I  Theory
1 Introduction: Choosing the Time Structure of Cash as the Variable
1.1 The problem
1.2 Structure of the text, and how to read it
1.3 What this text does not claim
2 The Business Model: Phi and the Generation of Cash Flow
2.1 Primitive sets
2.2 Schedules and spaces
2.3 The map from delivery to settlement
2.4 Generating the cash flow
2.5 Degrees of freedom of Phi
2.6 Three risk operations
2.6.1 Cost fixed by technology
2.7 Divergence between right and exercise
3 The Credit Position: kappa and the Lag tau
3.1 The gap between delivery and settlement
3.1.1 Existing theory for each term
3.1.2 Both sides of a transaction: $\kappa$ is antisymmetric
3.1.3 Additivity over parallel $\Phi$
3.1.4 Expressing the position as a lag
3.2 Decomposing the cash balance
3.2.1 The net form
3.2.2 Equity and capital providers
4 Information Structure and the Objective
4.1 Verifiable shared information
4.2 The objective: a cash constraint imposed path by path
4.3 Heterogeneity of discount factors
5 The Growth Constraint: CCC and the Self-Financeable Growth Rate
5.1 The cash conversion cycle
5.2 The fundamental inequality
5.3 Growth and free cash flow
5.4 Level and change are separate constraints
5.5 CCC is a sum of lags
5.6 The path constraint and the peak
5.7 Comparative statics
6 Surplus and Layers: Source, Durability, Mutability
6.1 The three-way decomposition of surplus
6.2 Surplus and cash
6.3 Layers: five levels ordered by mutability
II  The Space of Maps
7 A Catalogue of Phi: Seven Families, Twenty-Eight Types
7.1 How the catalogue is built
7.2 Family 1: one-off exchange
7.3 Family 2: continuing access
7.4 Family 3: renting an asset over time
7.5 Family 4: recovery through a complement
7.6 Family 5: outcome- and state-contingent
7.7 Family 6: intermediation
7.8 Family 7: separating beneficiary from payer
7.9 Assigning an observation to a type
7.10 Limits of the catalogue
7.10.1 The Phi of labour: no family is added
7.10.2 Composite contracts: combinations of existing types
7.10.3 Claims that circulate: outside the framework
7.11 A real firm is a bundle of Phi
8 A Subspace Under Constraints: Alone, Without Assets, Without Credit
8.1 The premises imposed in this chapter
8.2 Translating the premises
8.2.1 The financial constraint
8.2.2 The capacity constraint
8.2.3 Which one binds
8.3 What the cloud means structurally
8.4 Sieving the types
8.5 The credit bootstrap problem
8.5.1 Cash flow of the surviving types
8.6 Relaxing a premise: those who hold assets
8.6.1 The social background
8.6.2 The constraint does not loosen; it changes type
8.6.3 The objective bifurcates
8.6.4 The change in the objective can be expressed through parameters
8.6.5 Under R2 the feasible region is reversed
8.6.6 Family 3 revives, and a reconciliation with data
8.6.7 The structural role of pensions
8.6.8 Restating the path constraint
8.7 The formation of credit
8.7.1 Why credit attributable to an individual is zero
8.7.2 Separating three quantities
8.7.3 Two discontinuities, and a lag between them
8.7.4 Capital and credit are substitutes
8.7.5 Starting with the sign reversed
8.8 The trade-off between contract work and publishing
8.8.1 The conflict is not peculiar to individuals; the inability to parallelize is
8.8.2 Two kinds of credit
8.8.3 Whether the conflict arises depends on the quadrant aimed at
8.8.4 Partial conversion and the optimal allocation
8.9 Employment contracts reread
8.10 Limits of this chapter
9 Unmanned Operation: The Limit With the Operator Removed
9.1 The question
9.2 Formalizing “unmanned”
9.2.1 Automation is a stronger condition than measurability
9.2.2 What is required is not labour but availability
9.2.3 Where a free period fits
9.3 Decomposing the bootstrap
9.3.1 Each term and where it can be externalized
9.3.2 The dominant term by family
9.4 Limits of this chapter
10 The Supplier of the Information Structure: Settlement by Protocol
10.1 The premises imposed in this chapter
10.2 Translating the premises
10.2.1 Three functions the third party performed
10.2.2 A case split by where delivery resides
10.2.3 The binding constraint switches
10.3 Identifiers diverge from parties
10.4 Sieving the types
10.5 The collateral constraint
10.6 Observability
10.6.1 A population frame becomes available
10.6.2 What can and cannot be tested
10.7 Limits of this chapter
III  Method
11 Design of the Empirical Work: Connecting to Observation
11.1 What is to be tested
11.2 Five stages to pass
11.3 What to check at each stage
