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Commerce · III.01 · MMXXVI · daylight

La Bourse  /  Volume III  /  Nº III.01

What a Currency Is Made Of

Volume III — Money, Energy, Information


THE PLATE

A man marking a chart of bar graphs while a colleague beside him holds a tablet, daylight from the windows.
Plate III.01The Column of Figures.Money has never been a substance. It is the agreement that these two columns must always match, held by enough people, for long enough, that the agreement can be spent.

THE LETTER

You have handled money every day of your adult life and you have almost certainly never been told what it is. That is not an oversight. The question is genuinely difficult, it has been answered differently by serious people for two centuries, and most of the answers you were given as a child — it is backed by gold, it is printed by the government, banks lend out what savers put in — are either historically wrong or were true somewhere else a long time ago.

This matters more than it sounds. Volume III asks what a currency is actually made of, and every chapter that follows — energy denominators, local currencies, credit commons, interest, digital settlement — depends on getting this one right. If you believe a bank lends out deposits, you will design the wrong instrument. If you believe money is a commodity we happen to use for exchange, you will misprice every single regenerative asset you touch, because you will have assumed the medium is neutral and it is not.

So this chapter takes money apart into the jobs it does. There are four of them, they are separable, they have each existed alone, and — this is the part worth the price of the volume — three of them want the same thing and one of them wants the opposite. Nearly every monetary argument you have ever half-followed is that conflict, unlabelled.

Then we go to the balance sheet, because that is where the answer actually lives, and we take it from the most conservative source available: the Bank of England, in its own quarterly bulletin, stating in plain language what banks do when they lend.

You will not need any mathematics beyond compound interest. You will need a willingness to hold two columns in your head at once, which is the whole of double-entry bookkeeping and very nearly the whole of monetary economics.

— The Editors


DISCOVERY

What is already working

Money works. Start there, because the literature on money is unusually prone to alarm, and alarm is a poor instrument for design.

Every day, across the world, several hundred trillion currency units of obligation are created, transferred and extinguished with an error rate so low that nobody notices the system exists. That is a staggering piece of infrastructure and it has been running, in recognisably its present form, for longer than most nations. The interesting question is not how it fails. It is what it is doing so well, and which of its parts are doing which job — because once you can see the parts separately you can build with them.

The best evidence for separability is that each function has been observed running alone, in the field, for years at a time.

A unit of account with no coin: the Chilean Unidad de Fomento. Created by decree in January 1967 and published daily by the Banco Central de Chile, the UF is a unit that exists only as a number. Mortgages, rents, insurance contracts, court settlements and long construction contracts are written in UF. Nobody has ever held one, because there is nothing to hold. When a Chilean pays a mortgage of three thousand UF, the bank looks up the day's value — on the order of thirty-seven thousand pesos in 2024 — and collects a hundred and eleven million pesos. The unit of account is fully detached from the means of settlement, has been for more than half a century, and the detachment is the point: the contract holds its meaning through inflation that would otherwise have destroyed it. Robert Shiller's assessment of the indexed unit of account treats Chile as the working case, and it is.

A means of settlement with no bank: Ireland, 1970. From the first of May until the seventeenth of November — two hundred days — the Irish clearing banks were closed by an industrial dispute. The economy did not stop. People wrote cheques that could not be cleared, and those cheques circulated, endorsed on the back by each successive holder, functioning as transferable credit. Antoin Murphy's study of the episode is the standard account, and its finding is the one that matters here: the binding constraint on a payment system is not a clearing house. It is information about who is good for it — which in Ireland in 1970 was held by publicans, who knew their customers better than any credit file.

A ledger with no object at all: Yap. William Furness described the rai stones of the Caroline Islands in 1910, and Milton Friedman returned to them in 1991 for exactly the reason we return to them now. The great limestone discs, up to about three and a half metres across, were rarely moved when ownership changed. Ownership changed by public acknowledgement. One stone, lost overboard in deep water on the voyage home, continued to be owned, inherited and traded by people who all agreed it was down there. The stone was never the money. The community's memory was the money, and the stone was its filing system.

A credit instrument that outlasted three dynasties: the Exchequer tally. Notched hazel sticks, split lengthwise so that the grain of the split could not be forged, recorded debts to and from the English Crown from the twelfth century until 1826 — around seven hundred years of continuous service. Tallies circulated. They were discounted, assigned, and accepted in payment of taxes, which is what gave them their value. Glyn Davies traces the whole run.

