The book has two ways of reading, and behind them two ways of writing. Decomposition starts from an observable result, breaks it into terms, and checks that the terms are complete. Derivation starts from a world with nothing in it, adds one constraint at each step, and sees what grows from it. Each method has its own standards for choosing material. This appendix records those standards, and the problems found and corrected during writing, so that readers can judge how reliable the book's conclusions are, and so that others who want to write with the same methods can refer to them.
Decomposition and derivation answer different questions. Decomposition answers which terms a result is made of; its strength is that completeness can be checked: once every term is written out, any missing term is obvious. Derivation answers why an institution appears; its strength is that it transfers: when a constraint changes, rerunning the derivation suggests what new institution might grow. The first suits checking a product; the second suits imagining one.
Each of the four parts of the Decomposition view starts from an equation: realized return, the result the user actually obtains, the amplification factor, and net value. Equations were chosen by three standards. First, the left-hand side is an observable quantity, not a set of premises; only an observable quantity lets one check whether the breakdown is right. Second, the terms on the right do not overlap and together are complete. Third, every term has both a return side and a risk side, so that the account is not only about benefits.
During writing another structure was tried: Part One written as six premises on which financial markets rest. It did not lack content, but the boundaries between the premises were blurred and completeness could not be checked; it read less clearly than the decomposition of returns and was finally dropped.
The Derivation view follows three rules. Each step introduces only one new constraint and answers what would happen without it. Every mechanism is a response to a constraint, and the new problems the response brings become the constraints of the next step. Questions off the main line are listed as side branches and marked as not pursued. The derivation keeps only logical order; it is not history. Historical facts serve only as sources, such as the caps on interest rates in the Code of Hammurabi.
The persuasiveness of a derivation depends on its cases. Before a case is written, it must pass six questions:
Cases use physical goods where possible, such as grain, seed and storehouses, rather than money: money is only derived in Chapter 4, and using it earlier would presuppose an institution not yet derived. Each chapter adds "Today's counterpart" midway through the derivation, so that readers do not have to wait until the end of the chapter to see the connection to their own work.
One aim of the Derivation view is to let readers see what problem each theory arose to solve. To that end, the text first works the idea out on the island, and at the moment the derivation is complete, a principle card announces it. Before the derivation, the theory's name and its proposers do not appear. Readers thus meet the constraint first, then the mechanism that answers it, and only at the end learn what the discipline calls it and who proposed it, and when.
Each card has fixed fields: a one-sentence statement; the discipline and type it belongs to, for example "Economics › Information economics" and "Theoretical model"; its standing in the field; the constraint it answers; the premises under which it holds; the proposers and the year; and the question it leaves open. When Parts Two and Three re-examine an existing principle, the card is marked "Rerun: a principle re-examined" and has an extra field, "After the rerun", stating which premise changed once the parameter changed.
The cards follow three rules. First, cards are given only to theories; empirical studies and historical facts stay in the text as evidence. Second, "Standing in the field" records only facts with a source, such as the citation for a Nobel Prize in economics, a paper's own account of its aims, or a widely used name; it does not use judgments such as "most important" or "foundational". Several such judgments were found during fact-checking to have no source and were deleted. Third, each chapter has one to four cards; fewer is better than padding. The book announces fifty-seven principles in all, and re-examines principles thirteen times in later chapters; the seventy cards are arranged on the overview chart in the Epilogue by the order of derivation and the year they were proposed.
The first draft of Chapter 2 in the Derivation view violated the second question. It covered three things in one chapter: two people whose harvests fall in different seasons, lending seed to someone else, and lending between two generations. Each of the three can become a mechanism of its own; the first draft put them together so that the simulator would have the storyline of "a lifetime". On review, the chapter kept only the staggered seasons. Lending seed moved to Chapter 6, because planting an orchard requires borrowing for many years, which is exactly a mismatch of maturities. Lending between generations moved to Chapter 4, because Samuelson (1958) proposed that model precisely to explain money.
The same review also found a problem with the model. The first draft used a square root to represent satisfaction, which made consumption too sensitive to the interest rate: as soon as the interest rate was even slightly positive, the model had people eat little when young and a great deal when old, and the draft had to confine the interest rate to a very narrow range. This showed that the problem lay in the choice of model, not only in the parameters. The revision switched to the logarithm, the form used by Bernoulli (1738), under which the path is smooth across a reasonable range of interest rates.
The simulators' text and numbers were also found inconsistent several times. One simulator used random sampling; over ten years there were too few events, and the noise drowned the differences between the approaches, so it was changed to compute expected values. One prompt said that "insuring is much cheaper than bearing it yourself", yet by the model's own numbers the cost of insurance was slightly higher than the expected loss, so the wording was changed to say what was true. Since then the rule has been that every prompt in a simulator must be directly verifiable from the numbers drawn at that moment.
The numbers in the book are of three kinds. Numbers attributed to research or institutions name their source. Numbers marked "Illustrative" serve only to explain a mechanism. Numbers marked "author's estimate" were calculated by the author from public data; the methods and data are in Methods and data behind the author's estimates. Claims without a reliable source are not used as evidence: if no source can be found, the claim is deleted or turned into an explanation that can be calculated directly.
After the Decomposition view was finished, about 520 citations and numbers were checked one by one. Forty-one were found to be wrong and seventeen could not be verified; all were revised or deleted. Most of the errors were paraphrases and bibliographic details written from memory. The text and interactive figures of this book were written by Claude; the author was responsible for the concept, structure, direction and revision; fact-checking was done by Claude and reviewed by the author.