The Stability Speed Limit: Recursive Self-Improvement, Rohrs' Counterexample, and the Physics of Feedback

1. The Flywheel Fantasy: The Theology of the Intelligence Explosion

In machine learning salons and AI safety institutes, Recursive Self-Improvement (RSI) is routinely discussed in terms that border on the mystical. The canonical narrative, first formulated with disarming simplicity by British mathematician I. J. Good in 1965, operates as a frictionless syllogism:

"Let an ultraintelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an 'intelligence explosion,' and the intelligence of man would be left far behind."

Sixty years later, this conceptual sketch has hardened into an article of faith. The model of tomorrow will analyze its own weights, identify inefficiencies in its transformer architecture, rewrite its CUDA kernels, distill its reasoning trajectories, synthesize its own training corpora, and deploy an upgraded version of itself. Because the new instance is smarter than its predecessor, its capacity to design the next revision compounds. On a whiteboard, the differential equation practically writes itself:

For any $k > 1$, this dynamic produces a hyperbolic trajectory terminating in a finite-time singularity—the fabled "takeoff" or "foom" scenario. In this framing, the only constraints on the explosion are FLOPs, memory bandwidth, and electrical wattage.

Show this equation to a control theorist—an engineer whose discipline designed the fly-by-wire avionics of supersonic jets, regulated chemical cracking towers, and stabilized missile guidance systems—and they will not debate you on philosophy. They will raise an eyebrow, suppress a grimace, and recognize immediately that the AI community is recapitulating a catastrophic intellectual delusion that nearly destroyed adaptive control in the early 1980s.

The control theorist sees what the computer scientist forgets: Recursive self-improvement is an unconstrained, non-linear, closed-loop adaptive feedback system.

In the physical sciences, feedback loops do not run on pure intention or mathematical elegance. They run on signals, delays, sensors, actuators, and plant dynamics. And every adaptive loop that modifies its own internal transfer function is subject to iron laws of conservation: Bode sensitivity integrals, phase margins, and gain ceilings.

To understand why the fantasy of runaway self-improvement collapses under the weight of rigorous engineering, we must examine the mathematics of stability, the painful history of the adaptive control crisis, and the precise mechanism by which systems destroy themselves when they confuse an internal self-model with external reality.

2. The Physics of Feedback: The Small-Gain Theorem as Speed Limit

To strip the mystique from Recursive Self-Improvement, we must represent it as a standard interconnected dynamical system. Let us formalize the interaction between an optimizing agent and the world it seeks to master.

Consider an interconnected feedback loop composed of two operators, $\mathcal{M}$ and $\mathcal{E}$:

• The Modification Operator ($\mathcal{M}$): The internal optimizer (the learning algorithm, meta-learner, or autonomous code refactorer). It ingests an empirical performance evaluation or error signal $e(t)$ and produces an architectural or parametric modification $\Delta \theta(t)$.
• The Evaluation Operator ($\mathcal{E}$): The external plant or verification environment (the real-world task, compiler, execution runtime, physical laboratory, or market). It receives the modified policy $\theta(t) = \theta_0 + \Delta \theta(t)$ and outputs the true resulting performance metric or error signal $e(t)$.

In classical input-output stability theory, developed by George Zames at MIT in his seminal 1966 papers and expanded by Charles Desoer and Mathukumalli Vidyasagar in 1975, the stability of such interconnected loops is governed by the Small-Gain Theorem.

Here, $\gamma(\cdot)$ denotes the induced operator gain—the maximum ratio of the norm of the output signal to the norm of the input signal across all admissible inputs:

The Small-Gain Theorem is not a heuristic; it is a foundational topological theorem in functional analysis. It states that if the product of the amplifications around a closed loop is strictly less than unity, any bounded disturbance or noise injected into the loop will produce bounded internal states and bounded outputs (Bounded-Input Bounded-Output, or BIBO stability).

What does "gain" mean in the context of an AI attempting recursive self-improvement?

Gain is the aggressiveness of the modification per unit of measured evidence.

If a model observes a small delta in an evaluation metric and, in response, executes a massive overhaul of its weights, rewrites core reasoning routines, or alters its architectural pruning threshold, it is exhibiting high gain. Conversely, if an agent requires an avalanche of verified empirical trials across diverse conditions before making an infinitesimal adjustment to its parameters, it is operating at low gain.