Four cases, four continents, four centuries, one pattern: in each, the thing that did the work was a record of obligation, and the physical token — when there was one — was a convenience laid over the record. Alfred Mitchell-Innes, writing in the Banking Law Journal in 1913, put it in five words that the next hundred years did not improve on: credit and credit alone is money.

That is the credit theory of money, and it is not a fringe position. It is what you find when you look at the primary record of any monetary system closely enough. Which brings us to the arithmetic, and to the most conservative institution in this chapter.


THE ARITHMETIC

What works, what does not, and where the line sits

First, what a currency is made of by volume.

In March 2014 the Bank of England published two articles in its Quarterly Bulletin — "Money in the modern economy: an introduction" and "Money creation in the modern economy" — by Michael McLeay, Amar Radia and Ryland Thomas. They are the strongest single source in this chapter, and they say the following about composition: banknotes and coin make up about 3 per cent of the money in the economy. Everything else is bank deposits.

Check it a second way, on figures that share none of the bulletin's assumptions. Notes and coin in circulation stand on the order of £82 billion; broad money, M4ex, on the order of £2,920 billion.

  notes and coin in circulation        GBP     82 bn
  broad money (M4ex)                   GBP  2,920 bn
  --------------------------------------------------
  currency share    82 / 2,920                2.81 %
  deposit  share    100 - 2.81               97.19 %

Two routes, 0.19 of a percentage point apart. Ninety-seven per cent of the money in a modern economy is somebody's bank deposit, and every bank deposit is a bank's promise. A currency is made, by volume, of other people's debt.

Second, what a bank does when it lends.

Here is the sentence, from the bulletin, in the Bank's own words: whenever a bank makes a loan, it simultaneously creates a matching deposit in the borrower's bank account, thereby creating new money. And its corollary, stated just as plainly: rather than banks receiving deposits when households save and then lending them out, bank lending creates deposits.

Watch it happen on one mortgage.

  the advance                          GBP  200,000
  ------------------------------------------------
  ASSETS        + loan to customer     GBP  200,000
  LIABILITIES   + deposit in account   GBP  200,000
  ------------------------------------------------
  change in the bank's net worth       GBP        0
  change in broad money                GBP  200,000

Nothing was moved. No saver was debited. The bank wrote two entries, and the economy has two hundred thousand pounds it did not have. This is the endogenous money position: the money supply is an outcome of lending decisions, not an input to them. Richard Werner tested it empirically in 2014 by tracing a single loan through a cooperating bank's own accounting system; Zoltan Jakab and Michael Kumhof modelled the macroeconomic consequences in a Bank of England staff paper the following year.

Third, what actually constrains it — because something must.

Not reserves. Capital, funding and competition.

  risk weight, residential real estate            35 %
  minimum capital ratio                          8.0 %
  capital conservation buffer                    2.5 %
  ---------------------------------------------------
  total requirement                             10.5 %
  risk-weighted assets  200,000 x 0.35     GBP 70,000
  capital required       70,000 x 0.105    GBP  7,350
  money created per pound of capital           27.21 x

Seven thousand three hundred and fifty pounds of equity stands behind two hundred thousand pounds of new money. And the moment the borrower pays the builder, most of that deposit leaves for another bank and must be replaced at a price the lender does not set:

  drained to other banks, 60%              GBP 120,000  funded at 4.90%
  retained deposit,       40%              GBP  80,000  paying     1.20%
  loan yield                                     5.40%
  ---------------------------------------------------------------------
  margin on the drained portion            GBP     600
  margin on the retained portion           GBP   3,360
  net interest, year one                   GBP   3,960   =  1.98%

Fourth, the Balenciaga cut, and it is simply the same entries run backwards.

You were taught that repaying a loan returns money to the bank so it can lend it again. It does not. Repayment debits the deposit and credits the loan, and both disappear. Repaying a loan destroys money. Not metaphorically — the deposit that was created ceases to exist, and no announcement is made.

  deposit stock                            GBP   2,838 bn
  net paydown of 1% in one period                     1 %
  -------------------------------------------------------
  broad money extinguished                 GBP   28.38 bn

Twenty-eight billion pounds of medium of exchange removed from an economy in which nobody burned a note, nobody changed a policy and every individual household did the prudent thing. An economy that all saves at once, in a credit money system, is an economy quietly deleting its own means of payment. Hold that alongside every piece of advice you have ever been given about thrift.

