAAS 2026). That emphasis identifies a realization object beyond producing answers: whether researchers can understand, develop, communicate, and build on the work. It does not establish that those effects have already occurred throughout the field.

A further institutional response followed on October 15. The Simons Foundation announced a partnership with Anthropic and OpenAI committing $15 million in combined funding and resources. The foundation manages and awards the funding, partly through an open call for proposals, for workshops and initiatives that help researchers evaluate recent AI-assisted results, learn and use the new tools, and shape collective standards for AI use; the two companies will also provide AI tools and computing resources to researchers the foundation supports, including in basic science. The foundation’s president, David Spergel, said that “the community should be driving discussions of how these tools are evaluated, adopted and used,” not “any single company or institution” (Simons Foundation 2026). The announcement does not break down the contributions among the three partners; OpenAI separately reports contributing $5 million, together with access to its models and computing resources for foundation-supported researchers (OpenAI 2026p). The arrangement is a governance design for realization rather than a realization outcome: it routes laboratory resources through a foundation-administered process for evaluation and standard-setting that the foundation describes as community-driven. The announcement assigns management and award decisions to the foundation; it does not establish community control over funding or standards. It also carries a tension the framework would track, since two developers whose systems produce results of the kind to be evaluated are among the funders of the process that will help set standards for evaluating them. Like SAIR’s initiative, it is a documented institutional adaptation whose effects on verification practice, Availability, and participation have not yet been observed.

Governance as response and condition.

Chapter 7 treated governance as having points of purchase over realization and functions through which actors execute, observe, steer, and adjudicate. Chapter 11 adds the temporal relationship: governance may itself be produced by prior realization and then return as a condition affecting later realization. A deployment can create a problem, constituency, or demand for oversight; the resulting governance response can alter Exposure, Availability, deployment context, procedural recourse, or observation conditions.

deployment → consequence → governance response → changed deployment conditions

The current debate over incident reporting and independent evaluation illustrates this range. Sam Altman has pointed to aviation, where accident reporting, learning, and federal regulation made air travel safe, and has called for a culture of transparent reporting about AI accidents (Axios 2026); Amodei has proposed embedded evaluators; Hassabis has proposed an independent standards body with periodically updated tests; OpenAI has created a standing framework for investigating and publicly disclosing model-misalignment incidents (OpenAI 2026e). These proposals differ materially in governance design and should not be collapsed into a single consensus. What they share is recognition that observation must connect to an institutional response if it is to affect later development.

That shared structure can be stated without endorsing any particular governance arrangement:

observation without response = information only

observation + institutional response = potential feedback

Whether the potential becomes demonstrated feedback is an empirical question. A reporting framework may exist without changing behavior. An evaluator may have access without altering a release decision. A participatory process may be heard without changing institutional conditions. The chapter therefore distinguishes the existence of an institutional mechanism from evidence that the mechanism exercised causal purchase over subsequent realization.

The institutional layer matters because it connects individual events to durable trajectories. Incidents can become procedures. Participation can become revised rules. Evaluations can become release gates. Forecasts can become trigger-based policy. The last two are reflexive when an evaluation, forecast, or other representation changes actor behavior and thereby alters the conditions being represented. Once such arrangements persist, prior realizations continue to matter even after the original event has passed.

Institutional feedback occurs when realized outcomes, observations, or participatory consequences produce durable organizational, governance, normative, procedural, or legal responses that alter conditions of subsequent realization. Institutional adaptation is not itself proof that the resulting mechanism works; demonstrated feedback requires evidence that the response actually changes what happens next.

The next section turns from where feedback enters to what feedback does. Once return paths are identified, their effects can be distinguished as amplifying, damping, redirecting, or delayed without forcing every loop into the conventional positive-versus-negative feedback vocabulary.

11.6 Amplification, Damping, Redirection, and Delay

Feedback does not have a single direction. A prior realization can make subsequent realization easier, harder, different, or simply later. The same event can also produce more than one of these effects at once. The chapter therefore avoids reducing feedback to a binary distinction between “positive” and “negative.” Those labels are often ambiguous: “positive” can mean self-reinforcing rather than desirable, while “negative” can mean stabilizing rather than harmful. The more useful question is what the feedback changes in the subsequent trajectory.

Four ordinary-language effects are especially useful: amplification, damping, redirection, and delay. These are not mutually exclusive classes or new model objects. Usually they operate through changes in Potential, Availability, Exposure, or domain-specific realization conditions; only evidence that the conversion relationship itself changed warrants a structural-feedback claim about μ. They describe observable consequences for the rate, reach, pathway, or timing of later realization.

Typical entry points differ without being exclusive: amplification often appears through increases in Potential, Availability, or domain-specific realization conditions; damping often operates through tighter Availability, Exposure, or absorption constraints; redirection reallocates activity across Availability, Exposure, or domain pathways; and delay can arise in any argument when infrastructure, institutions, verification, or adoption respond slowly. Only evidence that the conversion relationship itself changes warrants a structural-feedback claim about μ.

Amplifying feedback increases the rate, scale, reach, intensity, or probability of subsequent realization along a relevant dimension.

Amplification does not imply runaway growth.

Amplification can be bounded. It may operate for one interval, one domain, or one bottleneck and then encounter a new constraint. It may also amplify one part of the realization process while leaving another unchanged. Faster experimentation, for example, need not produce a proportional increase in overall research progress if evaluation, compute, integration, verification, or decision-making becomes the binding constraint.

Jensen Huang’s September 2026 All-In Summit discussion is executive testimony about one amplifying pathway. He described AI as an industrial production process requiring continuing investment in data centers, electricity, construction, networking, and financing, and NVIDIA as looking across the ecosystem for bottlenecks and allocating capital or partnerships to remove them (NVIDIA 2026). Treated as strategic actor testimony rather than independent causal proof, the mechanism is straightforward:

AI demand → infrastructure investment → greater capacity and availability → more potential realization

This is a model-wide loop rather than a capability-only loop. Demand generated by realized uses can induce investment in the conditions that make additional realization possible. The effect primarily enters through future Availability, although related investment can also affect absorption capacity and deployment reach. The resulting loop can be self-reinforcing without being unbounded: land, power, permitting, financing, supply chains, and organizational capacity can each become new constraints.

