Chapter 1. One Line and Its Edges: What the Net Figure Settles and What Stays Outside

Twelve authored records put a change of arrangement to a decision maker as one subtraction, and every recommendation follows the sign of its result. This chapter shows that the subtraction settles direction and nothing else: the matters the records themselves call unknown sit outside it, the middle option each record offers is argued in words and left without a figure, and the records' units, labels and thresholds for reopening part in places from the figures they stand beside. It contributes to the debates on forward-looking costs, commensuration and the make-or-buy choice of governments a reading of where one designed record set draws the edge of its arithmetic.

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, net-cost-v1, takes three figures, an avoidable cost (avoided), a remaining cost (remaining) and an exit cost (exit), and reports three: the avoidable cost again, the remaining and exit costs together, and a net saving, the first less the other two, where a negative figure is labelled a net cost. Across the 6,540 cases the rule is run 113 times, in 23 programmes, and in all 113 the outputs follow that subtraction exactly.

The selection rule is one sentence: every authored case in AEGIS-CALC-v1 whose run executes net-cost-v1. It keeps 12 cases, all in the ninth published part. None is among the 89 cases that the seven earlier AEGIS papers read; the counting script reads their case lists and finds no overlap. The other 101 runs of the rule stand in 22 other programmes; they were left out so that every case read shares the same programme scope and the same form of record.

All 12 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 7 add that they are not actual 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; none has a source URL; and each awaits "materials for the overall judgment". The domains are Budget (6), Facilities and energy (2), Procurement and contracts (2), Maintenance and life cycle (1) and Personnel and welfare (1). Each case has its own deciding role; 7 of the 12 roles are marked "(setting)". Nine runs count in hundreds of millions of won (억원) and 3 in hundreds of millions of won a year (억원/년). The span from the registration of each question to its stated deadline runs from 18 to 345 days.

The fields read are the situation (summary), the question, the options (choices), the author's judgment mark (review), which names a recommended, an alternative and an excluded option with a reason for each, what is unknown (unknown), the inputs still needed (neededInputs), when the question would be opened again (reconsider), what would be watched afterwards (observation), and the run's input, output, assumptions and interpretation. AEGIS wrote them in Korean. The English quoted here was made once by the editorial session of this study, sentence by sentence, with nothing added; each case's English seed names the Korean original by its hash. The records' unit, 억원, is put into English as "hundred million won", and the figures stand as the records give them.

Every count comes from a script that reads only the study's own folder, and every classification is a rule on the Korean words or on the run's own numbers, stated beside its count in numbers.md. Two kinds of figure appear that the records do not state: shares of the avoidable cost, and the net saving that would follow if a cost stood at a record's figure for reopening. Both are labelled as this study's arithmetic on a stated reading.

The frame measure of the family's spine (five-word runs that recur in at least 5% of the population's filled items) was run on the Korean fields against all 6,540 cases. The situations, questions, options, unknowns, reopening lines, observations, run interpretations and run assumptions of the 12 cases carry no frame runs at all; the author's judgment mark carries 6%; the uncertain line carries 60% and the counter-evidence of the links between cases 100%. Those last two are frame and are not used as evidence. Two properties that the records share by design, that each offers options and that each has a reopening condition, are not findings either. What the paper reads is the wording peculiar to each case and the run's own figures.

1.2The sign sets the direction

Every case read in this section is an authored synthetic setting: its figures, units and schedules are the author's assumptions, and its English is this study's translation. The net figure carries the direction of every recommendation in the set. All 12 recommended options rest on the net saving by name, 9 of them state the run's own figure, and all 12 change the present arrangement: they launch, switch, approve or confirm. On the other side, 10 of the excluded options keep the present arrangement or reject the change. The author's mark places the options on either side of a single number, and the number decides which side is which.

The first case in the set shows the pattern whole. A plan to make core parts at home instead of importing them is set out in the author's words:

The run subtracts and reports:

And the author's mark, which the record is careful to say is not the output of a calculation, sets all three options against the figure:

The reason for the recommended option and the reason for the excluded one are the same reason seen from two sides: the figure is positive. The reason for the alternative is of a different kind. It speaks of a commitment that shrinks and a decision that takes longer, and it carries no figure. That difference recurs through the set and is taken up in section 1.3.

