Chapter 1. How Many Cohorts, and When the Last Ends: The Count and Its Clock

This chapter shows that eleven authored records turn a waiting list into cohorts by an exact count of seats and rest every recommendation on that count; that the count's only clock stops at the end of the first cohort, so that the time at which the last cohort ends is spoken of only where the record's figures happen to fit; that the order of the queue is left to an input the records say they lack; and that in a few places the records' words and figures part. It contributes to the debates on implementation, on rationing at the front line and on queues a reading of where one designed record set draws the edge of its calculation.

1.1Data and method

AEGIS publishes its authored cases as data files of one record a line, in 11 published parts. This study read all of them once, by GET, on 2026-10-06: 6,540 cases. One programme among them, AEGIS-CALC-v1, holds 196 cases that AEGIS describes as executing 12 kinds of calculation rule and keeping the input hash, the output and the replay. The rule this study reads, training-gap-v1, takes five figures: a number of posts, the number of people whose posts are changing, the seats of one training cohort, the months of the transition and the months of the training. It reports three: the people not taken in the first cohort, the minimum number of cohorts at the same seats, and the difference in months between the transition and the end of the first cohort. Across the 6,540 cases the rule is run 95 times, in 22 programmes.

The selection rule is one: every authored case in AEGIS-CALC-v1 whose run executes training-gap-v1. It keeps 11 cases. None is among the 78 cases that the six earlier AEGIS papers read. The other 84 runs of the rule stand in AEGIS's domain programmes, which describe themselves in a one-line label; they were left out so that every case read shares the same programme scope, quoted below, and the same form of record.

All 11 are typed realistic synthetic (현실형 합성) and give the same source role:

All share the programme scope of AEGIS-CALC-v1:

Every run states in its assumptions that its figures are values assumed by the author, and seven add that they are not actual data, or not actual personnel data. Every run has been executed and replayed with the same output; every fact check says there was no verification of real events or authority; every prediction performance is marked as not measured; none has a source link; every decision status says that a partial calculation is complete and that the materials for the overall judgment are awaited. The deciding roles are nine different officers, six of them marked as a setting, across three domains: education and training safety (seven cases), maintenance and lifecycle (two) and personnel and welfare (two).

Each record was saved as a snapshot in this study's folder with two fields removed, the source line and the group label, because some AEGIS records name a model there. The comparison population is kept in the same folder, reduced to the fields measured, with any model name in a programme's identifier shown as "[model]". The records are Korean. This study wrote the English once, sentence by sentence, from a table of translations kept with the study, and each English seed names its Korean original by hash. Every block quote below is that English.

The fields read are these: the situation (context, which AEGIS repeats as the summary), the question, the three choices, the author's judgment mark (review), with its recommended, alternative and excluded options and a reason for each, the needed inputs, the unknown, the condition for reconsidering (reconsider), the observation, and the run's input, output, assumptions and interpretation. A script computes from each record, and from nothing else, whether the three outputs follow the rule as read from them: people not taken equal the people due less the seats; cohorts equal the people due divided by the seats and rounded up; the difference in months equals the training less the transition, and zero where the training is shorter. The rule holds for all 11 runs and for all 95 runs of the rule across AEGIS. The number of posts, which every input states, enters none of the three outputs. One figure in this chapter is not the run's: the months after which the last cohort would end if the cohorts ran one after another, which is the number of cohorts times the months of training. The run does not compute it and the records do not state it, except in the two that say the schedule fits. Where this chapter gives it, it says that it is this study's arithmetic on that reading. Every other count is a stated rule on the Korean words or the run's figures, applied by the same script, and every number in this paper comes from it.

Before any field is used as evidence about the set, it is measured for frame: the share of its five-word runs that recur in at least 5% of AEGIS's items. The situations, questions, choices, unknowns, conditions for reconsidering, observations, run interpretations, run assumptions and link reasons are free of frame in Korean (0%), and the author's marks stand at 5%. Two fields are frame and are not read as findings: the uncertain line (61%), which repeats the same disclaimer after its own first phrase, and the counter-evidence attached to every link (100%). The programme scope and the source role are read once, as what AEGIS says the records are. That every record has three options and a condition for reconsidering is part of the form, not a finding.