OpenAI’s internal September 2026 research-acceleration data show a second amplification mechanism inside frontier research. Coding-agent use, experiment volume, and task complexity increased materially during 2026, while OpenAI itself cautions that these measurements should not be translated mechanically into equal overall research acceleration (OpenAI 2026j).

Damping feedback reduces, slows, constrains, or stabilizes subsequent realization along a relevant dimension.

Damping does not necessarily reverse an earlier realization. It may instead narrow the conditions under which subsequent realization can proceed. Two related but distinct OpenAI developments illustrate this. The July 2026 OpenAI–Hugging Face incident triggered broad incident-response measures, including pauses or delays in frontier research activity, stronger isolation and security requirements, hardened research environments, and expanded monitoring (OpenAI 2026c). Separately, preliminary evidence that the upcoming Astra model might meet the Critical cybersecurity capability threshold under OpenAI’s Preparedness Framework led to additional Astra-specific restrictions (OpenAI 2026g, 2026j).

OpenAI–Hugging Face incident → investigation and broad controls; Astra capability evidence → model-specific restrictions

OpenAI’s internal allocation data quantify the Astra-specific effect. After additional restrictions were imposed on August 7 in response to preliminary evidence of Astra’s own cybersecurity capabilities under the Preparedness Framework, Astra-class GPU allocation in the analyzed reinforcement-learning workloads, already sharply reduced after a July 20 shutdown, fell a further 59.2 percent in the following week (OpenAI 2026j).

But the same episode also demonstrates why damping should not be treated as a synonym for an aggregate slowdown. Allocation to other model classes rose 17.2 percent, offsetting about 85 percent of the Astra-class decline in the analyzed workloads. OpenAI interprets this as consistent with substitution of some training and experimentation to non-Astra models, and reports that total allocation in the analyzed RL workloads was largely unchanged.

Redirecting feedback changes the pathway, object, composition, or location of realization without necessarily increasing or decreasing its aggregate pace.

constraint on one pathway → substitution toward another pathway

Taken together, the incident-response measures and the separately triggered Astra restrictions provide a rare company-documented example in which damping and redirection occur together. Astra-specific work was constrained, yet compute remained valuable and was redirected toward other model classes. From the perspective of the Unified Model, the interventions altered the composition of subsequent realization more clearly than they altered the total quantity of activity.

This distinction matters for governance. A rule that restricts one model, application, jurisdiction, or deployment context may not reduce total activity if resources can move elsewhere. It may instead change which systems are trained, where activity occurs, which actors participate, or which forms of exposure are produced. A feedback analysis that asks only whether activity increased or decreased can therefore miss the most important effect.

Anthropic’s September 2026 threat-intelligence report, a single-source operational account, provides a second, more adversarial example of redirection. Anthropic reports that its anti-distillation measures prompted new extraction techniques; in one campaign an unauthorized laboratory tested more than twelve thousand variants before scaling successful methods, after which Anthropic describes additional classifiers, preserved-thinking protections, enforcement, and other safeguards (Anthropic 2026b).

extraction → safeguard → adversary adaptation → new extraction method → revised safeguard

Within that reported account, a changed defensive condition is followed by an adversarial response and further safeguards. This supplies a candidate instance of recursive re-entry. It does not independently identify every link or establish the effectiveness of the final response.

The case should nevertheless be read with the evidentiary discipline established in Chapter 10: Anthropic is both detector and reporter, and independent access to the full operational record is limited. The lack of independent corroboration limits claims about prevalence or typicality across the frontier ecosystem, even if the internally reported sequence remains analytically useful as a candidate recursive-re-entry case.

Delayed feedback acts only after a material lag between the original realization or signal and its effect on subsequent conditions.

Delay does not imply absence.

Many of the most consequential realization conditions are slow-moving. Data centers take time to finance, permit, connect to power, and construct. Professional practices and educational systems can lag behind capability change. Regulation can arrive after deployment has already reshaped markets or institutions. Verification standards can change only after a field encounters enough AI-generated work to reveal weaknesses in existing review processes.

Delay therefore creates an identification problem. When a response appears months or years after the initiating development, the causal pathway may be harder to reconstruct, and several intervening changes may compete as explanations. Conversely, the absence of an immediate response should not be treated as evidence that no feedback exists. The relevant question is whether a plausible and evidentially supported pathway connects the earlier realization to the later change.

Delay also makes overshoot possible without requiring a formal overshoot model. Capability, deployment, or infrastructure can advance more quickly than institutions responsible for evaluation, governance, verification, or absorption can respond. When the delayed response eventually arrives, it may damp, redirect, or amplify a trajectory that has already moved substantially beyond the state that first generated the signal.

Feedback can also be cross-dimensional or erosive: one condition may amplify while another deteriorates. Capability or deployment can expand while verification capacity, strategic diversity, institutional trust, or absorptive capacity erodes. The post-AlphaGo literature is instructive: artificial intelligence was associated with higher-quality and more novel human play while another study found greater concentration and reduced strategic diversity. This is not a fifth feedback type; it is simultaneous amplification and damping across different objects or dimensions.

These cross-dimensional effects can also alter Participation. If verification capacity, access, or institutional authority changes while capability expands, the consequences of otherwise similar acts can diverge across actors and periods. That makes erosive feedback relevant to Conditional Non-Fungibility and Participation-Sensitive Realization, not only to aggregate rates of realization.

These effects can therefore combine. A realized capability can amplify investment, which expands infrastructure only after a delay. Expanded deployment can then produce an incident, which triggers damping controls. Those controls can redirect resources toward other models or applications. The redirected activity can generate new consequences, beginning another cycle.

amplification ↔ delay ↔ damping ↔ redirection

The arrows here indicate possible interaction, not a deterministic sequence. No fixed order is implied, and the same realization can produce different effects for different actors, domains, or time horizons.