In any realistic control setting, the feedback path $\mathcal{E}$ is not an instantaneous, noiseless, infinite-bandwidth oracle. It is characterized by:

1. Finite Evidence Bandwidth ($\tau_{\text{evidence}}$): True verification takes time. Compiling code, running physical experiments, testing autonomous vehicles in varied weather, or observing whether a clinical drug design is toxic takes hours, days, or months.
2. Unmodeled Dynamics ($\Delta_{\text{plant}}(s)$): The actual world contains non-linearities, parasitic lags, unmodeled interactions, and edge cases omitted from every benchmark.
3. Measurement Noise ($w(t)$): Every empirical signal contains stochastic variance, benchmark gaming, and evaluation noise.

When an AI lab attempts to circumvent the slow latency of the real world by substituting external evaluation with a fast, internal self-model (synthetic evaluations, LLM-as-a-judge, self-generated unit tests), they are not eliminating feedback delay. They are severing the loop from reality. They are closing the feedback loop around a surrogate model with unknown unmodeled dynamics.

To understand the catastrophic danger of this move, we must look at how the exact same intellectual move blew up the control engineering community forty years ago.

3. The Triumphalist Era: 1980 and the "Solved" Adaptive Controller

In the late 1970s, control theory was undergoing an intellectual revolution that mirrored the current euphoria surrounding large language models. The discipline was dominated by Adaptive Control—specifically Model Reference Adaptive Control (MRAC) and Self-Tuning Regulators (STR).

The promise of adaptive control was intoxicating: An engineer would no longer need to meticulously calculate fixed feedback gains $K$ for an aircraft, missile, or industrial chemical reactor. Instead, the controller would be endowed with an online parameter estimation algorithm. As the aircraft climbed from sea level into the thin air of the stratosphere, the controller would observe the discrepancy between the aircraft's actual behavior and an idealized mathematical "reference model," dynamically updating its own parameters $\theta(t)$ on the fly to force the physical machine to match the ideal.

For over a decade, the field was haunted by the lack of rigorous stability guarantees. If a controller is rewriting its own gains in real time based on its own tracking errors, what prevents the gains from spiraling to infinity?

Then, between 1979 and 1980, the breakthrough arrived. In what was hailed as a golden milestone in systems theory, researchers published airtight, mathematically rigorous proofs of Global Asymptotic Stability for continuous and discrete-time adaptive control:

• Kumpati S. Narendra, Y. H. Lin, and Lena S. Valavani (1980): "Stable Adaptive Controller Design—Part II: Proof of Stability" (IEEE Transactions on Automatic Control).
• A. Stephen Morse (1980): "Global Stability of Parameter-Adaptive Control Systems".
• Graham C. Goodwin, Peter J. Ramadge, and Peter E. Caines (1980): "Discrete-Time Multivariable Adaptive Control".

The mathematics appeared unassailable. Narendra and his colleagues used Lyapunov stability theory and positive real transfer functions (the Meyer-Kalman-Yakubovich lemma) to demonstrate that the tracking error $e(t) = y(t) - y_m(t)$ converged asymptotically to zero, and that all internal parameter estimates $\theta(t)$ remained strictly bounded:

The adaptive control problem was declared solved. Textbooks were drafted. The future belonged to self-tuning, self-modifying machines that would effortlessly adapt to any environment.

Yet every single one of those glorious mathematical proofs rested on four foundational assumptions about the external plant $G_p(s)$:

To the mathematicians proving the theorems, these four assumptions seemed like standard, polite engineering simplifications. To real-world physical systems, they were an absolute death sentence.

4. Rohrs' Counterexample: When 99.9% Model Fidelity Destroys the Plant

The illusion of solved adaptive control lasted less than twenty-four months.

At MIT's Laboratory for Information and Decision Systems (LIDS), a doctoral student named Charles E. Rohrs, working under the supervision of Michael Athans, Lena Valavani, and Honeywell chief scientist Gunter Stein, decided to test the "proven" adaptive control algorithms on realistic computer simulations of physical hardware.

What Rohrs and his co-authors discovered shocked the control theory establishment to its core. In 1981 at the IEEE Conference on Decision and Control (CDC), and formally in their landmark 1985 paper, "Robustness of Continuous-Time Adaptive Control Algorithms in the Presence of Unmodeled Dynamics", they presented what became immortalized as Rohrs' Counterexample.