1.2What the count settles and where its clock stops

Everything in this section is read from authored synthetic cases, whose posts, seats and schedules are the author's assumptions. The first case states the arithmetic in its situation without disguise:

Its question asks, starting from the first cohort, into how many cohorts the sixty people should be divided. The run answers the question as asked. Sixty people at thirty seats need two cohorts, and the run says so in a sentence that gives the count and nothing else:

Nine of the eleven run interpretations take this form: they say that so many cohorts are needed, and nothing more. The recommendations follow. Every recommended option, or the reason the record gives for it, states the run's number of cohorts, in figures or in words. In the branch transfer the recommendation is the run's arithmetic written as a plan:

In the communications transition the reason given for the recommendation names its source outright:

This is the sense in which the count settles the decision. The question each record asks is, in most of them, a question about how many, and the run answers it exactly; the seats are taken as fixed, and the options that keep within them are the ones recommended. Read through Richard E. Matland, Synthesizing the Implementation Literature (1995), the records are written in the register the model calls administrative implementation, the case of low conflict and low ambiguity. That reading is this study's, and its use is to show what such a register leaves out, which is time.

The run does measure one span of time. Its third output gives the months between the end of the transition period and the end of the first cohort. In eight records it is above zero, because the training is longer than the transition; in three it is zero, because the training is the shorter. The output says nothing about the second cohort or the last. Two of the options the records offer show how closely their framing follows this one clock. In the posting change, the alternative delays the transition to twelve months, and twelve months is the length of the training; in the change of duties, the alternative extends the transition to eight months, the length of that training. Each delay sets the run's only time figure to zero. In the first of these, the same alternative takes all sixty into a single cohort, which the seats of thirty would split in two:

The excluded option of the same record also puts all sixty in one cohort, and is excluded because it uses twice the seats. The record does not say how delaying the transition changes the seats. It keeps the delay as an alternative and excludes the option that uses twice the seats.

Only two records speak of when the whole schedule ends. In both, the transition period is a deadline, twelve and eighteen months, and the run's interpretation goes beyond the count:

The arithmetic behind "fits" is not the run's. The run reports three cohorts and a difference of zero months for the first cohort; that three cohorts of four months make twelve, and three of six make eighteen, is the interpretation's own step. The second record says how it reads that step, in the reason for its recommendation:

Cohorts that do not overlap run one after another, and on that reading the last ends after the number of cohorts times the months of training. The two records whose interpretations speak of the deadline are the two whose figures make that product equal the deadline exactly. Across all 95 runs of the rule in AEGIS, the product falls within the transition period in three.

In the other nine records the product is longer than the transition period, and the records do not say so, because they do not compute it. On the reading the cyber record states, the last cohort would end between 14 and 37 months after the transition period ends; that range is this study's arithmetic, and the records do not say whether their cohorts overlap, so a reader cannot tell from them whether the reading applies. What the records do say about time is in the reasons for their recommendations. The recruit retraining recommends entering everyone within the transition schedule, and gives this reason:

Its run reports two cohorts of ten months against a transition of six. The new-equipment maintenance branch raises the question of pace in its situation:

Its question asks whether a schedule of five months' transition and seven months' training, with sixteen seats a cohort, will keep pace with the transition. The record answers it with the count:

The run behind this sentence reports six cohorts and a first cohort ending two months after the transition. Whether six cohorts of seven months are in balance with five months depends on how many run at once, and the record does not say. Paul A. Sabatier, Top-Down and Bottom-Up Approaches to Implementation Research (1986), argues that the time-frame used in most implementation research misses many critical features of policy-making; this study reads the difference between the question and the run as the same problem on a small scale, a period too short for what is asked of it. Here the period is set by the rule, and it ends with the first cohort. Read through John D. C. Little, A Proof for the Queuing Formula: L = λW (1961), the count cannot stand in for the clock; the reading is this study's. A number waiting fixes a time only together with a rate; the records fix the number and the seats, and the rate, how often a cohort's seats come round, is the thing the overlap of cohorts would decide.