Fifth, the four functions, and which of them conflict.

Jevons set out the classic four in 1875: unit of account, medium of exchange, store of value, and standard of deferred payment. Keynes, opening A Treatise on Money in 1930, ranked them: the money of account is the primary concept, and money itself is whatever discharges a contract written in it.

Three of the four want the same thing — stability and circulation. A unit of account is useful in proportion to how boring it is. A medium of exchange is useful in proportion to how fast it moves. A standard of deferred payment is simply the unit of account extended through time, so it inherits the unit's preference exactly.

The store of value wants the opposite. It rewards holding, and holding is withdrawal. Worse, it rewards appreciation — and an appreciating unit of account makes every debt heavier the longer it is owed:

  unit appreciating in real terms                  2 %/yr
  term of the credit contract                        30 yr
  --------------------------------------------------------
  (1.02) ^ 30                                     1.8114
  real cost of the final payment vs the first     81.1 % more

A perfect store of value is an impossible unit of account for anyone who owes anything. That is not an opinion about deflation; it is the compound interest of the thing, and it is why every long-dated credit system in history has either kept a mild positive drift in its unit or has periodically forgiven debts.

Sixth — the honest negative, and it lands on our own side.

The natural design response to all of the above is a carrying cost on holding: Silvio Gesell's stamp scrip of 1916, Irving Fisher's Stamp Scrip of 1933, the Wörgl experiment of 1932. One per cent a month, stamped on the note.

  demurrage                                        1 %/month
  effective annual carry  1.01^12 - 1        12.6825 %/yr

Now fund a forest. A regenerative capital project — woodland, soil restoration, a district heat network, a repairable product line — needs a million pounds assembled over twenty years before it is built. In a currency with no carry, you set aside £50,000 a year. In a currency with 12.68 per cent annual demurrage, the balance shrinks as you build it:

  (1 - 0.126825) ^ 20                            0.06638
  annuity factor  ((1+i)^20 - 1) / i              7.3615
  annual contribution required             GBP   135,842 /yr
  total contributed over 20 years          GBP 2,716,840
  the same fund in a zero-carry currency   GBP 1,000,000
  --------------------------------------------------------
  penalty factor                                  2.717 x

A currency designed to punish hoarding charges you 2.72 times as much to assemble twenty-year regenerative capital. The saving that funds long-lived regeneration is exactly the saving the design exists to discourage. That is the hardest thing in this volume and it is not softened here.

The threshold is computable. Solving for the demurrage rate at which the twenty-year penalty reaches 2×:

  demurrage at which a 20-year fund costs double   8.19 %/yr
  the same, per month                             0.658 %/month

Below roughly eight per cent a year the penalty is a nuisance a patient investor absorbs. Above it, no private party assembles twenty-year capital in that currency at all — and the economy becomes more dependent on bank credit, not less. A monetary reform intended to reduce the power of banks would, at Gesell's own rate, hand them the entire capital stock. Any design in this volume that carries a demurrage must therefore carry a second instrument beside it, and the rest of the chapter is about what that second instrument is.


DREAM

What becomes ordinary

In the economy that has taken this apart properly, money is not one thing pretending to do four jobs. It is three instruments, each doing one job well, and everybody knows which is which.

The unit of account is an index. It is published daily by a body whose method is open, whose basket is listed, and whose governance is boring in the way a weights-and-measures office is boring. Contracts are written in it — leases, wages, pensions, the price of a twenty-year timber offtake — and they hold their meaning across decades without anyone renegotiating. A twenty-year-old reading a contract her grandmother signed can tell what it was worth, because the number in it still means what it meant.

The means of settlement is fast, final, and cheap, and it carries a small carrying cost so that it circulates rather than pools. Nobody minds, because nobody saves in it, any more than anyone today saves in a train ticket. It is the instrument of the week, and it is designed for the week.

The store of value is an explicit claim on something that regenerates. Not a number in a currency, but a share of a woodland, a stake in a district heating network, a unit in a soil fund, a bond indexed to the same published unit the contracts use. When you save, you can say what your savings are made of, and so can your bank. The question what is my money invested in has an answer a person can read, which turns out to change what people invest in.