The one run whose figure is negative is read by its sign in the same way. A logistics service contract is about to expire:

Here the subtraction is run on keeping, not on switching, and its result is turned round to favour the switch. The excluded option is set aside by comparing two figures that the run does not itself compare:

This is the only record in the set whose alternative or excluded option carries a figure of its own, and the figure is one of the run's inputs set beside its output. The record still has only one line of arithmetic. What changes is the direction in which it is read.

In one record the rule itself becomes the recommendation. A plan to make medical supplies in-house rather than buy them asks whether the net saving should be settled by the difference between costs arising and costs avoided, and the recommended option is a rule:

and the excluded option is the rule with a term left out:

This record makes explicit what the others leave implicit: the recommendation is a sign test on a subtraction. Read beside Arkes and Ayton, The Sunk Cost and Concorde Effects (1999), the test keeps faith with the normative rule their article sets against the sunk cost effect, in that every term of it is a cost still to come or still avoidable; this is this study's reading of the rule, not a claim the article makes about it. Read beside Espeland and Stevens, Commensuration as a Social Process (1998), the test is, in this study's reading, commensuration in a pure form: facility, material and staff costs, and the quantities that cannot be switched, all become one signed amount.

Two smaller patterns support the first. Seven of the excluded reasons say, in nearly the same words, that keeping the present arrangement does not explain or secure a cost advantage; 4 others say that the avoidable cost would go on being borne or that the chance of a saving would be missed. The calculation's own sentence mostly stops at arithmetic, but in 2 records it goes on to say that the figure is the grounds for the switch, and in one that it determines whether to switch and on what scale. There the record lets the number speak for the decision.

On this study's arithmetic, dividing each positive net saving by its avoidable cost, the share that survives runs from 19% to 58%. The records never compare these shares; the direction is set by the sign alone.

1.3What stays outside the line

The cases read here are authored synthetic settings too, so what they call unknown is the author's setting and says nothing about any real project. The records name, in their own words, what the subtraction does not hold. In 9 of the 12, what is called unknown is a matter of quality, performance, reliability, capacity or the life of equipment; in 8 it is a further cost, price or investment; in 6 it is the terms of a contract or the scope of a rule. Six of the situations already name, beside their figures, a matter the run leaves out.

Quality beside the figure

The plan to remodel ageing base facilities states its saving and its doubt in one breath:

What "must be taken into account" returns among the things the record calls unknown, the life of the equipment and the upkeep that follows, and the excluded option is the one that would answer that doubt directly, building anew "to cut off the problem of equipment life at its root", set aside because it has no cost advantage against the figure. The record holds both the figure and the doubt; only the figure is counted.

The plan to contract out a medical post is written the same way, its saving followed at once by the quality of contracted care that "must be confirmed together". The plan to contract out equipment maintenance names what it does not know:

while its recommended reason holds that the scope of contracting can be controlled by contract. Hart, Shleifer and Vishny, The Proper Scope of Government (1997), argue that where contracts are incomplete a contractor's incentive to cut cost is typically too strong, because the effect on quality that cannot be written into the contract is ignored. The records do not take that argument up, and it is not tested on them here. Read through it, in this study's reading, the records show the shape the argument describes: a cost stated exactly on one side, and on the other a quality named as unknown and left to be checked after the switch. No real contract is in question here.

Further costs and a figure for what is unknown

The make-at-home case for medical supplies shows the gap at its narrowest. The situation says what the switch brings:

The record then names as unknown the very costs the situation says will arise:

The run nonetheless has figures for them, 250 for the cost left after the switch and 30 for the cost of escape, which its assumptions call values assumed by the author. The figures are the author's stand-ins for what the record says it does not know. The record does not hide this; its assumptions say it. What the reader can see is that the sign test of the recommended option rests on stand-ins for the costs that the situation names first.

The inputs each record still needs point the same way. All 12 lists name a cost statement, a quotation, an estimate or a price for the very figures the run has already used, and in all 12 the list is the same as the run's own list of missing decision inputs. Only 4 lists name anything on quality, reliability, performance or protection. In the terms of Williamson, The Economics of Organization (1981), the records describe the choice between governance structures, buying, making, contracting, bringing back in, but what they ask for next is the price of each, not the attributes of the transaction that the transaction cost approach dimensionalizes. That is this study's reading of the records through the article's note, not the article's.