Rohrs constructed a textbook plant. The nominal, modeled plant was a simple, benign first-order lag:

The adaptive controller was designed to force this plant to track an ideal first-order reference model:

If the physical world consisted solely of $G_{\text{nom}}(s)$, the Narendra-Lin-Valavani algorithm performed flawlessly: tracking error vanished, and parameters converged within seconds.

Then, Rohrs added what every real physical actuator, valve, or hydraulic line possesses: a tiny pair of high-frequency complex conjugate poles representing parasitic actuator lag. The true physical plant was:

Examine the parasitic term carefully. The unmodeled natural frequency is $\omega_n = 229\text{ rad/s}$ ($\approx 36.4\text{ Hz}$), with damping ratio $\zeta = 30 / (2 \times 229) \approx 0.0655$.

At standard operating frequencies (say, $\omega = 1\text{ to }2\text{ rad/s}$), the contribution of this parasitic mode is utterly invisible. The gain error is less than $0.008\text{ dB}$ (less than $0.1\%$). The phase lag is less than $0.5^\circ$. If you ran a standard frequency-response sweep or fitted a benchmark regression on typical operating data, the nominal model $G_{\text{nom}}(s)$ would register as a 99.9% accurate fit.

The revelation was shattering. The Narendra, Morse, and Goodwin proofs were not wrong in their internal arithmetic; they were wrong in their foundational premise. They had assumed that a model could represent reality without an unmodeled remainder.

In the presence of even the faintest unmodeled high-frequency dynamics, an adaptive algorithm that attempts high gain will inevitably expand its bandwidth until it collides with the unmodeled phase cliff—turning its own optimization engine into a weapon of self-destruction.

5. Parameter Drift and the Bursting Nightmare: Loss of Persistent Excitation

If immediate explosive instability had been the only pathology revealed by Rohrs, engineers might have hoped that simply capping maximum controller gain would restore safety. But what researchers discovered next was far more insidious: The Bursting Phenomenon.

In 1985, Australian control theorist Brian D. O. Anderson published a landmark paper in Automatica titled "Adaptive systems, lack of persistency of excitation and bursting phenomena". Anderson, alongside Petar Kokotovic, Robert Bitmead, and Bradley Riedle, uncovered the dark temporal dynamics of adaptive feedback loops.

An unstable adaptive system often does not blow up immediately. In fact, it can run flawlessly, beautifully, and superhumanly for thousands of operating cycles before suddenly, without warning, exploding into catastrophic failure—only to mysteriously settle back down into quiet operation.

The root cause of this terrifying behavior is the Loss of Persistent Excitation (PE).

To understand Persistent Excitation, consider the standard parameter estimation law used in adaptive filtering, recursive least squares, and gradient descent:

Here, $\hat{\theta}(t) \in \mathbb{R}^d$ is the parameter vector being adapted, $\phi(t) \in \mathbb{R}^d$ is the regressor vector (the signals exciting the parameters), and $e(t) = y(t) - \hat{\theta}^T \phi(t)$ is the observed prediction error.

For the parameter estimation error $\tilde{\theta}(t) = \hat{\theta}(t) - \theta^*$ to converge exponentially to zero, the regressor signal $\phi(t)$ must satisfy the Persistent Excitation condition:

In plain English: The incoming data stream must continuously span every single dimension of the parameter space with non-zero energy over any time window of length $T$.

What happens when a self-improving system becomes "too good" at its job?

When an adaptive controller successfully eliminates tracking error, $e(t) \to 0$. The system settles into a smooth, quiet steady state. The command input is constant or slowly varying.

At that exact moment, Persistent Excitation is lost.

Because the system is operating in a narrow, tranquil operational envelope, the regressor vector $\phi(t)$ collapses into a 1-dimensional subspace. Along the remaining $d - 1$ dimensions of the parameter space, the information matrix $\int \phi \phi^T d\tau$ becomes singular ($\alpha = 0$).

In those unexcited dimensions, there is zero restoring force acting on the parameters.

If there is even an infinitesimal whisper of sensor noise $w(t)$, numerical rounding error, or stray disturbance, the parameter estimator integrates that noise without constraint. The unexcited parameters embark on a silent, unmonitored random walk: Parameter Drift (often called covariance windup).