And every bank statement shows its own provenance. Beside each deposit is a line saying what created it — a loan advanced, a wage paid, a government payment made — because the information was always in the system and nobody had bothered to show it. It costs nothing to display and it ends, in one generation, the entire confusion this chapter was written to clear up.

Interest rates still exist. Banks still lend, still fail, still get resolved. Nothing here abolishes credit or risk, and nothing here requires a new philosophy of value. It requires that the three jobs stop being performed by one overloaded instrument, and that the accounts say what they mean.


DESIGN

The three layers, built

The mechanism is an unbundling, and it is deliberately conservative: nothing in it is new, and every layer has a working precedent named in Discovery.

Layer one — the unit of account. A published index, computed daily from a declared basket, by a named authority, with the method open to inspection. Chile has run one since 1967. The design decisions are three: what is in the basket, who recomputes it, and how a dispute about the value on a given day is settled. That third question is where most indexed units die, so settle it first: the published value on the day is final and is not restatable, exactly as the UF's is.

Layer two — settlement. Whatever discharges a contract written in layer one. This is where finality, speed and cost live, and where a carrying cost may reasonably sit — but at a rate below the eight per cent threshold computed above, and applied only to balances held beyond a stated window, so that ordinary working balances are untouched. A settlement layer that punishes a payroll account has misidentified hoarding.

Layer three — the store of value. Explicit, dated claims on regenerating stocks, denominated in layer one, settled in layer two. This is where saving goes, and it is the answer to the honest negative: you do not solve the hoarding problem by making saving expensive. You solve it by making saving specific. A pound sitting idle is withdrawn from circulation; a pound in a woodland bond is in circulation the moment it is subscribed, and it is regenerating besides.

Governance, in the order it has to be decided.

  1. Who publishes the index, and who can change the basket. Name them, name the notice period, and publish the change history. Whoever holds this holds real power, which is why it belongs to a body with a statute and a public method rather than to whoever built the software.
  2. Who audits the stocks behind layer three. A regenerating asset that nobody measures is a story. Annual measurement, named method, named verifier, published result.
  3. How the layers convert, and what happens when they cannot. Every multi-layer money in history has been tested at the conversion point. Write the suspension rule before you need it, publish it, and make it dull.
  4. What is legal tender for what. Tax acceptance is the strongest single determinant of whether a unit is used, which is the durable insight of the chartalist tradition from Knapp through Goodhart and Wray, and the reason the Exchequer tally circulated for seven centuries.

Sequence. Layer one first, alone, for at least two years. An index with no currency attached is cheap, uncontroversial, immediately useful for writing long contracts, and it builds the only thing that matters — a track record of a published number that nobody has fiddled. Layer three second, as indexed instruments issued against real stocks. Layer two last, because settlement is the part with the network effects and the regulatory perimeter, and because by then you will have two years of evidence that the index holds.


DESTINY

How it holds when you stop pushing

It holds through three properties, and they are the same three that have carried every durable unit of account in the record.

It is used for something people cannot avoid. Tax, rent, wages, mortgage. A unit that is optional everywhere is ornamental. The tally circulated because the Exchequer took it back; the UF persists because Chilean mortgages are written in it and a mortgage is not a hobby.

Its method is published and its history is immutable. Not the value — the method, and the record of every change to it. The moment a basket can be quietly revised, the unit becomes a policy instrument and stops being a measure.

Somebody's ordinary work depends on it being right. An index maintained as a side project is an index that will be wrong in the third year, on a bank holiday, when nobody is looking.

Now the failure modes, named honestly, because a design with unnamed failure modes is an advertisement.

Basket capture. Whoever sets the basket sets the real value of every long-dated contract in the system. This is a governance problem, not a technical one, and it is the reason layer one belongs to a statutory body with a published method and a notice period — never to the issuer of layer two, whose incentives run the other way.

The savings layer becoming a shadow currency. If claims on the woodland start being used to settle ordinary payments, layer three has silently become layer two and has acquired all of layer two's liquidity risk with none of its buffers. Watch for secondary trading volume rising while redemption stays flat; that is the signal, and it arrives early.

Demurrage arbitrage. If a carrying cost applies at a stated moment, balances will move out the day before and back the day after, which produces the liquidity spikes without the circulation. Accrue continuously rather than stamping periodically, and the arbitrage has nothing to bite on.