11.3.1 Stage 1: operationalization
11.3.2 Stage 2: population
11.3.3 Stage 3: measurement
11.3.4 Stages 4 and 5: how the values obtained are used
11.4 Reconciliation versus verification
11.5 Where each stage is handled in this text
11.6 Priorities for the survey
11.7 Variables to record
11.8 What must be pre-registered
12 Selection Bias: Decomposing the Distortions That Enter Observation
12.1 The problem
12.2 Conditioning on survival: a circularity in the framework
12.2.1 The direction of the distortion reverses with what is conditioned on
12.3 Selection into disclosure: correlated with the axis of interest
12.4 Age: a problem of domain, not of bias
12.5 Age, period and cohort are not identified
12.6 Retrospective narrative
12.7 Mistaking the unit: what a row denotes versus what its values denote
12.8 Selection of variables: the gaps are not random
12.9 The observation frame in practice
12.10 How to proceed
12.10.1 Declare the frame in advance and track forward
12.10.2 Collect the failure side explicitly
12.10.3 Lower the unit of analysis from the firm to Phi
12.10.4 Group by the shape of the constraint, not by industry classification
12.10.5 Where a distortion cannot be removed, state its sign
12.10.6 A rule for using well-known firms
13 A Taxonomy of Verification Obstacles: Six States
13.1 Why a taxonomy is needed
13.2 Six categories
13.3 The taxonomy also serves as a test before starting
IV  Empirics
14 Measuring the Theoretical Quantities: What Could and Could Not Be Measured
14.1 Purpose of this chapter
14.2 The primitive sets made concrete
14.3 The observed range of the map Phi
14.4 Cumulants and the credit position
14.4.1 D, P and kappa in family 2
14.4.2 CCC by medium
14.4.3 kappa in the corporate statistics
14.5 Measuring the growth constraint
14.5.1 The corporate sector over time ($m∕\mathrm{CCC}$)
14.5.2 g* including depreciation and investment
14.5.3 g* by industry
14.5.4 The $m$ of small firms is decided by directors’ remuneration
14.5.5 Comparison with unincorporated businesses
14.5.6 By industry (FY2024)
14.6 Right and exercise, and cognitive surplus
14.6.1 phi-cog is measurable
14.6.2 A detour through the menu
14.7 The information structure G made concrete
14.8 The three-way decomposition of surplus
14.9 The terms of the launch cost
14.10 Quantities relating to selection and identification
14.11 Quantities that could not be measured
15 Empirics of families 2 and 5: prepayment and outcome-contingent forms
15.1 The propositions tested in this chapter
15.2 Family 2: prepaid payment instruments
15.2.1 Data source and population
15.2.2 Measuring the residence period
15.2.3 Separating the alternative
15.2.4 What could not be tested
15.2.5 The absence of per-firm data
15.2.6 The nature of the remaining obstacle
15.3 Family 5: fee-charging employment placement
15.3.1 Data source and population
15.3.2 The choice of contractual regime
15.3.3 Fees per placement by occupation
15.3.4 Why the measurability hypothesis cannot be tested
15.3.5 Fees and turnover
15.3.6 Assignment of obstacles
15.4 Comparison of the two families and its methodological implications
15.5 The structure of the data source
15.5.1 The detailed search
15.5.2 Outcomes of the three routes
15.5.3 The mismatch of recording granularity
15.6 What was reached and what was abandoned
15.6.1 Subjects abandoned
15.6.2 Subjects possible under conditions
15.6.3 What families 2 and 5 reached
15.7 A quantity that is not tabulated: the credit position of sole proprietors
16 Evidence From the Corporate Statistics: kappa and CCC Across Firms
16.1 Position of this chapter
16.2 Hot and cold are not one-dimensional
16.3 Data source
16.4 Size and the direction of credit
16.4.1 The implication tested
16.4.2 Result
16.4.3 The error in the reasoning
16.4.4 The sign splits by industry
16.4.5 Implication for Chapter VII
16.5 Is $\mathrm{CCC}$ a leading indicator of the cycle?
16.5.1 The implication tested
16.5.2 Result
16.5.3 The synchronous negative correlation may be a denominator effect
16.5.4 That the sign splits by industry is a finding
16.6 An observation not anticipated: the long-run rise in CCC
16.6.1 The growth constraint has not worsened, however
16.7 Levels by industry (for reference)
16.8 Decomposing the rise in CCC
16.8.1 Shift-share decomposition
16.8.2 Components of the within-industry effect
16.9 Separating the contemporaneous negative correlation
16.9.1 Result
16.9.2 Lag structure
16.10 The effect of the scope of inventories on the conclusions
