Haute Lumière
Commerce · II.08 · MMXXVI · daylight
Networks, Trust, and Topology
Volume II — Foundations: The Paradigm and the Science
THE PLATE
THE LETTER
You already know that trust is worth money. Everyone does. What almost nobody has is the number, and without the number trust stays where it has been for a century — in the paragraph of the strategy deck that comes after the numbers and before the photographs.
This chapter gives you the number, and then it gives you the number's honest error bars, because a figure quoted without its interval is not evidence, it is decoration.
Here is what is actually established. Generalised trust — the share of people in a population who say that most people can be trusted — correlates with national income growth at a magnitude large enough to matter and small enough to be argued about. It correlates with lower procurement costs inside firms, with faster credit, with more trade across borders, and with the willingness of strangers to do business at all. Kenneth Arrow said the load-bearing sentence in 1972 and it has aged well: virtually every commercial transaction has within itself an element of trust, and much of the economic backwardness in the world can plausibly be explained by the lack of mutual confidence.
What Arrow did not have, and what the fifty years since have built, is the arithmetic. Trust is infrastructure. Infrastructure has a capital cost, a maintenance cost, a capacity, and a rate of return. This chapter computes all four, and then computes the thing almost no treatment of social capital will touch: what it costs the people a high-trust network keeps out.
The reason to do this properly is not fairness in the abstract. It is that a network which excludes is also paying for its exclusion, in a currency it can read — supplier price, hiring quality, option value — and once that figure is on the same page as the trust dividend, opening the network stops being an ethical argument and becomes a procurement decision.
Two topologies run through everything below. A trust network, where the cost of assurance is paid up front in relationship and is then nearly free per transaction. A contract network, where almost nothing is paid up front and every transaction carries its own freight. Neither is the good one. They have different cost curves, they cross, and the crossing point can be calculated.
— The Editors
DISCOVERY
What is already working
Start where the evidence is strongest, which is inside firms that already treat trust as a procurement instrument rather than a virtue.
Toyota's supplier network, measured. Jeffrey Dyer and Wujin Chu surveyed 344 supplier–automaker relationships across the United States, Japan and Korea and asked a question nobody had costed: what does the least trusted buyer pay to transact, against the most trusted one? The answer was roughly five times. Procurement transaction costs — the searching, the quoting, the contracting, the inspecting, the arguing — scale down by a factor of five as trustworthiness goes up, between firms selling the same components into the same industry in the same decade. That is not a soft finding about culture. It is a line item, and Toyota has been running the experiment in public since the 1960s through its supplier associations, where competing suppliers share process improvements with each other because the network, not the dyad, is the unit that captures the gain.
The Maghribi traders, and the Genoese. In the eleventh century a coalition of Jewish merchants trading across the Mediterranean solved the oldest problem in commerce — how do you send goods a thousand miles with an agent you cannot watch — without any court that could reach the agent. Avner Greif's reconstruction from the Cairo Geniza documents shows a pure trust network doing real work: an agent who cheated any member was never employed by any member again, the information travelled by letter faster than the agent could, and the whole apparatus ran on reputation with no enforcement cost per transaction at all. Genoese merchants, working the same sea in the same century, built the opposite thing — bilateral contracts, notaries, courts, written law — and paid for it on every single voyage. Greif's reading of the two systems is contested, sharply and well, by Jeremy Edwards and Sheilagh Ogilvie, and the dispute is worth reading because it is a dispute about exactly what this chapter measures: how much of the Maghribi advantage was reputation and how much was law nobody catalogued. What is not contested is the outcome. The coalition was superb and it ended. The expensive system is the ancestor of every commercial code now in use.
The diamond trade, still running. Lisa Bernstein documented the New York Diamond Dealers Club in 1992: a market moving enormous value on a spoken phrase — mazal u'bracha — with disputes going to the club's own arbitration, and the sanction for losing being expulsion from the only room where the business happens. Per transaction it is close to the cheapest exchange system ever operated by human beings. It is also, for most of its history, close to the most closed, and the second half of that sentence is where the arithmetic gets interesting.
M-Pesa, and what a settlement layer does to a trust network. Kenya's mobile money system did not create trust between strangers; it made trust unnecessary for one specific act — moving value — by putting a ledger and an agent between them. Tavneet Suri and William Jack's long-run study found access to the agent network lifted an estimated 194,000 households, about 2 percent of Kenyan households, out of extreme poverty, with the largest effects among female-headed households. The mechanism was topological: the network got a hub that everyone could reach, so the cost of reaching a distant counterparty stopped scaling with social distance.
