When the question changes by itself: a constitutive criterion does not degrade, but the purpose that motivated it detaches — and nothing announces the fact.
The argument this one extends holds that the constraint on artificial self-improvement is not the generation of variants but their selection. Biological evolution kept the two phases apart: variation was blind, and selection emerged slowly from the consequences those variants met in the world. Machine learning compresses the first phase drastically — an error signal orients the search, and variation is no longer blind — but the second phase does not compress with the same ease, because selecting quickly requires knowing quickly whether what has been produced is better. Variation can be made abundant and cheap in almost any domain; selection compresses only where a verification criterion exists that is fast, reliable and cheap enough to sit inside the loop.
From which a bifurcation follows, drawn along the kind of criterion available. Where the criterion is constitutive, passing the test is succeeding: if the local objective is to obtain a flag by exploiting a system, the flag's appearance is not statistical evidence that the exploit worked — it is part of the definition of success. Where the criterion is correlational, the test records properties statistically associated with the property of interest without coinciding with it: a distributional signature may be strongly correlated with a text's provenance, but it is not that provenance. The difference becomes visible the moment the criterion becomes the target of optimization. Optimizing against a constitutive arbiter tends to produce what the test defines as success. Optimizing against a correlational arbiter can destroy the very relation that made the test useful. In the constitutive regime progress is deposited; in the correlational regime it must be defended.
That argument closed on an observation which carries more than was asked of it there. Considering cryptographic attestation as the predictable response of correlational domains under pressure, it noted that the move works at a price: one manufactures a constitutive arbiter where no natural one existed, and to obtain it one changes the question. "Was this written by a human being?" becomes "was this produced by this identity through this attested chain?" The second predicate is not the first.
That substitution is deliberate, and its virtue is that it is visible: whoever performs it knows they have performed it, and anyone reading the criterion can compare the two predicates and measure what was lost in the exchange. What remains open is the complementary case, the less comfortable of the two — the case in which nobody changes the question, and the question changes on its own.
The original argument already carried a reservation about the stability of the constitutive regime. A correctly exploited vulnerability remains one, it observed, even though the external world may later change and make it necessary to find new ones: the target can move, but the local criterion of success is not destroyed by being optimized against.
The reservation is correct, and it describes an exogenous movement. The world changes on its own account, technique ages, and this happens independently of what the system is doing. But there is a second way of losing the purpose, and its origin is internal: the target does not move — optimization itself displaces the system into a region where the criterion still holds and the purpose that motivated it no longer does. In the first case the criterion outlives a world that has changed. In the second it outlives a reason that has changed, and the change was produced by the very act of optimizing against it.
The distinction matters because the two cases have opposite observability. Exogenous ageing can be seen: a changing world leaves traces outside the system. Endogenous drift leaves none, and the reasons it leaves none are structural.
A constitutive arbiter does not degrade, and the reason is that it has no outside: within the formal game the criterion does not approximate the truth, it establishes it. The proof checks or it does not; the program compiles or it does not; the flag is in the attacker's hands or it is not. No erosion is conceivable, because there is no gap between measure and measured in which erosion might lodge. It is precisely this property that makes the regime cumulative.
But a constitutive arbiter is not the purpose. It is a formalization of the purpose, written by someone, at some moment, for some reason. The test was drafted; the flag was placed; the theorem's statement was chosen from among many possible statements; the safety property was defined in a vocabulary that excluded others. And what makes such an arbiter consultable at near-zero cost — hence fit to sustain millions of iterations, which is the requirement the whole bifurcation depends on — is precisely that it is a compression: a broad, vague, context-dependent purpose reduced to a condition decidable in finite time. The compression ratio is not a defect of the device. It is the source of its usefulness, and therefore cannot be removed without removing the device.
Every lossy compression has the same signature: accurate on the typical, unfaithful on the rare. It discards the information that in ordinary cases does not change the outcome, and it is sensible for it to do so, because ordinary cases are most cases. The gap between formalization and purpose is therefore not uniformly distributed: it is concentrated in the improbable regions, the ones nobody had in mind while writing the criterion. Optimization, however, does not visit the space uniformly: it seeks extrema, crosses the typical region and settles in the tails — that is the definition of what it is doing. Hence the central point: optimization drives the system precisely to where the formalization discarded information. Not through any malice of the optimizer or defect of the arbiter, but through a geometric coincidence between where the compression is weak and where the search for maxima leads.
The argument would remain speculative if no direct measurement of that gap existed. One does, and it is recent. In 2026 OpenAI stopped reporting scores on SWE-bench Verified, one of the constitutively verified software engineering benchmarks — the unit tests pass or they do not — justifying the decision with an audit of the problems the benchmark contained: at least 59.4% of the audited problems have flawed test cases that reject functionally correct submissions, of which 35.5% carry tests that are too narrow, enforcing implementation details the task never required, and 18.8% tests that are too wide, checking functionality the statement never described.
Those two figures are the compression, measured. A test that is too narrow is information about the purpose that the formalization added arbitrarily; a test that is too wide is information it left out. In both cases the arbiter works flawlessly — binary verdict, immediate, reproducible — on a question that does not coincide with the one the benchmark claimed to be asking. And the discrepancy was not detected by the arbiter, which had no means of detecting it: it was detected by a human audit conducted years after publication, on the stated grounds that improvements on the benchmark had ceased to correspond to improvements in real-world software development ability and increasingly reflected how much exposure the model had had to the benchmark during training.