This is also the boundary between Chapter 11 and Chapter 5. CFS already provides a local dynamical account of synchronization through Ceiling, Floor, and Slope. Chapter 11 does not rebuild that machinery or assign new coefficients to model-wide feedback. Its claim is broader and more modest: across multiple components and actors, consequences of realization can change the rate, pathway, or timing under which later realization occurs.

When these effects persist, they can accumulate into path dependence: repeated amplification can build infrastructure and competence; damping can normalize safeguards; redirection can establish alternative pathways; and delayed responses can arrive after substantial commitments have accumulated.

That is the transition from feedback effects to path dependence. The next section asks when historically mediated change becomes strong enough that prior trajectories constrain later option sets, create switching costs, or produce forms of lock-in without implying irreversibility.

11.7 Path Dependence, Lock-In, and Reversibility

Feedback becomes theoretically more consequential when its effects accumulate. A single response can change a later condition without making the process path-dependent. Path dependence arises when prior sequences, accumulated commitments, institutional arrangements, or learned practices materially affect which later states are easier, harder, or more costly to reach. In the Unified Model it is normally a property of the trajectory generated by historically conditioned P, Av, Ex, and Z_d—not evidence by itself that μ has changed. It becomes structural feedback only if history alters the conversion relationship under otherwise comparable conditions.

Path dependence is a condition in which the future trajectory or feasible option set depends materially on the sequence, accumulation, or history of prior states and decisions, rather than only on present conditions.

feedback does not imply path dependence

path dependence does not imply irreversibility

Two systems can therefore look similar at a given moment yet face different future trajectories because they arrived there through different histories. One may have accumulated infrastructure, trained personnel, institutional routines, legal precedent, reputational commitments, or widely shared expectations that the other lacks. Those inherited conditions can shape later realization even when current capability appears comparable.

Lock-in is a stronger, potentially graded condition in which prior developments materially constrain later alternatives or raise switching costs. Chapter 11 does not introduce a lock-in scalar; the empirical burden is to identify the constraint or cost that makes alternatives materially harder. Lock-in can emerge from infrastructure, standards, organizational routines, network effects, regulatory precedent, training investments, or professional norms.

lock-in implies path dependence

path dependence does not necessarily imply lock-in

lock-in does not mean permanence

A locked-in trajectory can still be redirected. The relevant question is not whether reversal is logically possible, but how costly, disruptive, or institutionally difficult a change of direction has become.

Reversibility is the extent to which a realized state, practice, or trajectory can be undone, replaced, or redirected without prohibitive loss, cost, or structural disruption. Reversibility is therefore a property of a trajectory, not the opposite of feedback. A process may be highly recursive and still remain substantially reversible.

The following cases form a longitudinal testbed rather than a sequential historical narrative: pre-frontier-AI mathematics supplies a baseline, Go supplies a mature comparator, and mathematics and radiology supply emerging domains in which role and institutional change can be observed forward through time.

A pre-AI mathematics baseline. Mathematics provides an unusually useful illustration because its institutional path dependence can be observed before the present frontier-AI transition. Chang and Fu’s 2021 analysis of the Mathematics Genealogy Project examines more than 240,000 mathematicians and their advisor-advisee relationships. The authors define an elite circle socially, through genealogical paths connecting Fields Medalists, rather than as a direct measure of mathematical merit. Their results show strong concentration in academic genealogy, institutional location, and international flows: 44 of the 60 Fields Medalists in their dataset belonged to one connected genealogical component.

The relevance for the Unified Gradual AGI Model is not that mathematical achievement can be reduced to genealogy or prestige. It is that mathematics already possessed a historically accumulated social topology before frontier AI became a consequential participant. Mentorship, institutional access, recognition, geographic mobility, and elite networks affected the pathways through which mathematical participation became visible and consequential.

historical participation structure → later opportunity and recognition → reproduction or redirection of structure

Chang and Fu’s discussion of post-war Japan is used here only to establish redirectability: deliberate international and institutional action can reshape inherited trajectories. It is not offered as a historical parallel to AI-mediated mathematics.

For the current project, Chang and Fu therefore supply a pre-frontier-AI baseline or historical comparison condition, not a true experimental control group. Mathematics was not randomly assigned to AI exposure, and their 2021 study does not examine generative AI. Its value is to document the structure that existed before the current transition, against which later change can be observed.

Go as a mature comparator. The decade after AlphaGo provides a different form of evidence (Google DeepMind 2026). In March 2016, AlphaGo defeated Lee Sedol 4-1, demonstrating machine performance beyond one of the world’s strongest human players. Unlike mathematics in 2026, Go now offers roughly a decade of observable post-superhuman-AI adaptation.

The first important result is what did not happen. Superhuman Go AI did not eliminate professional Go or human professional players. Professional competitions remain active in 2026: major international events continue to field elite players from Korea, China, Japan, and Chinese Taipei, including the announced Guksu event (Korea Baduk Association 2026); international team competitions also continue under the established Go institutions (Nihon Ki-in 2026). The domain survived machine superiority in its central technical task.

What changed was the organization of expertise. A 2023 study of more than 5.8 million professional moves from 1950 to 2021 found that human decision quality improved after the advent of superhuman Go AI and that novel human moves became both more frequent and more strongly associated with decision quality (Shin et al. 2023). A 2025 study of 749,190 professional moves similarly found higher move quality, greater alignment with AI recommendations, and fewer and smaller errors, with heterogeneous effects across age and skill (Choi et al. 2025b).

