Chapter 1. One Product per Line: What the Total Settles and What Stays Outside

Seventeen authored records price something by multiplying quantities by unit prices and adding the lines, and in most of them the recommendation carries the total into a budget, a ceiling or a tender. This chapter shows that the arithmetic is the one thing in these records that is settled; that the records make its total a reference figure while calling the same inputs fixed in one place and assumed in another; that they protect the line against a single averaged price; and that the budget, the costs beyond the price, the basis of allocation and, in places, the unit a total is labelled with stay outside the lines. To the debates on the line item, on anchors and reference classes, on the cost beyond the price, on allocation and on mental accounting, it contributes a reading of how a designed record turns a reproducible total into the figure that later prices are measured against.

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 (UTC): 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, line-cost-v1, takes for each line a quantity and a unit cost (quantities, unitCosts), with a quantity unit and a cost unit, and reports the line-by-line products, their total and the unit. Across the 6,540 cases the rule is run 160 times, in 24 programmes, and in all 160 every product, total and unit follows that rule exactly.

The selection rule is one sentence: every authored case in AEGIS-CALC-v1 whose run executes line-cost-v1. It keeps 17 cases, all in the ninth published part. None is among the 101 cases that the eight earlier AEGIS papers read; the counting script reads their case lists and stops if any case is shared. The other 143 runs of the rule stand in 23 other programmes, where the cost units include minutes, hours, indices and synthetic budget units as well as won; they were left out so that every case read shares one programme scope, one form of record and money as its unit.

All 17 are typed realistic synthetic (현실형 합성) and give the same source role:

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

Every run says in its assumptions that its figures are values assumed by the author, and 7 add that they are not actual data, prices, quotations or a survey. Every run has executed and been replayed with the same input and output, no record has a source URL, and each awaits "materials for the overall judgment". The domains are Procurement and contracts (10), Budget (4), Protection of civilians (1), Disaster support (1) and Logistics and supply chains (1). The 17 cases name 16 deciding roles, 7 of them marked "(setting)".

The fields read are the situation (summary), the question, the three 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 case would be calculated or opened again (reconsider), what would be recorded afterwards (observation), and the run's input, output, assumptions and interpretation. AEGIS wrote them in Korean. The English quoted 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 count money in ten thousand won (만원), a million won (백만원), ten million won (천만원) and a hundred million won (억원), and count things with Korean counters. The translation keeps every figure as the records give it and renders each unit literally, so that "5 ten million won" stands for 5천만원, and it keeps "dong" for the counter 동 that the tent record uses.

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. One kind of figure appears that the records do not state: a line's share of a run's quantity or of its total. It is labelled as this study's arithmetic.

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 17 cases carry no frame runs; the author's judgment mark carries 5%; the uncertain line carries 62% 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 total becomes the reference

Every case read in this section is an authored synthetic setting: its quantities, prices and units are the author's assumptions, and its English is this study's translation. The one thing settled in these records is the arithmetic. Every product equals its quantity times its price, every total equals the sum of its lines, and every run was replayed with the same result. In 12 of the 17 the question states the run's total, and in 11 it asks whether to fix it, reflect it in a budget, approve it, put it out to bid or order on it. In 12 the recommended option names the total and turns it into something: a line in the draft budget or the budget allocation, a procurement total, a ceiling, a reserve price, the baseline of a contract.

The first record in the set shows the pattern whole. Two batches of vehicles of different series are priced line by line, and the author's mark sets three options against the total:

The recommended reason rests on two words: the inputs are "fixed", so the basis is "clear". The run's own note says something else about the same inputs:

and the record names as unknown "the possibility of market changes in unit prices". The record does not hide a contradiction; it speaks in two registers. In the author's mark the quantities and prices are fixed, as the setting's own figures; in the run's note they are assumed, because the setting is made. The mark's word carries the total into the budget, and the note's word keeps the doubt.

Three records use the first register in their recommended reasons, and six call the basis "clear". Two let the doubt into the situation itself. The maintenance parts record ends its situation with it:

and then recommends:

The word "candidate" is the one place in the set where a recommended total is held short of final. The clothing record states the condition outright:

Its recommended reason then treats that condition as met, "a simple total with fixed issue quantities and unit prices", while its unknowns include "changes in the number of people to be issued" and it would reopen "if demand among those to be issued changes by 10% or more or the unit price rises by more than 10%". Within a few lines the record holds the condition for its total, the claim that the condition is met, and the margin by which it may not be.