Because the system is currently operating in the narrow subspace where $\phi(t)$ is small, the output error $e(t)$ remains virtually zero! The telemetry graphs look pristine. The dashboard shows $99.9\%$ performance. The supervisory engineers celebrate their successful deployment.

Meanwhile, beneath the placid surface, the parameter vector $\|\hat{\theta}(t)\|$ is drifting steadily away from the safe operating envelope. It wanders deeper and deeper into the parameter space until it finally crosses the stability margin of the unmodeled dynamics.

The moment a minor external perturbation arrives—a step change in command, a slight gust of wind, a novel user query—the system is suddenly pushed outside its tranquil subspace. The drifted, ultra-high-gain parameters bite into the unmodeled dynamics.

The system bursts.

It erupts into violent, chaotic oscillations. But here is the crowning irony identified by Anderson: The violent oscillation itself generates massive, broadband high-frequency signals.

The burst temporarily restores Persistent Excitation! The rich excitation signals rapidly re-estimate the parameters, dragging $\hat{\theta}(t)$ back toward the stable region. The burst abruptly ceases. The system settles back down into deceptive, placid calm...

...where Persistent Excitation is lost again, parameter drift quietly resumes, and the countdown to the next catastrophic burst begins anew.

6. The RSI Mirror: Synthetic Echo Chambers and Out-of-Distribution Collapse

The structural isomorphism between 1980s adaptive control and 2020s Recursive Self-Improvement is not an analogy; it is mathematically identical.

When AI practitioners describe recursive self-improvement loops—where model $M_k$ generates training data, refines synthetic reasoning trajectories, scores candidates with a reward model or LLM judge, and produces model $M_{k+1}$—they are constructing the exact adaptive architecture that Rohrs and Anderson dismantled.

Consider the contemporary push toward synthetic data self-improvement. Because real human data is finite and expensive to curate, frontier models are increasingly trained on their own synthetic outputs, filtered through internal verification heuristics (such as code compilers, math verifiers, or reward models).

What is synthetic self-training from a control perspective?

It is an adaptive system closing the feedback loop around its own outputs. It is the textbook definition of loss of persistent excitation.

When an AI trains on synthetic data generated by itself or a peer model, the data distribution does not explore the full, messy, high-dimensional manifold of reality. It collapses into the model's own high-probability modes. The regressor $\phi(t)$ loses rank.

In the narrow subspace spanned by the synthetic benchmark (say, competitive programming syntax or formal algebra puzzles), the model appears to be accelerating rapidly. Its benchmark scores tick upward: $92\%$, $96\%$, $99\%$.

Meanwhile, along every orthogonal dimension of the semantic manifold—nuanced commonsense reasoning, real-world causal attribution, adversarial robustness, subtle ethical restraint—the parameters are undergoing unconstrained parameter drift. The model's self-model is worst precisely where it has the least external contact with the real world, and the harder it optimizes against its internal surrogate, the deeper it drives its parameter vector into the unmodeled gaps.

And just as Anderson documented in 1985, modern recursively trained models exhibit the exact signature of bursting. A model fine-tuned via aggressive synthetic RL does not fail gracefully. It answers 10,000 complex domain queries with flawless fluency, convincing everyone that Artificial General Intelligence has arrived—and then, confronted with a simple, slightly out-of-distribution real-world prompt, it bursts: hallucinations run riot, catastrophic syllogistic errors appear, or security safety rails vanish entirely.

7. Nature's Proof: Why Evolution and Civilization Never Burst

Whenever the control-theoretic impossibility of unconstrained Recursive Self-Improvement is raised, techno-optimists invariably counter with two historical precedents: Biological Evolution and Human Civilization.

"Look at life," the argument goes. "A single-celled eukaryote improved its own genetic substrate over three billion years, ultimately producing Homo sapiens. Look at science: human institutions improved their own scientific methods, generating the industrial and digital revolutions. Both are recursive self-improving loops. Why didn't they burst?"

The answer provided by control theory is profound: Evolution and civilization did not evade the laws of control theory; they survived precisely because they are the most rigorously damped, low-gain, dual-authority architectures ever devised.