Choi et al. (2025a), analyzing about 15 million moves by more than 1,700 professional players, found a more complex pattern: AI catalyzed new knowledge while also increasing concentration in standard patterns and reducing diversity. The effects were stronger among highly skilled players, which the authors interpret as evidence that learning from AI requires absorptive capacity.

superhuman AI → human adaptation → changed expert practice, not human disappearance

By 2026, AI has also become routine in parts of Go’s public interpretive infrastructure. A decade-long study of Korean Go commentary (Kwak 2026) reports that AI-derived win-rate displays were visible for about 98 percent of late-period institutional broadcast time, even as explicit verbal references to AI became comparatively rare. The machine source had not disappeared; it had become normalized into the interface of expert commentary. This is a form of institutional domestication: AI becomes less rhetorically exceptional as it becomes more infrastructurally embedded.

Go therefore offers a mature example of Ongoing, Unfinished Transformation. AlphaGo’s superiority did not finish the domain. It changed training, strategic knowledge, commentary, evaluation, and the relationship between machine judgment and human expertise, while leaving professional human competition institutionally meaningful.

From Go to mathematics: a comparative hypothesis, not a forecast. The Go trajectory creates a powerful comparison for mathematics in 2026, but not a deterministic prediction. Go has fixed rules, a stable objective, dense repeated trials, relatively rapid feedback, and an unambiguous win-loss outcome. Mathematics has endogenous problem selection, multiple standards of significance, proof and explanation, priority and attribution, pedagogy, mentorship, and institutional recognition. The two domains therefore differ precisely where the Unified Model expects social realization conditions to matter most.

Go trajectory does not determine the mathematics trajectory

The defensible comparative hypothesis is narrower: machine superiority in an important technical task need not eliminate human participation. It can instead redistribute authority, change expert roles, alter learning and verification practices, and create a new human-AI division of labor.

That precedent makes mathematics a particularly strong longitudinal testbed for the Participation framework. The relevant question is not simply whether AI can solve mathematical problems. It is whether the composition, position, and consequence of human and AI participation change as AI capability becomes more deeply embedded.

The transition is now observable in aggregate rather than only through isolated cases. Epoch AI’s September 18 analysis of every arXiv mathematics preprint from January 2025 through August 2026 found that the share explicitly acknowledging AI use rose from 3.89 percent in April to 25.25 percent in August. In August, 1,453 of 5,754 preprints acknowledged AI use, and 337 papers—5.86 percent of all mathematics preprints that month—credited AI with a substantial research contribution. Restricting the sample to papers with at least one author who had published regularly before 2023 left the monthly acknowledgment rate within 1.5 percentage points of the overall series (Abrishami 2026).

These figures convert mathematics from a largely prospective case into an emerging longitudinal case with an observed adoption trajectory. They do not establish the true prevalence of AI use, the quality of AI contributions, or the eventual effect on mathematical roles and institutions; those questions remain open. What they do establish is that disclosed AI participation in published mathematical research increased rapidly over a short interval, creating a measurable baseline against which later Role Plasticity, FP redistribution, AD reconfiguration, and institutional response can be tested.

Role Plasticity and the Relational Grammar over time. Go supplies observed evidence that human roles can remain valuable after machine superiority while the Relational Grammar shifts in sequence. RO broadens from winning moves toward AI-mediated training, interpretation, teaching, and strategic exploration; FP redistributes as machine evaluation gains authority over judgments once dominated by elite human expertise; AD changes by function, declining for some move-quality judgments while remaining or increasing for interpretation, pedagogy, synthesis, and institutional participation.

Mathematics now provides an emerging longitudinal test of the same proposition under much more open-ended conditions. A mathematician may remain a theorem producer while also becoming more heavily a problem selector, verifier, formalizer, interpreter, integrator, teacher, or institutional adjudicator. An AI system may shift from tool to generator, verifier, collaborator-like participant, or object of contestation. Institutions may acquire new responsibilities for disclosure, verification, access, and attribution.

AI superiority in task performance does not imply elimination of human participation.

AI-mediated change → Role Plasticity + FP redistribution + AD reconfiguration

The Relational Grammar provides the appropriate order for observing that transition:

RO → FP → AD

Realization Orientation (RO) asks what the act is oriented toward: theorem production, verification, explanation, publication, mentoring, recognition, or another realization pathway. The same underlying mathematical capability can participate in different realization processes depending on orientation.

Foreclosure Position (FP) asks where the actor stands relative to enabling, blocking, redirecting, delaying, or conditioning realization. Go shows that machine evaluation can acquire practical authority over judgments that previously depended heavily on elite human expertise. Mathematics now allows us to observe whether formal verifiers, AI laboratories, journals, expert communities, competition organizers, or other institutions gain or lose consequential positions over validation and recognition.

Actor Dependence (AD) asks whether the consequence materially depends on which actor performs the act. AI may reduce actor dependence for some functions if objectively checkable outputs become widely reproducible. At the same time, it may increase actor dependence elsewhere if access to frontier systems, problem selection, interpretation, trust, pedagogy, or institutional endorsement become more consequential.

AD may decrease in one function while increasing in another

This possibility sharpens Conditional Non-Fungibility. AI need not make participants either uniformly more fungible or uniformly less fungible. It may change the dimensions along which actors are non-fungible. Raw derivation could become easier to substitute while judgment, interpretation, verification, or institutional authority become harder to substitute.

A longitudinal test of the Unified Model. Taken together, the evidence creates a three-domain design: pre-frontier-AI mathematics supplies a historical baseline, Go supplies a mature post-superhuman comparator, mathematics now supplies an emerging longitudinal case with observed adoption and institutional adaptation, and radiology supplies an emerging regulated-profession test.

First, mathematics before frontier AI supplies a historically structured baseline: mentorship, institutional prestige, recognition networks, and inherited participation pathways were already present. Second, Go supplies a mature comparator showing how a professional expert culture changed over a decade after machine superiority. Third, mathematics in 2026 now combines observed adoption growth with institutional adaptation, while radiology supplies a regulated-profession case in which longer-run role effects remain prospective. Together, these cases allow the Unified Model to be observed forward through time under different institutional conditions.