The section's finding, then, is that the calculation settles how many cohorts the seats require, exactly and in every record, and that the recommendations rest on it; that its clock measures only the first cohort; and that the records speak of the whole schedule where their figures fit it, and elsewhere speak of balance and of no gap in words that the run does not support or contradict.

1.3What the records leave open

Everything in this section is again read from authored synthetic cases. The count tells how many cohorts; it does not tell who is in the first. On this the records are explicit, and they place it among what they do not know. Seven of the eleven name priority as unknown, in phrases such as these:

The same branch transfer opens by naming priority as something its situation requires:

No recommendation sets an order. Two records recommend taking people "in turn", without saying in what turn. An order appears only among the alternatives, and the records give a cost for it in the same breath:

Both reasons are about the people at the back of the queue. Richard C. Larson, OR Forum—Perspectives on Queues: Social Justice and the Psychology of Queueing (1987), holds that attitudes to queues may depend more on factors other than the wait itself, among them a violation of first in, first out. The records name the order and do not decide it; the recommended options keep to a count that is the same whatever the order. Read through Peter Hupe and Michael Hill, Street-Level Bureaucracy and Public Accountability (2007), with its picture of a policy system as a nested sequence of decisions, the records take one decision in the sequence, how many groups, and leave the next, who is in each, to a level the record does not hold. Lars L. G. Tummers and colleagues, Coping During Public Service Delivery (2015), list rationing among the ways frontline workers cope with workload; a cohort with fixed seats rations in time, and in these records the rationing rule beyond the seat count is left to an input the records say they lack. These readings are this study's.

The other unknowns point the same way, from the decision toward the place where it is carried out. Eight records name the actual seats, room or capacity as unknown, although each run takes the seats as a fixed figure. Others name the schedule of new equipment or a new system, how many leave their posts, and the room among instructors. The needed inputs repeat the pattern: a roster of who wishes to move, a confirmation of seats for each cohort, a schedule of equipment, criteria for qualification. Benny Hjern and David O. Porter, Implementation Structures (1981), argue that programmes are carried out by clusters of parts of several organisations, so that an analysis rooted in one is inadequate; the records' list of what they lack reads as a list of the other parts of such a cluster, the training site, the equipment programme, the people themselves. That reading too is this study's.

The records also say what they would watch, and every observation is kept cohort by cohort. Three name the time at which the transition is complete or the equipment is placed; three name those still waiting; two set a unit of time, weekly or monthly. The last cohort's end, which the run does not compute, is what these observations would record after the fact:

The last thing the records leave open is the agreement between their words and their figures. They part in several places, and in none does the record set the two side by side. The branch transfer's situation, quoted above, says those due reach double the seats; its figures are ninety due and fifteen seats, six times the seats. Its condition for reconsidering uses the same measure:

By the record's own figures the condition is already met: double the seats is thirty, and ninety are due. Four other records set their condition for recalculating at the number already due, so that any rise at all reopens them:

The options for more seats show the same parting. Four records offer an alternative with a different number of seats. In one, more seats give fewer cohorts: twelve seats instead of ten take the communications transition from three cohorts to two. In the other three, the new number of seats gives, by the run's own rule, the same number of cohorts as the present one. Thirty seats instead of twenty-five still need two cohorts for forty-five people, and twenty instead of fifteen still need three for forty-five, which the cyber record's alternative states as "3 or fewer". The recruit retraining's alternative, whose "entry standard" of 40 this study reads as seats, says more:

The run for the same record reports two cohorts at the present thirty seats. The alternative's "three cohorts" is not a figure the run gives. This study does not say which the author meant; it reports that the option and the run of the same record give different counts of the cohorts the option would reduce.

The section's finding is that the records leave three things open at the edge of their calculation: the order of the queue, which they name as unknown and do not decide; the end of the last cohort, which they would observe but do not compute; and, in a few places, the agreement between the ratios and counts their words state and the figures their runs hold. The literature on implementation from the bottom up would place the first two at the point of delivery.