16.10.1 Two cross-sections
16.10.2 The level is understated roughly twofold
16.10.3 The effect on differences is small, but not negligible
16.10.4 Correcting the definition worsens the elasticity slightly
16.10.5 Verdict
16.11 An observation the simplified capacity constraint does not fit
16.11.1 The observation
16.11.2 Inconsistency with the simplification
16.11.3 Why the theory is not revised from this observation
16.11.4 The simplified capacity constraint
16.12 Limitations of this chapter
16.13 On both implications being rejected
17 The Price of Externalization: Platform Fees
17.1 The implication tested
17.2 Result: a ladder of rates
17.3 A natural experiment within one platform
17.4 A counterexample: price discrimination by size
17.5 Verdict
17.5.1 The risk component: untested
17.6 Practical implications
17.7 Limits of the measurement
17.8 How the institutional layer acts
17.9 Assessing feasibility of further investigation
17.9.1 Runner-up: decomposing lambda
17.9.2 Questions abandoned
17.10 Limits of this chapter
18 Evidence From Protocol Records: M(t) and the Rate of Modification
18.1 The implications tested
18.1.1 What was fixed in advance
18.2 Results
18.3 Quantities measurable from the same records
18.3.1 The rate of response to unforeseen states
18.3.2 Duration of the procedures
18.3.3 Locked state $B$
18.3.4 Rates
V  Conclusion
19 Where This Stands: What Was Established and What Remains Open
19.1 What was established and what was not
19.1.1 Derived as theory
19.1.2 Judged empirically
19.2 Fixing the implications in advance
19.3 Open problems
19.3.1 (i) No measurement exists
19.3.2 (ii) Ill-posed hypothesis
19.3.3 (iii) Not identified
19.3.4 (iv) Access constraint
19.3.5 Matters of the framework’s descriptive range
19.3.6 Items with no obstacle
19.3.7 Priorities
19.4 Known weaknesses of the framework
19.4.1 (A) Excessive assumptions of independence
19.4.2 (B) Excessive assumptions of exogeneity
19.4.3 (C) Level and change are not separated
19.4.4 The three types, and mid-level theory
VI  Appendices
A Supplement: proofs concerning method
A.1 Correlation induced by conditioning on a collider
A.1.1 The choice of formalization
A.1.2 Implications not treated in the body
A.2 Non-identification of age, period and cohort
A.2.1 Why the argument is made in a linear model
A.2.2 Implications not treated in the body
A.3 Preference for variance under a deadline
A.4 Substitutability of capital and credit
A.4.1 The meaning and the limits of “perfect substitution”
B Notation
C Correspondences with existing theory
D List of pre-registered implications
D.1 The list
D.2 Where registration changed the verdict
D.3 Defects that arose in operating the registry
E Revision history
E.1 History of versions
E.2 Claims withdrawn
E.3 Corrections deriving from measurement
E.4 Corrections deriving from reasoning
E.5 A record of pre-registration at work
E.6 Making assumptions explicit
E.7 Introducing the lag
E.8 Re-evaluating the relation to existing theory
E.9 Filling in definitions
E.10 Examining reversibility, and a correction
E.11 Examination from the worker’s viewpoint
E.12 Extending the taxonomy of obstacles
E.13 Extending the taxonomy of biases
E.14 Reorganizing the list of open problems
E.15 The means of reproduction were not included
E.16 Removing a description resting on a single observation
E.17 Setting theorem-type body text in roman
E.18 Testing implication Y, and a defect in the registration
E.19 A route for testing the deductions of Part II
E.20 Registering implications Y and Z
E.21 Checking the scope of inventories
E.22 Filling in operationalization and reorganizing the list of open problems
E.23 Placing the empirical design first
E.24 Implication Z tested
E.24.1 Implications Phi1–Phi4: three different failures
E.24.2 Dropping the symbol for the production function
E.24.3 Defining the relation between classes of agents and individuals
E.24.4 Revising the verdict on implication D
E.25 Giving deductive grounds for choosing families 2 and 5
E.26 Removing references to places that do not exist
E.27 Resolving a contradiction in the description of phi-cog
E.28 Extending the scope of inventories to 62 industries
E.29 Stating the handling of per-firm data
E.30 Multiple definitions of a symbol
E.31 Correcting a count
E.31.1 Calling the types a “basis”
E.32 Considered but not adopted in the body
E.32.1 Describing an allocation that is not an interior solution as one
E.33 Changes of structure
F Data sources