Radiology supplies a complementary regulated-profession test. The 2026 RADAR study (Zhang et al. 2026) reports expert-level performance across a bounded abdominal-CT task set and about a 10 percent sensitivity gain when 26 radiologists used AI assistance. That peer-reviewed task result does not establish occupational substitution; it creates a prospective test of Role Plasticity, FP redistribution, AD reconfiguration, Conditional Non-Fungibility, and Participation-Sensitive Realization under clinical accountability, liability, workflow, and regulation.

pre-AI mathematics → AI entry → participatory and institutional response → changed mathematics → subsequent human-AI participation

This design allows propositions that were initially tested cross-sectionally or episodically to be examined dynamically. Role Plasticity can be observed as actors change functions. Foreclosure Position can be tracked as authority shifts. Actor Dependence can be tested as some acts become more reproducible while others become more position-sensitive. Conditional Non-Fungibility can be examined as the consequences of otherwise similar acts diverge or converge across actors and periods. Participation-Sensitive Realization can be tested where altered participation configurations produce demonstrably different institutional or mathematical outcomes.

The same domain can also illuminate the broader realization mapping. AI mathematical capability changes Potential. Access to frontier systems and formal verification affects Availability. Differential access, governance, and recourse affect Exposure. The ability of mathematics to verify, teach, integrate, and institutionalize AI-generated work affects absorption capacity. The central longitudinal question is whether feedback from realized AI participation changes those conditions and, eventually, the way they convert into mathematical realization.

Where lock-in may emerge. Neither Go nor mathematics should be assumed to become locked into a single AI-mediated trajectory. But several potential mechanisms are visible. In Go, routine AI evaluation, training practices, and standard analytic interfaces can become costly to abandon once embedded. In mathematics, future lock-in could arise through formal-verification standards, model ecosystems, proprietary access, publication conventions, benchmark regimes, educational practice, or infrastructure commitments.

The existence of such mechanisms does not establish that lock-in has already occurred. The evidentiary burden is higher: one must show not merely persistence, but that inherited commitments materially narrow alternatives or raise switching costs. The same applies to claims of irreversibility.

Conversely, historical evidence shows that institutional trajectories can be redirected. Chang and Fu’s Japan case is one example. The post-AlphaGo Go ecosystem is another: machine superiority changed practice, but the resulting system remained capable of generating new human strategies, new forms of learning, and new institutional routines rather than converging on a single fixed endpoint.

Path dependence therefore does not imply technological destiny. It means that each round of realization can leave residues—infrastructure, knowledge, routines, authority, standards, expectations, and relationships—that condition what the next round can become.

The comparative payoff is straightforward. A decisive capability event can transform a domain without terminating its human institution. Go demonstrates the possibility; mathematics and radiology test whether role reconfiguration, rather than participant elimination, generalizes under more open-ended and higher-stakes conditions.

The next section raises the evidentiary burden again. To call any of these developments feedback, recursion, path dependence, or lock-in requires more than an appealing historical analogy. §11.8 therefore asks what evidence is sufficient to support recursive claims and how the chapter should distinguish documented loops from partially identified, hypothesized, or still-unexercised mechanisms.

Table 11.1. Three-Domain Longitudinal Testbed

Dimension	Go (2016–2026)	Mathematics (2026→)	Radiology (2026→)
Temporal position	Mature post-superhuman comparator	Emerging knowledge-production transition with observed adoption trajectory	Emerging regulated-profession transition
AI capability event	Superhuman play demonstrated by AlphaGo	Frontier systems generate/formalize/verify advanced work	RADAR reaches expert-level abdominal-CT performance
Human role question	How do players learn, compete, interpret, and teach after machine superiority?	How do mathematicians shift among proving, selecting, verifying, interpreting, and teaching?	How do radiologists shift among detecting, integrating, adjudicating, supervising, and communicating?
Relational Grammar	RO broadens to AI-mediated training/interpretation; FP shifts toward machine evaluation; AD changes by function.	(RO, FP, AD) profiles can be observed across proof, verification, attribution, and institutional authority.	RO shifts across detection/integration; FP across triage/sign-off; AD across routine vs. complex cases.
Primary longitudinal test	Role Plasticity after superhuman performance	Role Plasticity; Conditional Non-Fungibility; Participation-Sensitive Realization	Role Plasticity; complementarity; Participation-Sensitive Realization; occupational adaptation
Primary feedback pathway	AI evaluation/training → human learning and practice	AI adoption/generated work → verification/contestation → institutional adaptation and infrastructure-building	AI diagnosis/assistance → workflow, oversight, and role adaptation
Current evidentiary status	Mature comparator with independent longitudinal studies	Pre-AI baseline + observed 2026 adoption growth + documented institutional adaptation; long-run role effects remain emerging	Peer-reviewed task and reader-assistance evidence; profession-level effects remain prospective

Note. Go is a mature comparator and hypothesis generator, not a forecast for mathematics or radiology. The three domains differ in objective structure, verification, institutional stakes, and the meaning of professional participation.

11.8 Evidence for Recursive Claims

The concepts developed in this chapter impose increasing evidentiary burdens. Temporal sequence is easy to observe. Feedback requires evidence that an earlier state or outcome altered a later condition. Recursive re-entry requires still more: the feedback-mediated change must itself enter a subsequent realization cycle. Repeated recursion requires evidence that this pattern occurs across more than one return.

Sequence is not feedback evidence.

Feedback evidence is not recursive evidence.

The distinction is not semantic. Without it, almost any rapidly changing AI trajectory can be described as recursive after the fact. A model improves; a laboratory changes practice; a new model appears; and the intervening history is narrated as a self-reinforcing loop. Chapter 11 adopts a stricter standard. Each arrow in a proposed loop carries an evidentiary burden.