The middle option without a figure

Every one of the 12 records offers a middle course: a prototype stage, a half-and-half split, core work kept in-house, a half-yearly call-up, a shorter renewal, small items first, new materiel first, some courses first, two arrangements side by side, a small quantity, a divided timing, a trial. The run gives none of them a figure. In 11 records the reason given for the middle course says that the saving shrinks, is spread or comes later, and in 5 of these that it comes later; in 9 it says that a risk, a shock or a burden shrinks. The trade is put in words and left there:

Dixit, Investment and Hysteresis (1992), gives one way to name what these options offer: waiting has positive value because time brings information about a project's prospects. The article's argument concerns firms and their investment and is not carried over as a claim about the records. Read beside it, in this study's reading, a single positive figure today does not by itself price the information a pilot would bring. The records' own words point to that information, verifying the effect of education, looking at the results first, but the run has no term for it, and the recommended option in every record is the full change.

Two records go further. Their reopening condition presupposes the very course the author did not recommend. The energy equipment record recommends confirming the whole switch, yet says it would be reviewed again on a trial's results:

The medical post record recommends confirming the switch to contracting, yet names as its way back the side-by-side running it offered as the alternative:

In both, the condition for opening the question again is written for the middle course, while the mark recommends the full one, and the record leaves the two side by side.

Units and labels that part from the figures

Three records count in amounts a year. In two of them the situation states the cost of leaving, which is the kind of cost paid once, as a yearly amount too, and one of them then watches for it as a yearly payment:

The plan to bring contracted maintenance in-house does the same, stating its contract exit cost as an amount a year. The relocation record runs the other way. Its run counts in plain amounts, with no year attached, but its words speak of a year at both ends. The situation sets the terms:

The question adds that keeping the facility costs 200 "a year", and the run's own sentence reads the result the same way:

A yearly upkeep is set against a remaining and a vacating cost whose period the record does not give, and the difference is read as a yearly saving. The subtraction is exact; the time base of its terms is not stated, and the words supply one for the result only.

A label parts from its figure in the first case. The situation calls 600 "the remaining and closing costs" and 400 "the exit cost"; the run gives the name "remaining and closing costs" to 1000, the two together. In the same case the net saving happens to equal the sum subtracted, both 1000, which is true of no other run in the set, and the question asks about a change that avoids 2000 of import cost "and leaves 1000 hundred million won". Whether that names what is left to pay or what is left as saving cannot be told from the figures, since both are 1000. The translation keeps the Korean's ambiguity rather than resolve it.

Thresholds for opening the question again

Three records name a figure at which the question would be opened again, and the three figures sit at three different places relative to the run. The plan to bring maintenance in-house sets its figure where the saving vanishes:

That is the avoidable cost itself, and on this study's arithmetic the net saving at that point is 0. The joint purchasing record sets its figure at the present total:

That is the remaining and exit costs as the run now has them, so any rise at all reopens the question, while the net saving at that figure would still be 50, on the same arithmetic. The online education record names a figure for the remaining cost alone:

The figure 20 is the present total of the remaining and closing costs, while the remaining cost alone is now 12. If the line is read as it is worded, the remaining cost alone at 20 with the closing cost unchanged, the net saving at that point would be 20; if 20 is read as the total, it would be 28, the present saving. Both are this study's arithmetic on the stated readings; the record does not say which it means.

One record states its threshold in words rather than a figure, opening the question again if "the net saving disappears". Eight of the 12 reopen on costs rising or going beyond a figure or an estimate; 4 on quality, results or access. Every observation sets what comes afterwards against the calculation, an estimate, a criterion, the budget or the course of keeping, and 8 name a time to look. The records thus promise, for the most part, to watch the figure. Hefetz, Privatization and Its Reverse (2004), finds monitoring and management among the most important explanations of both contracting out and contracting back in. Read beside that finding, the records place their monitoring where their arithmetic is, on whether the costs come out as calculated, and leave the quality they named as unknown to the reopening lines of a few. That is a reading of the authored set, not a claim about practice.

1.4What the chapter adds

The subtraction gives each record one exact, replayable figure whose sign carries the recommendation in all 12 cases, the negative one included. What the records themselves call uncertain stands beside the figure, named in words and left without a number, and their units, one label and their thresholds for reopening show where words and figures part. For the debates on commensuration and on the make-or-buy choice, this is a concrete picture of a common metric with its edges in view.