Chapter 1
Introduction: Choosing the Time Structure of Cash as the Variable

1.1 The problem

The standard variables for describing a firm are revenue, margin, and market share. This text uses none of them. It describes a business model through the time structure of cash.

There is a reason for the choice. What keeps a firm in existence is not a condition on profit but a constraint on its cash balance, and that constraint is imposed path by path rather than in expectation (Section 4.2). Any framework that treats survival and growth must take the time structure of cash as a first-class object.

The standard variables are not discarded. The income statement, the balance sheet, and the cash-flow statement appear as projections of the object constructed here, each collapsing one of its indices (Table 2.1). This text does not posit quantities separate from accounting; it keeps the indices that accounting collapses.

1.2 Structure of the text, and how to read it

The text has six parts.

Parts I and II are deductive; Part III supplies the procedure that connects theory to evidence.

Part II proceeds in three stages. It first enumerates the space generated by the degrees of freedom of $\mathrm{\Phi }$ (Chapter 7), then derives the subspace that survives constraints on capital and labour (Chapter 8), and finally treats the limit in which the operator is removed (Chapter 9). All three are deduction, not evidence.

The absence of a separate part on applications is deliberate. An application is warranted once the theory has passed through evidence, and the empirical work here is not complete. Deduction under constraints is not application; it is the operation of cutting the space of maps with a constraint, and it therefore belongs in Part II.

Chapter 14 opens Part IV and tabulates, for every symbol introduced in the theory, the value that could be measured and the fact that could not. Each later chapter also opens with a table of the theoretical quantities it handles, so that one can trace where each symbol was measured.

Depending on the reader’s interest, the following routes are suggested.

• Theory alone: Parts I and II. Proofs of the propositions are in the body; only the proofs of methodological claims are collected in Appendix VI
• Practical design: Chapter 5 and Part II
• The magnitudes the theoretical quantities actually take: Chapter 14
• Survey method: Parts III and IV

Numerical examples accompany most sections. The notation is listed in Appendix A.4.1.

1.3 What this text does not claim

To forestall misreading, the scope is limited in advance.

First, this is not a predictive theory. Most of the implications fixed in advance and tested in Part IV were rejected. The framework works as a descriptive instrument, but this text has no established result about what the quantities it describes predict.

Twenty-two implications were nevertheless fixed in advance. There are two reasons.

The first is that a descriptive framework can supply an after-the-fact account of any fact whatever. That something can be explained is no evidence that the framework is right. Unless the implications are fixed in writing before the observations and the ones that miss are left standing as misses, there is no way to distinguish the framework working from the author having reasoned backwards. The places where an after-the-fact story was nearly adopted are listed in Section 19.2. The fixed implications are not claims of the framework; they are a constraint imposed on the author’s own interpretation.

The second is that an implication failing and the framework being rejected are different events. Whether the descriptions $\mathrm{CCC}$, $\kappa$ and $\mathrm{\Phi }$ work is one question; what those quantities predict is another. A failed implication refutes a conjecture about the latter, not the former (Section 16.13).

Second, this text is not normative. It does not argue which $\mathrm{\Phi }$ is desirable, only which $\mathrm{\Phi }$ is feasible under the constraints.

Third, most of the individual components have counterparts in existing theory. Appendix A.4.1 is divided into three layers separating the existing theory that explains each term, the part that connects them, and the organization contributed here. The contribution of this text lies in the connection, not in the novelty of the elements.