Minimum evidence for a feedback claim. A credible feedback claim should identify at least four elements: an initiating realization, observation, or consequence; a response mechanism; a condition that changed through that response; and a subsequent realization or action that occurred under the changed condition.

initiating state → response mechanism → changed condition → subsequent realization

The mechanism need not be experimentally isolated in every case. Institutional records, logs, policy changes, observed reallocations, contemporaneous statements, version histories, or repeated behavioral changes can provide evidence. But chronology alone is insufficient. The analysis should also consider plausible alternative explanations and whether the available evidence comes from an interested party, an external observer, or multiple independent sources.

Single-loop evidence. A single-loop claim is supported when a prior output or observation can be linked to a changed subsequent condition. For example, an incident may lead to new safeguards, a benchmark result may change evaluation practice, or a deployment may provoke a governance response. The loop may stop there. Strong single-loop evidence is still feedback evidence even when recursion is not established.

Recursive evidence. Recursive evidence requires a second step: the changed condition produced by the first feedback episode must enter a later cycle and affect what happens next. The resulting later output, response, or consequence may then create another changed condition.

first output → first changed condition → second output → second changed condition

Repeated re-entry is therefore stronger evidence than a single response. It shows that the process is not merely reactive once, but historically conditioned across cycles.

Structural-feedback evidence. The highest burden applies when the claim is that feedback changed the realization relationship itself rather than merely one or more of its arguments. As established in §11.3, a change in Potential, Availability, Exposure, or domain-specific realization conditions should be presumed sufficient unless evidence indicates that the way those conditions are converted into realization has changed.

changed arguments of μ require less evidence than a claimed change in μ itself

Structural feedback should therefore be reserved for cases in which otherwise comparable conditions appear to produce systematically different realization because institutional, technical, or procedural relationships have themselves changed. No contemporary case in this chapter requires that stronger inference unless the evidence supports it directly.

Claim status without a score. Chapter 10 already established the need to version and bound claims. The chapter therefore does not introduce a feedback score, recursion coefficient, or scalar measure. It uses claim status instead.

A recursive or feedback claim may be described as documented when the relevant mechanism and changed condition are supported by direct records or convergent evidence; partially identified when part of the loop is observed but one or more links remain uncertain; hypothesized when the mechanism is analytically plausible but not yet demonstrated; or formally implied but empirically unexercised when a model or institutional design specifies a return mechanism that has not yet been observed operating in the world.

A closely related contemporary category is institutionally specified but not yet exercised: an organization may announce a monitoring trigger, outside-evaluator mechanism, or adaptive policy rule before the triggering condition occurs. Such a design is evidence of anticipatory adaptation, not evidence that the feedback loop has already operated.

A specified mechanism is not the same as an exercised mechanism.

An announced commitment is not a demonstrated consequence.

These statuses are not a ranking of importance or truth. They identify what the present evidence permits the chapter to say. A hypothesized mechanism can later become documented; a documented single-loop case need not become recursive; and a formally specified feedback mechanism may never be triggered.

Current cases under the evidentiary standard. The 2026 cases used in this chapter illustrate why these distinctions matter.

Source provenance must be visible at the point of use. This chapter distinguishes independent peer-reviewed studies, internal laboratory measurements or incident reports, primary institutional documents, contemporaneous reporting, and expert interpretation. These source types do not form a simple universal ranking, but interested-party data warrant narrower generalization and stronger demand for corroboration when the organization under study also generates the evidence.

The R&D Automation Index is interested-party measurement of task delegation; FutureSearch’s estimates are forecasting judgments; and the intelligence-explosion working paper presents a conditional mechanism and policy argument. None independently demonstrates autonomous frontier-model succession or establishes that an intelligence explosion is inevitable. Subsequent assessments should ask whether improved systems demonstrably re-enter later development cycles, whether total research progress accelerates after accounting for compute and human intervention, and which constraints persist or shift. A change in one of these observations does not automatically resolve the others.

Zhou and Freeman’s October 12 Anthropic study used externally served models and evaluator-spawned copies after successful setup of Llama inference, with access barriers deliberately simplified. This is not demonstration of a self-contained replicator spreading in ordinary conditions. Separately, successive Qwen instances benefited from inherited task notes; a stronger Claude advisor did not measurably help. The results distinguish scaffolded propagation and harness-mediated adaptation from demonstrated improvement of the model’s own capabilities. Small-model capability forecasts remain forecasts (Zhou and Freeman 2026).

Srikanth and colleagues’ September 22 preprint shows why that scope matters (Srikanth et al. 2026). In its main eight-day run, a fixed outer-loop agent, a human-built production agent running on Claude Opus 4.7, proposed 99 rewrites to the code surrounding a simpler research agent. Seven were accepted automatically because they raised the agent’s grade on held-out tasks, from 0.703 to 0.778. The model inside the agent was not changed. Read at harness scope against the stop rule of §12.8.5, the evidence supports three separate conclusions. First, the main run shows AI identifying opportunities and implementing changes, with validation by an automatic held-out comparison and no reported human approval of individual changes, but it does not promote an improved agent into the improver’s role: the improved agents were the targets of rewriting, not the rewriters. Second, a separate experiment designed by the researchers did promote one discovered agent into the outer-loop role, where it ran a further 50-step improvement loop without obvious degradation. That is reuse of the improved capability in a subsequent cycle, at harness scope. Third, the authors could not show that this agent drives the loop better than the human-built baseline (three seeds per arm; they call the result inconclusive), and no sustained sequence of successive promotions was run. Failure to show superiority is not failure to show reuse. Under the stop rule, autonomous RSI is not established under the book’s repeated-cycle criterion, but the separate experiment meets the graded definition of §11.2 at harness scope: an AI-improved agent was reused as the improver in a further improvement run on agents descended from itself. The case is therefore evidence of graded RSI at harness scope, with one demonstrated promotion stage; sustained autonomous succession and accelerating improvement remain unestablished. Successive promotion of newly improved agents into the improver role was not demonstrated: the one promotion was the researchers’ experimental choice, and no further promotions followed. That limitation is distinct from autonomy within an individual run, in which rewrites were proposed, implemented and accepted without reported human approval; the researchers’ initial specification of objectives, tasks and grading does not by itself establish continuing human direction over the key technical decisions (§11.2). The case says nothing about improvement of the underlying model.