And the one that ends most attempts: the index is right and nobody uses it. A unit of account with no obligatory use is a research project. If, after two years, no contract that matters is denominated in it, the honest conclusion is that layer one was never the binding constraint and the effort belongs elsewhere — probably in layer three, where the asset is real and the demand is already there.


DELIGHT

What it feels like

There is a specific pleasure in the moment the two columns are understood, and it is not intellectual. It is the relief of an object that has been strange becoming an object that is merely made of parts.

Money stops being weather. For most of a life it arrives and leaves according to forces that are described on the news in the passive voice, and one absorbs a low background sense that the rules are held by somebody else. Then you see the two entries, and both of them are just writing, and the writing was done by people who could have written something else. Nothing about your balance changes. Everything about your posture towards it does.

And then the second pleasure, which is quieter and lasts longer: you start to see the three jobs everywhere. In the loyalty points that are a unit of account with no store of value. In the favour owed to a neighbour that is a store of value with no settlement. In the childhood currency of swapped cards, which had a unit, a medium and a store, and which every eight-year-old in the playground understood perfectly well.

You already knew this. You have been operating a multi-layer monetary system since you were seven. What the chapter did was give the layers names, so you can build with them on purpose.


OPERATIONALIZE THIS

At the level of finance

The instrument is an indexed regeneration note: a long-dated obligation whose principal is denominated in a published index and whose security is the regenerating stock it finances. It is the smallest piece of the three-layer design that can be issued by a single organisation, this year, under existing law, and it puts layer one and layer three into the world without touching settlement at all.

The structure.

The arithmetic that decides it.

  principal                                GBP 5,000,000
  real coupon on indexed principal                2.25 %
  expected index drift                            3.10 %
  nominal bank facility it replaces               6.75 %
  -----------------------------------------------------
  all-in nominal  (1.0225)(1.031) - 1           5.4197 %
  spread vs the facility                        1.3303 points
  annual saving                            GBP    66,513 /yr
  over the ten-year term, undiscounted     GBP   665,125

The number that decides it, and it belongs on the front page of the paper:

   (1 + real coupon) x (1 + expected index drift) - 1   <   nominal cost of debt

If that holds, the note is cheaper money and should be argued as cheaper money, not as a values proposition. The breakeven is exact: at an index drift above 4.40 per cent the note costs more than the facility, and the honest paper says so and states who bears that risk. It is the issuer. That is the trade — the issuer takes index risk and buys a covenant structure and a longer term.

Balance-sheet treatment. The note is a financial liability at amortised cost, with indexation running through finance costs as it accrues — the same treatment your auditors already apply to any index-linked instrument. On the asset side, capitalise the regeneration expenditure and depreciate over the stock's regenerated life rather than its extracted life. An asset whose measured condition is improving should not be running down a schedule that assumes it is falling. This is a conversation about useful economic life, which your auditors have every year.

The counterparty. First issue internal: treasury to a business unit, documented in a fortnight, no external party, no prospectus. Second issue to a known institution with a long horizon and a reason to care about the stock — a local authority pension fund, a cooperative bank, a credit union, a foundation endowment. Only on the third do you approach a market, and by then you are presenting two completed cycles and an audited covenant rather than a proposal.

The first ninety days.

DayActionArtifact
1–15Choose the stock and its measurement standardThe named method
16–30Baseline the stock; have it verifiedThe signed baseline
31–45Choose or construct the index; publish the basketThe published method
46–60Draft the note: principal, coupon, covenant, termTerm sheet
61–75Run the decision inequality; take one signatureThe one-page credit paper
76–90Issue internally; publish the first index valueA live instrument

APPRECIATIVE QUESTIONS

Twelve, for a room

Discovery — what is already working

  1. Where in this organisation do we already keep a stable unit of account that is not the currency — a point, a credit, a standard hour, a tonne — and what made it trustworthy enough that people write agreements in it?
  2. Think of a time somebody here was paid in something other than money and it worked better than money would have. What was exchanged, and what made it hold?
  3. Which of our obligations to each other have never needed a contract, and what is the record-keeping that makes those work?

Dream — what becomes possible

  1. If everyone here could say what their savings were made of, in one sentence, what would change about where they put them?
  2. Imagine our long contracts written in a unit that held its meaning for twenty years. Which contract would we rewrite first, and what would we then be able to commit to?
  3. If money in this organisation moved twice as fast and pooled half as much, what work would suddenly be affordable?