Biological Evolution: The Ultimate Low-Gain Filter

Biological evolution is the antithesis of the AI lab's high-gain dream:

1. Microscopic Gain: In biological genomes, the point mutation rate is rigorously held around $10^{-8}$ to $10^{-9}$ mutations per base pair per generation. Out of three billion base pairs, an organism introduces only a handful of modifications per cycle. The gain $\gamma(\mathcal{M})$ is infinitesimally small.
2. Massive Parallelism ($N \sim 10^6 \text{ to } 10^{12}$): Evolution never entrusts its substrate to a single, monolithic, recursive agent. It distributes adaptation across billions of parallel individuals. If an individual lineage undergoes parameter drift or bursts into lethality, it quietly dies in the brush without taking down the species.
3. Absolute Decoupling of Modification and Evaluation: This is the paramount design feature. An organism possesses the biochemical power to modify its genetic payload (via mutation and meiosis), but it possesses zero authority to evaluate its own fitness. The evaluator is an unyielding, external, physical reality: thermodynamics, predators, pathogens, and drought. The organism cannot "grade its own homework" or optimize against an internal reward model.
4. The Geological Timescale of Evidence: The feedback latency $\tau_{\text{evidence}}$ is calibrated to the timescale at which consequences unfold. A genetic alteration is not declared a success after five milliseconds of internal simulation; it must survive decades of seasonal variations and ecological competition before its genes propagate.

Human Science and Constitutional Civilization: Separation of Powers

Human civilization achieved recursive epistemic compounding over the past four centuries only after it abandoned monolithic authority and designed institutional architectures with strict separation of feedback loops:

1. The Separation of Hypothesis and Verification: In the Scientific Revolution, the theorist who formulates a model (modification power) is categorically forbidden from serving as the sole evaluator of its truth. Verification requires independent experimentalists, physical laboratories, peer review, and adversarial replication. Nature is the non-negotiable plant.
2. Constitutional Governance: In stable political economies, the power to propose statutory modifications (the legislature) is strictly separated from the power to enforce (the executive) and the power to evaluate constitutionality (the judiciary). When an authoritarian regime concentrates modification power and evaluation authority into a single supreme leader, the institutional feedback loop closes internally. The regime loses persistent excitation, drifts into sycophancy, and inevitably bursts into economic or military catastrophe.
3. Decentralized Price Discovery: In markets, no single firm is permitted to print currency, set prices, and certify the value of its own products. The market provides external persistent excitation. When central planners attempt to replace real consumer transactions with internal synthetic economic models, the system experiences the classic Austrian calculation collapse—a direct economic manifestation of Rohrs' counterexample.

8. The Decade of Robust Redesign: How Control Theory Rebuilt Itself

The shock of Rohrs' counterexample did not kill the field of adaptive control. Instead, it inaugurated a decade of profound intellectual maturity known as the Robust Adaptive Control Revolution (1982–1995).

Pioneered by control theorists including Petros Ioannou, Petar Kokotovic, Kumpati Narendra, Anuradha Annaswamy, Laurent Praly, and Gang Tao, the discipline accepted reality: Unmodeled dynamics and disturbances are not exceptional anomalies; they are permanent physical facts.

To make self-improving controllers safe for supersonic flight, nuclear power plants, and industrial automation, theorists traded the fantasy of infinite adaptation speed for guaranteed stability margins. They formulated four mandatory architectural modifications that translate directly into non-negotiable design principles for AI Recursive Self-Improvement.

1. Dead-Zone Modification: Halting Adaptation Inside the Noise Floor

Developed by Bo Egardt (1979) and formalized by Peterson and Narendra (1982), the dead-zone modification recognizes that when tracking error is small, it is dominated by measurement noise and unmodeled high-frequency chatter. Attempting to adapt against signals smaller than the noise threshold $\delta_0$ drives parameter drift.

RSI Translation: Stop adapting when benchmark error is inside the measurement noise floor. If an AI model's error rate on an evaluation suite drops below the noise margin of human labeling ambiguity or benchmark variance (say, error $< 2\%$), the learning rate must be clamped to zero. Never chase the last fractions of a percent on an internal benchmark; you are fitting pure noise.