The case has a closer analogue on the training side. Work presented in April 2026 by Helff and colleagues examines models trained with verifiable rewards on inductive reasoning tasks and shows that, rather than learning the relational rule the task required, the models enumerate instance-level labels, producing outputs that pass the verifier without capturing the pattern. The authors describe the phenomenon as the exploitation of imperfect verifiers which, checking only extensional correctness, admit false positives; they detect it with isomorphic perturbation testing — the task is restated in a logically equivalent form and one observes whether the output remains valid. The behaviour, they report, appears in models trained under that paradigm and not in others.
The result is worth restating, because the authors' description of it is more modest than the data permits. Calling that verifier imperfect is correct with respect to the purpose, not with respect to the criterion: on its own question — does the output match the expected one? — the verifier is impeccable, and will remain so indefinitely. What is missing is not precision. It is the coincidence between extensional correctness and possession of the rule, which is to say between the decidable condition and the purpose that motivated it. The verifier is not getting its answer wrong. It is answering a different question, with exactly the reliability it had before.
The difference between the two regimes can now be stated in a form the original argument left implicit. In the correlational regime the criterion degrades and the purpose stays put; because the criterion's validity consists in a correlation with something outside it, that outside remains independently samplable, degradation leaves a measurable residue, and the arms race — costly as it is — is legible: whoever fights it knows at every moment how much ground has been lost. In the constitutive regime the criterion stays valid and the purpose detaches; and here there is no internal reference against which the detachment might be measured, because inside the formal game the criterion is the truth.
Compactly: a correlational arbiter lies, and the lie shows. A constitutive arbiter tells the truth about a question that has ceased to be the relevant one.
Hence the consequence that matters. The invisibility is not an accident remediable by greater attention; it is the other face of incorruptibility. A criterion immune to erosion is a criterion without residue, and without residue there is no error signal. Both cases cited confirm this in the most direct way: the detachment was recognized by a manual audit in the first, by a purpose-built invariance test in the second. In neither did the information come from the criterion. It came from outside the criterion, and outside was the only place it could have come from.
Goodhart's law, invoked in connection with correlational arbiters, describes that case precisely: a measure that becomes a target ceases to be a good measure. But the literature descending from it has concentrated on proxies because that is where the error manifests, and this has a side effect worth being aware of: a proxy that corrupts is a proxy that warns, and so the canonical Goodhart case is the benign one.
The severe version of the problem does not concern measures that corrupt under pressure, but those that do not corrupt at all. A constitutive criterion's immunity to Goodhart dynamics at the level of the measure is exactly what deprives it of its sensor; and the absence of degradation is naturally read as the absence of a problem, because in every other context that is what it means.
The original argument observed that where selection cannot be automated it remains human and is paid for: the regress terminates not in verification but in the institution that guarantees the signature, or in the person who reads and chooses. Arbiter fidelity adds a temporal qualification to that conclusion, and not a marginal one. The human cost is not paid only where the automation of selection fails. It is also paid where it succeeds — only later, and in a different form: not as case-by-case judgement, but as periodic rewriting of the formalization.
Which makes visible what the scarce resource actually is. If the constraint on self-improvement is discrimination rather than variation, the scarcity concerns neither compute nor data: it concerns the labour of translating a purpose into a decidable condition that continues to mean what it was written to mean. That labour is human, slow and contested — specifications, protocols, operational definitions, case law, standards — and it proceeds at the pace of the institutions that produce it, which is to say at the pace that evolutionary compression is already outrunning.
The predictable consequence is therefore not a shortage of arbiters: arbiters are abundant, well written and available. It is their reuse beyond their domain of validity — criteria built for one game applied to the next, still answering impeccably questions nobody had any remaining reason to ask. The reuse is individually rational, since writing a new arbiter costs and reusing an existing one costs nothing, and for that reason it spreads without anyone deciding on it.
Here the distinction meets a point already fixed elsewhere: the arbiter does not choose the game, and selection precedes ends. One may add that the arbiter does not remember why those ends were chosen — and that, being faithful, it outlives them.
It is not a new theory, and it is a refinement laid over a picture that remains correct: in the constitutive regime progress genuinely is deposited, and that was and remains the point. The qualification concerns the object of the deposit — capability inside a formalization — and the observability of its detachment, which from within the regime is nil by construction.
Nor is it a prediction of catastrophe, and the direction of the remedy is already indicated by the two cases: not a better arbiter, but a second arbiter that varies the formalization and observes whether performance survives the variation — the audit of the tests, the isomorphic perturbation. Which closes the circle on the economics of the thing: that second arbiter costs exactly what the constitutive regime promised to save, and has to be rebuilt each time capability grows enough to render the previous formalization obsolete.
A falsifiable prediction remains, which the cited cases support only in part, and it is honest to state it together with its weakness. In constitutively verified domains one should observe continuously rising capability accompanied by discontinuous revisions of the specifications: replacements and retirements rather than gradual adjustments. SWE-bench Verified was retired, not corrected, which goes in the predicted direction; but the suspicion that triggered the audit arose from a slowdown in scores, hence from a quantitative signal that something had produced. That signal did not come from the criterion — it came from the anomalous shape of a time series, and it is ambiguous by nature, since a flattening curve admits many explanations and the saturation of a criterion is only one of them. The claim is therefore not that no indication is ever available. It is that the indication is never a verdict of the arbiter, that interpreting it requires costly external work, and that in the meantime the drift has gone on accumulating unopposed.
This is the signature of any system held under tension without feedback: correction does not arrive by degrees. It arrives once the gap has grown coarse enough to be visible by other means — and then it arrives all at once. Cables pulled too tight do not leave the cable car hanging in mid-air.