Design — what we build

  1. What stock do we hold that is measurably regenerating, and who would lend against its condition if we could prove it?
  2. Who would we trust to publish an index we all wrote contracts in, and what would they have to do to earn that?
  3. What is the smallest indexed instrument we could issue to ourselves this quarter, and what would we learn from it that no model would tell us?

Destiny — how it holds

  1. What would make our unit of account still credible in ten years, when everyone who designed it has gone?
  2. Who is obliged to accept it, and for what? If the honest answer is nobody, what is the first obligation we could create?
  3. What is the first sign we would see that the index had started being managed rather than measured, and who would notice it first?

WORKS CITED

McLeay, M., Radia, A. and Thomas, R. (2014). "Money creation in the modern economy." Bank of England Quarterly Bulletin, 2014 Q1, 14–27.

McLeay, M., Radia, A. and Thomas, R. (2014). "Money in the modern economy: an introduction." Bank of England Quarterly Bulletin, 2014 Q1, 4–13.

Mitchell-Innes, A. (1913). "What is Money?" The Banking Law Journal, May, 377–408.

Mitchell-Innes, A. (1914). "The Credit Theory of Money." The Banking Law Journal, 31, 151–168.

Knapp, G. F. (1924). The State Theory of Money. Macmillan (trans. H. M. Lucas and J. Bonar).

Keynes, J. M. (1930). A Treatise on Money, Vol. 1: The Pure Theory of Money. Macmillan.

Jevons, W. S. (1875). Money and the Mechanism of Exchange. Appleton.

Furness, W. H. (1910). The Island of Stone Money: Uap of the Carolines. Lippincott.

Friedman, M. (1991). "The Island of Stone Money." Hoover Institution Working Paper E-91-3. Reprinted in Money Mischief (1992), Harcourt Brace.

Murphy, A. E. (1978). "Money in an Economy Without Banks: The Case of Ireland." The Manchester School, 46(1), 41–50.

Radford, R. A. (1945). "The Economic Organisation of a P.O.W. Camp." Economica, 12(48), 189–201.

Davies, G. (2002). A History of Money: From Ancient Times to the Present Day, 3rd edn. University of Wales Press.

Graeber, D. (2011). Debt: The First 5,000 Years. Melville House.

Ingham, G. (2004). The Nature of Money. Polity.

Goodhart, C. A. E. (1998). "The two concepts of money: implications for the analysis of optimal currency areas." European Journal of Political Economy, 14(3), 407–432.

Wray, L. R. (2012). Modern Money Theory: A Primer on Macroeconomics for Sovereign Monetary Systems. Palgrave Macmillan.

Werner, R. A. (2014). "Can banks individually create money out of nothing? — The theories and the empirical evidence." International Review of Financial Analysis, 36, 1–19.

Werner, R. A. (2016). "A lost century in economics: Three theories of banking and the conclusive evidence." International Review of Financial Analysis, 46, 361–379.

Jakab, Z. and Kumhof, M. (2015). "Banks are not intermediaries of loanable funds — and why this matters." Bank of England Staff Working Paper No. 529.

Shiller, R. J. (1998). "Indexed Units of Account: Theory and Assessment of Historical Experience." NBER Working Paper No. 6356.

Banco Central de Chile. Unidad de Fomento, daily series. Established by Decree 40 of 20 January 1967.

Gesell, S. (1916). The Natural Economic Order. (English edn, Peter Owen, 1958.)

Fisher, I. (1933). Stamp Scrip. Adelphi.

Basel Committee on Banking Supervision (2017). Basel III: Finalising Post-Crisis Reforms. Bank for International Settlements.

Federal Reserve Bank of St. Louis. Velocity of M2 Money Stock (series M2V), FRED database.

Ostrom, E. (1990). Governing the Commons: The Evolution of Institutions for Collective Action. Cambridge University Press.

Note on figures. Every number in this chapter and its apparatus is computed in lib/verify/III_01.py and printed by python3 lib/verify.py III.01, with its inputs, its units and its source. The UK monetary aggregates are approximate 2023 levels and the composition result is checked against the Bank of England's own stated 3 per cent by a second route that shares none of its assumptions; the two agree to 0.19 of a percentage point. Reported circulation multiples for the Wörgl scrip vary by more than an order of magnitude between accounts and none is reproducible from a surviving ledger, so no claim here rests on them.