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

Abstract

Abstract First, the criterion is observer-relative. "Graduation" is defined as the point at which the time required to complete an action falls below the time required for a human to recognise it and respond. Whether one is in time is a property of the system-observer pair, not of the system alone; crossing that line is something we allow to happen. Second, a positive definition of the tier, and its distinction from "no dissipation." The precise proposition is that screening length is undefined here — not that it is very large, and not that local absorption is absent. Absorption does exist in this tier (non-adopters, incompatible substrates, air gaps, patches), but such absorption reduces the total extent of the reach, not its range: it is a multiplicative susceptible fraction, not an along-the-path decay. There is absorption but no distance upon which that absorption can act, so screening length remains undefined. Section 2 gives two discriminating criteria for this distinction and three falsification paths that do not require conversion into physical distance. It further locates the claim algebraically: screening length is a ratio whose numerator is transport and whose denominator is local dissipation, and every historical jump in transport has altered the numerator alone. Third, the structural signature: push and recall are asymmetric. Pushing is costless, instantaneous and global; recall is physical and counted per machine. "Fix it after something goes wrong" therefore fails in this tier: the feasibility of isolation tends to zero while the necessity of backup peaks. Fourth, the open-loop gain has a self-contained closed form that yields three things at once. Linearizing the drive on the structural stock at the operating point, the open-loop gain equals the ratio of the drive-feedback coefficient to the spontaneous loss rate. The closed form simultaneously gives: the loss of stationarity at gain one; the fact that whether the stock degrades after removal of external drive is exactly the boundary between gain below one and gain at or above one; and the fact that the drive-feedback coefficient is the numerator of the gain. The three measurements of Section 7 are therefore not three unrelated actions but three readouts of the same expression. Fifth, the decoupled cell and its coordinate placement. Above the two reversible classes (no hysteresis; metastable hysteresis) and the one-way discrete transition of open social systems, this paper introduces decoupling-type loss of stationarity. It is not a fourth item on a one-dimensional ladder; it is one cell on the plane spanned by the two open-loop gains of the autonomous branch and the human self-sustaining branch: the two loops have decoupled, and the two gains lie on opposite sides of one. "No return channel" thereby acquires an exact meaning — that branch has no fixed point to return to — and this holds irrespective of the shape taken by the ratio of the two branches' readouts. Sixth, the criterion is operationalisable in three measurements, only one of which is a positive detection. Decoupling is read from the coupling product between the branches; whether the open-loop gain has crossed one is read from the drive-removal experiment; the drive-feedback coefficient is read from whether success flows back into authority. The first two are claims of the form "some quantity is equivalent to zero" and must proceed by two one-sided tests with pre-registered equivalence margins and reported power. Only the third is a positive detection, and it reads institutional arrangements rather than system state, so it alone can be executed repeatedly in advance. "All three true" does not constitute conservatism of the conjunction; the reason and the composition discipline are given in 7.4. Seventh, the retrospective statistic has a stretch with no discriminating power, and that stretch has been measured against one family of alternatives. The log slope of the ratio of the two branches' growth rates has near-zero discriminating power against the alternative "steep but bounded" prior to the autonomous branch's inflection; adding second-order curvature separates them, but the condition under which curvature discriminates (that the observation window covers the inflection) is unknowable in advance. What generalizes is not those two numbers but a design principle: the reported separation is a property of the chosen comparison branch, not of the statistic. Eighth, the self-defeating character of early-warning quantities. The three occurrences above — distinguishability may jump within a single step; the discriminating condition for curvature is unknowable in advance; the drive-removal experiment is valid only while the observed party is passive — are three appearances of one thing. The general form: in this tier, the validity condition of any quantity usable as an early warning is coupled to the occurrence condition of the event being warned of, and the sign of that coupling is invariably negative. Section 11 gives its falsification form. Ninth, effective backup count is two distinct quantities, one bounded above and one not. The supremum of the second-moment version is the reciprocal of the correlation coefficient, independent of the number of copies, and it is a genuine supremum. The tail version (at least one survives) has no supremum: it grows without bound in the number of copies, only extremely slowly — at correlation 0.9, raising the count from one thousand to one hundred million raises the tail effective backup count from 1.83 to 2.58. Both yield "more copies buy nothing," but on different grounds, and neither substitutes for the other. Tenth, two readouts for observational independence, with opposite biases. Beside the participation ratio, this version supplies a readout based on the over-dispersion of the alarm count. On a joint calibration the over-dispersion readout recovers the true block count to within one percent while the participation ratio is optimistically biased. The two use different information — second-moment structure versus joint counts of tail events — so their divergence is itself a signal. Eleventh, the necessity–feasibility scissors, and one action conclusion. The necessity of cold zones rises monotonically with phase and diffusion; feasibility falls monotonically with the same two; the curves cross near the early-formation stage. That structure is the dilemma of control of technology; the contribution here is to give the crossing a position determined by the order in which the graduation line and the distribution line are crossed. The question thereby shifts from "should cold zones be built" to "how much window remains," and the closing of the window is defined by the three measurements of Section 7.