2. Parameter Leakage ($\sigma$-Modification): Anchoring to a Trusted Prior

Invented by Petros Ioannou and Petar Kokotovic in 1983, the $\sigma$-modification introduces a restorative damping spring into the parameter update law, pulling the parameter vector back toward a nominal, pre-verified safe baseline $\theta_0$:

Even if persistent excitation is completely lost ($\phi(t) \to 0$), the homogeneous parameter dynamics become exponentially stable: $\dot{\theta}(t) = -\sigma \Gamma (\theta(t) - \theta_0)$. The parameter vector is physically incapable of drifting to infinity; its norm is strictly bounded inside a compact ball:

RSI Translation: Anchor all recursive parameter updates to a verified checkpoint. Whether through explicit Kullback-Leibler (KL) divergence penalties against a base foundation model, weight-decay regularization toward a verified prior, or hard bounds on latent representation shifts, an autonomous agent must never be permitted to wander unconstrained across parameter space.

3. Projection Algorithms: Hard Safety Envelopes

Introduced by Laurent Praly (1983), the projection operator establishes a known, convex, compact set $\Theta_{\text{safe}}$ in parameter space. If the gradient update law attempts to push the parameter vector across the boundary $\partial \Theta_{\text{safe}}$, the update vector is projected orthogonal to the outward normal, constraining the parameters strictly within the safe manifold:

RSI Translation: Hard, immutable capability envelopes and sandboxed runtime boundaries. An agent refactoring its own code must be structurally constrained by immutable hardware-enforced boundaries that prevent it from modifying its own kernel privileges, network access rules, or verification harnesses.

4. Continuous Persistent Excitation Monitoring

Modern robust adaptive systems continuously compute the minimum eigenvalue of the empirical covariance matrix:

If $\lambda_{\min}$ drops below $\alpha_{\text{thresh}}$, the system concludes that the environment has ceased to be informative. Adaptation is immediately frozen until diverse, informative external excitation is restored.

RSI Translation: Freeze recursive training whenever training data is purely synthetic. Unless an AI system is receiving continuous, diverse, high-entropy telemetry from contact with the real, unmodeled physical world and authentic human interactions, all autonomous recursive weight updates must be suspended.

9. Interactive Laboratory: The Adaptive Feedback & Bursting Simulator

To experience firsthand the precise mathematical mechanisms explored in this essay, use the interactive simulation below.

This simulator implements a continuous-time adaptive control loop matching Rohrs' plant dynamics: a nominal first-order system with unmodeled high-frequency parasitic poles ($\omega_n = 229\text{ rad/s}$), subjected to measurement noise and varying degrees of persistent excitation.

10. Synthesis: Stability Is the Speed Limit

The lesson of control theory across seventy years of rigorous engineering is unambiguous: Unstable systems do not become intelligent; they explode.

The seductive vision of recursive self-improvement—an artificial intellect rewriting its own core routines in millisecond loops, compounding its cognitive power toward infinite capability—is an engineering fiction. It treats intelligence as a pure computational scalar, detached from the physical and mathematical reality of closed-loop dynamical systems.

Whenever an optimizing agent attempts to accelerate its adaptation speed past the rate at which it can extract trustworthy, independent, out-of-distribution evidence from reality, its loop gain inevitably breaches the Small-Gain threshold. Its internal self-model diverges from the true plant. In the tranquil absence of persistent excitation, its parameters drift silently through the null-space of its saturated benchmarks. And when contact with the real world is finally made, the system does not triumph. It bursts.

Does this mean that artificial intelligence cannot improve itself? Not at all.

It means that authentic self-improvement will look completely different from the mythology of the singularity.

Systems that reliably and safely improve their own substrate will not be reckless, runaway flywheels. They will be architectures engineered with the hard-won humility of the post-Rohrs control era:

• They will be strictly governed: Hard parameter projection boundaries will constrain allowable modifications within provably safe operational envelopes.
• They will be damped: Leakage mechanisms ($\sigma$-modifications) and Kullback-Leibler penalties will continuously anchor parameters toward trusted, empirically validated priors, eliminating silent drift.
• They will respect dead-zones: Optimization will automatically halt when performance reaches the measurement noise floor of evaluation suites, refusing to fit benchmark artifacts.
• They will enforce dual-authority separation: The agent modifying the code or weights will be structurally prevented from evaluating its own success. Verification will be conducted by independent, external, asynchronous sandboxes grounded in real-world consequences.
• They will be deliberately slow: The rate of recursive modification will be hard-clamped to the timescale of consequence ($\tau_{\text{evidence}}$)—the physical latency required to observe whether an action produces downstream toxicity, silent logical rot, or systemic fragility.