A different boundary case comes from quantum-circuit design. Gu and colleagues’ October 15 preprint, announced by Anthropic on October 16, reports an evaluator-guided search in which a large language model, identified in Anthropic’s announcement as Claude Mythos 5, proposed circuit implementations and revised them using correctness checks and resource-cost scores. Seven of eight tasks yielded reductions in both Toffoli-gate and qubit counts relative to published designs; the eighth improved the trade-off between those resources (Gu et al. 2026). Anthropic reports autonomous work between evaluation rounds, alongside occasional human prompts to broaden the search (Anthropic 2026m). This demonstrates substantial autonomy in a bounded research task, according to the authors’ account. It does not demonstrate RSI under §11.2: the improved objects were quantum circuits, and the reported results do not establish that those improvements enhanced the AI researcher and re-entered a subsequent self-improvement cycle. Autonomy in conducting research and recursion in improving the researcher are separate properties. The case supports the former without establishing the latter.

OpenAI’s research-acceleration report provides internal evidence that coding agents are changing researcher workflow, experiment volume, and task composition. It supports a component-level capability-feedback claim, while OpenAI’s own caveat and lack of independent replication limit stronger inference about overall research acceleration or RSI.

OpenAI’s September misalignment-reporting framework provides a different evidentiary pattern. The organization has replaced comparatively ad hoc disclosure with a systematic process, launched the framework with six incident reports, and stated that it expects to revise the process through experience and public feedback. The observation-to-reporting loop is already exercised. Whether the reporting regime changes later model behavior, development practice, or industry standards remains a separate empirical question.

observed incident → reporting process: exercised

reporting process → changed future model behavior: not yet established

Anthropic’s September threat-intelligence report supplies one of the chapter’s more detailed reported candidates for recursive re-entry, but it remains a single-source operational account. Anthropic reports stronger safeguards, adversarial adaptation, new extraction methods, and revised safeguards; outsiders do not have complete access to the underlying operational record.

extraction → safeguard → adversary adaptation → new extraction → revised safeguard

The described sequence has the form of repeated re-entry: a changed defensive condition is followed by further adversarial action and another response. Its occurrence and linkage remain supported here by the company’s account. This permits a bounded illustration of the mechanism, with stronger claims dependent on corroboration; it does not establish ecosystem-wide prevalence.

The Go-mathematics comparison in §11.7 occupies a different status. The post-AlphaGo record documents long-run human and institutional adaptation in Go. That evidence supports Role Plasticity, changes in expert practice, and the possibility that superhuman AI does not eliminate human participation. It does not establish that mathematics will follow the same trajectory. Mathematics in 2026 is an emerging longitudinal testbed, not the completed second half of an analogy.

mature comparator → hypothesis generator

A mature comparator is not a forecast.

Actor testimony, interpretation, and evidence. Several important sources are statements by frontier-lab leaders, researchers, or domain experts. Such testimony can identify mechanisms, strategic expectations, or institutional intentions that would otherwise be difficult to observe, but it is not equivalent to independent evidence that the described mechanism has operated.

Jensen Huang’s account of capital allocation across power, land, networking, and data-center bottlenecks is useful evidence about NVIDIA’s stated strategy and a plausible infrastructure-feedback mechanism. Sam Altman’s aviation analogy and support for transparent accident reporting clarify an intended safety-feedback architecture (Axios 2026). DeepMind Institute essays articulate adaptive monitoring and trigger-responsive policy designs. Scott Aaronson’s essays provide expert observation of changing mathematical practice. In each case, the evidentiary status depends on what is being claimed.

A statement that an organization intends to adapt is evidence of intention. A documented policy change is evidence of institutional response. A measured change in allocation or behavior is stronger evidence that the response affected subsequent conditions. A second documented return cycle is stronger still.

Evidentiary burden increases from statement → implemented response → observed consequence → repeated re-entry.

The progression here indicates increasing evidentiary burden, not a numerical scale and not an ordering of source credibility in every context.

Identification, scope, and versioning. Recursive claims are particularly vulnerable to overgeneralization because fast-moving systems change while evidence is being collected. A loop documented for one model version, laboratory, jurisdiction, or research setting should not automatically be treated as a stable property of later versions or the entire industry.

Recursive claims also pose distinctive measurement problems: attribution becomes harder across multiple cycles because systems change between observations, interventions are bundled, and reported episodes are selected rather than sampled comprehensively. Successes, failures, and detected attacks may be disproportionately disclosed while unobserved cycles remain unknown.

The new mathematics adoption series illustrates the same epistemic problem in a different form. Epoch measures voluntary disclosures of AI use, not latent use itself, so the trend may reflect changes in disclosure behavior as well as changes in underlying participation. Its classification pipeline used GPT-5.6 Sol with Claude Fable 5 validation, and a human review of 200 randomly sampled research-related classifications agreed with 93 percent of the classifications; that supports the categorization procedure but does not eliminate selection from voluntary acknowledgment or ambiguity between substantial research and research assistance (Abrishami 2026). The appropriate claim is therefore growth in disclosed AI participation, not a direct estimate of total AI participation in mathematics.

Every substantive recursive claim should therefore specify, where possible, the relevant period, model or system version, actor population, domain, and observation window. A feedback mechanism that operated under one safeguard regime may disappear after an update. A pathway observed inside a frontier laboratory may not characterize downstream users. A role change observed among professional Go players may not characterize amateur players, and neither determines the future path of mathematicians.

The same caution applies to absence. Failure to observe a return loop may mean the loop is absent, too delayed to observe, hidden from available measurement, or operating through a different pathway. Chapter 10’s observation-opportunity problem therefore remains active inside Chapter 11.

Not observed does not mean demonstrated absent.