Where the setting is larger, an excluded option makes the claim for the arithmetic directly. The acquisition record sets aside one more check:

What is consistent is the product; what is assumed is each factor. The run confirms the first, and its assumptions say of the second that the figures "are not actual acquisition plan data". The medical sets record goes a step further and gives the assumed price the standing of a market price:

The run's note on the same prices ends:

Read beside Tversky and Kahneman, Judgment under Uncertainty (1974), the pattern has, in this study's reading, the shape of an anchor: a relevant value is made available first, and later values are to be judged by adjustment from it. The article describes a heuristic, not a record, and nothing here shows that anyone would adjust too little. What the records show is where they place the starting value. Eight of the 17 plan to record the gap between the assumed or estimated price and the actual one, and 4 keep what they record as the basis for a next or later round:

Flyvbjerg, Curbing Optimism Bias and Strategic Misrepresentation in Planning (2007), argues for basing projections on the actual performance of a reference class of comparable actions. In this study's reading, an observation line of this kind describes the first entries of such a class: an assumed price set beside an actual one, and kept for next time. The figure the records fix first, though, is the assumed total, and the actual prices are to be recorded as departures from it.

1.3What stays outside the lines

The cases read here are authored synthetic settings too, so what they leave out is the author's setting and says nothing about any real purchase. The records are plain about the limits of a line. Ten name as unknown a market price, a change of unit price, a price gap or the exchange rate; 5 name a change in quantity, people, meals, priorities or runs; 3 name a further cost or allowance that no line holds.

The line against one price

The records defend the line. Four excluded options would merge the lines, average them, bundle them or use one price, and 3 of the reasons for excluding them say that this would distort, hide or weaken something. The vehicles record has already given one such reason: two series with different required performance, merged into one line, distort demand itself. The communications equipment record names the averaged price exactly:

The figure is the run's total divided by its quantity in all, 4200 over 800, as this study's arithmetic confirms. It is the one figure among the options that the run implies but does not report, and the record excludes it. Hou, Line Item and Budget (2023), argues that the advantages, convenience and conciseness of the line item explain its survival. In this study's reading these records give the line one further advantage, which the working paper's note does not name: it keeps apart prices that a single average would hide. That is the records' argument, voiced by the author's mark, not the working paper's.

Allocation questions and the product

Five questions in the set ask for a basis, a ratio or a range of allocation, and only one of them states the run's total. The last four records ask not whether to fix a total but how to divide one. The consumable parts record sets its problem out at length:

Its run multiplies three quantities by three prices and adds them, and its interpretation claims more than the output shows:

No output of any of the 17 runs carries a share. On this study's arithmetic, dividing each line by the run's own figures, the three kinds hold 50%, 33% and 17% of the quantity and 35%, 35% and 29% of the cost. The highest-priced kind is the smallest by quantity and 29% of the cost. That is the gap the situation describes in words, the few high-priced items whose room to negotiate is buried under a basis of quantity; the run could show it, and its output does not. Noreen, Conditions under Which Activity-Based Cost Systems Provide Relevant Costs (1991), contrasts one allocation basis proportional to volume with several cost drivers, and finds the conditions under which the second give relevant costs quite stringent. The record's recommended option keeps share of quantity as "the basic frame" and moves the high-priced items into "a separate procurement line". In this study's reading, it answers the trouble with a single volume basis by drawing a new line rather than choosing a new basis.

The repair record asks at what ratio to divide construction costs between two years. Its lines put 18 sites at one unit price and 12 at another, and the products come out equal, 108 and 108. On this study's arithmetic the first year would hold 60% of the sites and 50% of the cost. One option speaks of halves:

while the recommended option assigns "the high-priority sites to the first year". The run's interpretation says only that multiplying sites by prices and adding them "yields the total construction cost of each year". What the record calls unknown is when the data assessing the urgency of repair at each storage facility will be updated. The multiplication takes the split of sites as given; it cannot say whether that split follows priority.

The fuel transport record asks how the number of runs each type of vehicle makes should enter the unit price, and its situation begins:

Its run counts something else:

The quantity multiplied is vehicles, not runs. The question names one driver of cost, and the run multiplies by another. This is the only record of the 17 that shows such a gap, and the record gives no reason for it.

