Loop Decoupling and the Loss of Stationarity: Time-Side Criteria and Cold-Zone Feasibility for Tier-Three Risk

First, the criterion is observer-relative. "Graduation" is defined as: the time a system needs to complete an action is shorter than the time people need to recognise it and then respond. Whether there is time is a property of the pair consisting of the system and the observer, not of the system alone. Where that line is crossed, we are the ones who let it be crossed. Second, a positive definition of the tier, and a three-way split of the denominator. The precise claim is that the screening length is undefined here. The local-dissipation slot has three possible fates that must be kept apart: positive (finite screening length), zero or negative (screening length divergent or imaginary), and a slot that cannot be pointed at at all. For the third to stand, a criterion distinguishing it from the second is required; Section 2 gives two. Third, the structural signature: push and recall are asymmetric. Pushing is zero-cost, instantaneous and global; recalling is physical and counted per machine. Hence "fix it after it goes wrong" fails on this tier: the feasibility of isolation falls to near zero while the necessity of backup peaks. Fourth, effective backup count has two upper bounds, and they are not equal. The second-moment version, n_eff = n / [1 + (n − 1)ρ], is bounded by 1/ρ regardless of n; the tail version (at least one survives) has a different and higher floor. The former is the right quantity for counting observation lines, the latter for counting backups. Both say that adding copies buys nothing, but their floors differ and they cannot be substituted for each other. Fifth, the fourth class of transition and its coordinate placement. Above the two reversible classes (no hysteresis; metastable hysteresis) and the one-way discrete jump of open social systems, this paper gives a fourth class: decoupled loss of stationarity. It is not a new codimension-one bifurcation. It is an existing phase-transition boundary — open-loop gain equal to one, the global loss of existence of any fixed point — in the case where the two branches sit on opposite sides of it: after the autonomous branch's positive-feedback loop decouples and closes, its gain crosses one while the human self-sustaining branch remains below one. "No return path" thereby acquires a precise meaning: that branch has no fixed point to return to. Sixth, the criterion is operationalisable, in three measurements. Whether the loops have decoupled is read from the coupling product between the branches; whether the open-loop gain has crossed one is read from a drive-removal experiment, that is, whether the system degrades once external input is withdrawn; the drive-feedback coefficient is read from whether success flows back into authority. All three must hold for a fourth-class verdict; any one failing rules it out. The third reads institutional arrangements rather than system states, so it is the only one of the three that can be executed repeatedly in advance. Seventh, the retrospective statistic has a stretch with no discriminating power, and that stretch has been measured. Before the inflection of the autonomous branch, the log-slope of the ratio of the two growth rates has almost no power against a "steep but bounded" alternative. Adding second-order curvature separates them, but the condition under which curvature discriminates — the observation window covering the inflection — is unknowable in advance. The weight must therefore fall on the mechanism-side measurements. Eighth, a second axis and three lines. Holding and diffusion mode (closed control, open diffusion, covert self-retention) is a second axis that does not determine, and is not determined by, capability. The graduation line, the distribution line and the lock-in line rewrite the three phases as an order in which separately interrogable lines are crossed, and who crosses the distribution line decides which path is taken. Ninth, the necessity–feasibility scissors, and one action conclusion. The necessity of a cold zone rises monotonically with phase and diffusion; its feasibility falls monotonically with the same two; the curves cross near the emerging phase. This structure is the dilemma of control of technology; the increment here is a computable location for the crossing, fixed by the order in which the graduation and distribution lines are crossed. The question therefore changes from "should a cold zone be built" to "how much window is left", and the closing of the window is defined by the three measurements of Section 7. The conclusion is to act while the window is still open.