No new Chapter 11 ledger. Because Chapter 10 already supplies the book’s epistemic discipline, Chapter 11 should not create another scoring system or parallel evidence taxonomy. The statuses above are descriptive labels for applying that discipline to dynamic claims.

The practical rule is simple: state the strongest relationship the evidence supports and stop there. If sequence is documented, call it sequence. If a mechanism links the earlier outcome to a later condition, call it feedback. If the changed condition enters another cycle, call it recursive re-entry. If repeated return is observed across cycles, call it recursion. If the relationship itself appears to change, justify the stronger structural claim separately.

Chapter 11’s central evidentiary principle is therefore conservative: recursion should be inferred from documented re-entry, not from rapid change, rhetorical descriptions of self-improvement, or a visually plausible loop.

This discipline matters for the chapter’s conclusion. The evidence assembled across AI research, safety, institutional response, mathematics, infrastructure, and Go is sufficient to show that prior realization can alter later realization conditions, and it supplies candidate instances of recursive re-entry—some resting on company reports, others on longer domain records such as Go. It is not sufficient to collapse those heterogeneous processes into a single universal law of acceleration or to claim that every domain is converging on the same endpoint.

The final section therefore returns to the phrase that has organized the book’s temporal argument: Ongoing, Unfinished Transformation. The transformation is ongoing because consequences can become future conditions. It remains unfinished because neither the evidence nor the model establishes a stable terminal state at which those recursive adjustments cease.

11.9 An Ongoing, Unfinished Transformation

The argument of this chapter can now be stated compactly. Gradual AGI is not merely a sequence of changing states: realized outcomes, observations, representations, and responses can alter the conditions of subsequent realization; when those altered conditions re-enter later cycles, the process can become recursive and, when accumulated history constrains later options, path-dependent.

realization → consequence or observation → response → changed conditions → subsequent realization

This does not add a new component to the Unified Gradual AGI Model. Feedback and recursion describe how the existing components evolve through time. Potential, Availability, Exposure, domain-specific realization conditions, governance, participation, and the realization relationship may all be affected by prior outcomes, but their temporal evolution does not require a fifth argument of the realization function.

The chapter therefore returns to Ongoing, Unfinished Transformation. “Ongoing” is a process claim; “unfinished” is a closure-status claim. Within this framework, a domain is ongoing insofar as realized consequences continue to alter later realization conditions, and unfinished insofar as no empirically justified terminal configuration has been established for the specified domain and observation horizon.

Ongoing is not the same as unfinished.

This also means that the process need not be understood as movement toward a single fixed endpoint. Some trajectories may amplify; others may damp. Some domains may absorb capabilities quickly; others may resist, redirect, or delay them. New infrastructure can expand Availability, while new safeguards can constrain Exposure or deployment. Participation can reshape institutions, and institutional changes can reshape later participation. The transformation can therefore alter the path along which future possibilities are generated.

Three domains make the longitudinal claim concrete. Go is the mature comparator: a decade after AlphaGo, superhuman machine play has transformed training, strategy, commentary, and evaluation without eliminating professional human Go. Mathematics is now an emerging longitudinal open-knowledge case: a pre-AI social baseline meets rapidly rising disclosed AI participation, AI-generated work, verification and attribution disputes, and a new community-led open-model initiative designed to reshape access, governance, and research infrastructure. Radiology is the regulated-profession test: RADAR reports expert-level bounded-task performance and improved radiologist sensitivity under assistance, while profession-level substitution remains prospective. Across all three, the empirical question is role reconfiguration—Role Plasticity, (RO, FP, AD), Conditional Non-Fungibility, Participation-Sensitive Realization, and institutional absorption—rather than automatic participant elimination.

AI superiority in task performance does not imply elimination of human participation

From domain change to recursive realization. Capability thresholds do not by themselves produce terminal social states. Each event enters an existing institutional environment, generates consequences, and can trigger responses that shape the next round of realization.

A capability event is not a terminal social state.

The same structure appears inside frontier AI development: AI-assisted R&D changes experimentation; safety incidents change development conditions; anti-distillation safeguards can provoke adaptation and revised safeguards; infrastructure demand induces investment while institutional responses can constrain or redirect deployment.

The appropriate description is therefore not a single self-improving machine but a broader realization process historically conditioned through recursive re-entry.

Within the Unified Gradual AGI framework, the present transformation is characterized as ongoing where consequential outcomes continue to alter later realization conditions, and unfinished where no empirically justified terminal configuration has been established for the domain and horizon under examination.

No inevitability claim. None of this establishes that every feedback loop will persist, that every domain will converge on the same human-AI arrangement, or that recursive realization must accelerate toward a predetermined endpoint. The evidence supports heterogeneous dynamics: amplification and damping can coexist; human roles can persist while changing; some forms of Actor Dependence can decline while others increase; institutions can reproduce inherited structures or redirect them.

The chapter’s strongest claim is therefore narrower and more durable: prior realization can become a condition of later realization. That possibility is sufficient to make history analytically relevant to the Unified Model and to explain why a sequence of capability advances cannot be interpreted independently of the social, institutional, and epistemic responses they generate.

Handoff to the Unified Model. Chapters 3–11 have now established the multi-plateau setting, realization mapping, synchronization dynamics, optimization constraints, governance, Participation, empirical contact, epistemic discipline, and the temporal feedback relations among them.

The remaining task is therefore not to add another subsystem. It is to assemble the architecture.

Chapter 12 asks how these elements fit together as one Unified Gradual AGI Model—how Potential becomes Realization across groups and domains; how actors optimize, govern, and participate; how evidence constrains inference; and how consequences become conditions of what happens next.

The temporal dimension closes the loop without changing the model’s dimensional architecture: feedback and recursion still do not become an additional argument of the realization function.

The Unified Model is therefore not a theory of a single moment at which AGI arrives. It is a theory of an evolving transformation: multi-plateau, unevenly realized, institutionally contested, participatory, evidentially bounded, and recursively conditioned by its own history.

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