Costs beyond the price

Some costs the records name lie outside every line. The acquisition record says that some costs are left out of its lines and that, for that reason, 60% to 70% of its total may be opened again later.

The total that the recommended option would fix "as the baseline" is, in the record's own words, a figure of which most may be reopened, and the same option would fix "subsequent changes in negotiation clauses". The personnel contract puts a similar question about a smaller item:

and its recommended option would contract at the ceiling and "limit the scope of overtime and allowances in a separate clause". In the vehicles record the further cost is maintenance, and it appears only in the alternative, which would add it to the unit price to take in "the life-cycle costs that purchase costs alone fall short of".

Ellram, Total Cost of Ownership (1995), presents an approach that looks beyond the price of a purchase to many other purchase-related costs. Greenleaf, Johnson, Morwitz and Shalev, The Price Does Not Include Additional Taxes, Fees, and Surcharges (2015), review research on prices divided into a base price and mandatory surcharges, and the concern that totals are underestimated. In this study's reading, these records divide their prices in a similar way: the lines carry the base, and the equipment, the allowances and the maintenance are named beside them and handed to a clause, a later round or the option not recommended. The records write the division down; whether anyone would underestimate a total is not something they can show, and this paper does not claim it.

The budget the total is set against

Three questions ask whether a total fits a budget or goes beyond it. None of the three records states the budget, and all three ask for the budget limit among the inputs still needed. The training meals record puts the comparison in its situation:

and lists "Details of the training budget limit" among its needs. The shelter record names the gap as its unknown:

The run produces one side of the comparison the question asks for, and the other side is not in the record. Wanat, Bases of Budgetary Incrementalism (1974), explains the growth of budget requests through concepts in the participants' own vocabulary. This study borrows only the point that the words matter, and notes that the words the records use for these totals, "within the allocated budget", "beyond the allocated budget", are words of a comparison whose second term the setting does not supply.

Units, periods and labels

The 17 runs use 9 distinct cost units. Three are amounts per period, a year or a month, and two carry a price per item onto the total. The vaccination run multiplies doses by a price per dose and reports its total under that same unit. Its interpretation reads:

while the unit the run gives its prices, and writes again beside its total, reads:

The interpretation names a sum in ten thousand won; the label beside it names a price per dose. The meals run does the same with "ten thousand won per thousand meals". The software record runs the other way. Its situation prices each contract "a year", its question speaks of "yearly maintenance unit prices", and its recommended option restates the total as "22.8 hundred million won a year", while the run's own unit names no period:

Thaler, Mental Accounting Matters (1999), describes how expenditures are labelled and grouped into categories, how often accounts are evaluated and how narrowly or broadly they are defined. Read through that note, in this study's reading, the label beside a total is part of how the total is held: as a price per dose or a sum, as a yearly figure or a figure with no period. The arithmetic is right in all three runs; what parts from it is the label.

What would reopen the question

Every record says when it would be looked at again, and in nearly all the condition is a change in an input. Eleven reopening lines turn on price and 14 on quantity, demand, mix, priorities, sites or make-up. Five name a percentage, most often 10%, and the tents record names 20%. One names a sum of money:

On this study's arithmetic, 1 ten thousand won is 25% of the lower price per dose and 17% of the higher, so one threshold in money is two different thresholds in proportion. More telling is the verb. Seven reopening lines say that the case would be opened again; 10 say only that the figure would be calculated again. In those 10 a change in price or quantity sends the record back to the multiplication, which will return a new total, and the line does not say that the recommendation itself would be weighed again. The design makes the arithmetic the place where change is absorbed.

1.4What the chapter adds

The total of a line-cost run is the one thing these records settle, twice over, in the run and in its replay. They make it the figure that a draft budget, a ceiling, a reserve price or a contract holds, and plan to measure actual prices as departures from it, while the doubts they record sit in the factors rather than the product. They keep separate lines against a single average, yet the allocation questions they ask need a basis that no product supplies, and the budget, the costs beyond the price and, in three runs, the meaning of the unit written beside the total stay outside the lines. To the debates on the line item, anchors and reference classes, the cost beyond the price, allocation and mental accounting, this is a case of a designed record in which the most certain figure is the one built most directly from assumptions.