When Correction Stops Arriving in Time Comparing completion time with detect-and-restore time: an observer-relative criterion, its lower bound, and a per-cell measurement protocol

Abstract On the question whether a given system already constitutes general intelligence, mutually contradictory verdicts now coexist and neither side can refute the other: the developer announces arrival on the strength of scores across benchmarks, commentators point out non-arrival on an economic definition, and both cite the same public material. This is not caused by insufficient evidence. It is caused by the form of the definitions. Every current criterion writes the property to be judged as a property of the tested system alone, while half of the quantities on which the verdict actually depends do not belong to that system. This paper does not define general intelligence and takes no part in the semantic dispute over that term. It adds one independent dimension on the engineering-safety side only. Given a domain and given an observer, if the time the system needs to finish an act is shorter than the time that observer needs to recognise the act was wrong and restore the state, the system is said to have crossed the overtake threshold on that domain for that observer. The verdict is therefore a relation among system, domain and observer rather than a property of the system; false-alarm tolerance and response time both belong to the observer, so two observers returning opposite verdicts on the same system is not a contradiction. The lower bound on the criterion comes from change-point detection: identification delay is no smaller than the detection threshold divided by distinguishability, and distinguishability carries the tail index. Four items are home-grown, summarised as: the pairing rule, the quantification of censoring, per-cell registration, and the organisational corollary. First, the criterion is rewritten from a comparison of scalars into a comparison of distributions, with a closed form: when the two times are independent on the log scale, the overtake probability depends only on the log of the median ratio divided by the pooled log standard deviation. At a pooled log standard deviation of 1.414, a fourfold margin in medians corresponds to an overtake probability of 0.163, and holding that probability to 0.05 requires a median ratio of 10.2. Second, a reading discipline is fixed: detect-and-restore time can only be estimated from events that were in fact detected, so the estimate is systematically short, and the direction of the bias makes the observer look safer than he is. At a censoring fraction of 0.30 and a log standard deviation of one, the observed median is 0.680 of the true value and the overtake probability computed from the observed sample is 0.348 of the true value. Third, per-cell registration with three falsifiable predictions. Fourth, an organisational corollary with numbers: an organisation aggregates false-alarm tolerance by maximum while its distinguishability is capped by channel fidelity, so an organisation crosses the threshold earlier than any of its members; with thirty members, a log standard deviation of 0.5 and channel fidelity 0.7, the organisation's identification delay is 1.70 times that of its typical member. Section 8 executes the protocol once, on the first cell, finding and exploiting unknown vulnerabilities. The execution is a box scan rather than a point estimate, because neither side has clean conventions: completion time supports an interval only, and detect-and-restore time is subject to censoring. Across the whole registered box of eighty-one cells, the smallest overtake probability is 0.861 and the median is 0.997; all eighty-one exceed the decision level of 0.05, so the cell is crossed for the observer specified, and the verdict does not change with the choice of parameters inside the box, closing at grade A on the three-grade scale. Section 8.4 removes the dependence on those endpoints altogether: the verdict would flip only if the true detect-and-restore median fell below about half a day, whereas the smallest median in the registered box is thirty days, so the conclusion survives an error of nearly two orders of magnitude in the endpoints. Replacing the observer with three parties whose restoration chains differ in length gives overtake probabilities of 0.998, 0.294 and 0.017 on the same cell, turning the verdict from crossed to not crossed — a numerical instance of observer relativity. One further consequence of the bound is directly useful for policy: on a cell where identification time already exceeds completion time, improving after-the-fact correction cannot move the verdict back across the threshold; only raising distinguishability can. Detection and measurement infrastructure is therefore not administrative overhead. It is one of the few movable items on the right-hand side of this criterion. Limitations. The criterion presupposes passivity and does not apply to systems that change themselves because they are observed; data on the completion side come from developers' own reports and support intervals only, not point estimates; and the criterion cannot say in advance when a given cell will be crossed. Every number in this paper is a demonstration or a box scan and must not be read as a measurement of any real system; a point execution against a real catalogue remains pending, and a runnable pipeline for it is published with the paper.