And the weak ties, which are the part everyone quotes and almost nobody checks. Mark Granovetter asked professional and technical workers in Newton, Massachusetts how they had found their jobs. Of those who found work through a personal contact, 16.7 percent saw that contact often — twice a week or more. 55.6 percent saw them occasionally. 27.8 percent saw them rarely. So 83.4 percent of contact-found jobs came through someone the job-finder saw less than twice a week. Fifty years later, Karthik Rajkumar and colleagues ran the causal version at a scale Granovetter could not have imagined: five years of randomised variation in LinkedIn's recommendation algorithm across 20 million people, producing roughly 2 billion new ties and about 600,000 new jobs. Moderately weak ties — around ten mutual connections — did the most work. The strongest ties did the least.
One tie in every 3,333 created led to a job. That is a low rate and it is the correct rate: it is what a mechanism looks like when it is real, large and cheap rather than dramatic.
Five cases, one pattern. In each, somebody found that the expensive part of a transaction was not the goods, and changed the structure that carried the assurance rather than the structure that carried the goods.
THE ARITHMETIC
What works, what does not, and where the line sits
First, the return on trust, stated with its interval.
Stephen Knack and Philip Keefer ran the first serious version in 1997 across 29 countries, using the World Values Survey question on whether most people can be trusted — a measure that runs from about 5 percent agreement in the lowest samples to over 60 percent in the Nordic countries. Their result:
a 10 percentage-point rise in generalised trust
is associated with about 0.8 pp of additional annual growth
in income per head Knack & Keefer (1997), n = 29Paul Zak and Stephen Knack extended it to 41 countries in 2001 and got a consistent slope from a different specification: about 1.0 pp of growth per 15 points of trust — that is 0.67 pp per ten points.
Compound them and the stakes become visible. Take a twenty-point move in generalised trust, which is roughly the distance between a mid-table European country and a Nordic one:
Knack & Keefer slope 20 pts x 0.080 pp/pt = 1.60 pp/yr
over 25 years 1.0160^25 = 1.4871 = +48.7 % income per head
Zak & Knack slope 20 pts x 0.067 pp/pt = 1.33 pp/yr
over 25 years 1.0133^25 = 1.3925 = +39.3 % income per headForty to fifty percent of income per head over a working lifetime, attributed to a single survey question. That is an enormous claim and it is exactly the sort of claim that should be met with suspicion.
So here is the first honest negative, and it is about our own headline number. Sjoerd Beugelsdijk, Henri de Groot and Anton van Schaik put the trust coefficient through extreme bounds analysis in 2004 — the technique that asks whether a result survives every reasonable choice of control variables rather than the one the author chose. In the original 29-country sample the trust effect held up. In the extended sample it did not survive robustly. The honest summary is that the effect is real in the data we have, is smaller than the enthusiastic literature reports, and is not securely identified by cross-country regression alone.
The strongest causal evidence comes from a different route: Yann Algan and Pierre Cahuc used the inherited trust of American descendants of immigrants — trust carried across an ocean and several generations, and therefore not caused by the destination country's current growth — as an instrument, and found a significant causal effect of trust on income per head. Christian Bjørnskov's later work suggests the channel is not investment but governance quality and schooling. Nathan Nunn and Leonard Wantchekon showed the mechanism running the other way in time: individuals whose ancestors were most intensively raided during the slave trade are measurably less trusting today.
Read all of that as one sentence: the direction is established, the mechanism is partly established, and the magnitude is a range rather than a coefficient. Quote it that way and a sceptic will stay in the room.
Second, what the other topology costs.
A contract network does not ask you to know anybody. It charges you instead. John Wallis and Douglass North measured the American transaction sector — everyone whose work is the transfer of ownership rather than the making of anything — and found it rose from roughly 25 percent of GNP in 1870 to something over 45 percent by 1970. Half the economy, buying assurance.
At the tail it is dearer still. The World Bank's enforcing-contracts indicator, before the Doing Business programme was discontinued in 2021 over data irregularities, put the cost of taking a commercial dispute through the courts at about 21.5 percent of the claim in high-income OECD countries, over roughly 589.6 days, and about 41.6 percent of the claim across Sub-Saharan Africa. Those are the enforcement tail, not the routine cost — and the routine cost is what most transactions actually pay.
Third — the model, and the cut that the intuition does not survive.
Price both topologies per member per year. A trust network of n members holds n(n-1)/2 active relationships. Each member maintains n-1 of them. Give each relationship two hours of genuine contact a year, which is one hour twice — a floor, not a norm — and value a working hour at 75 currency units fully loaded. So each tie costs its holder 150 per year.
trust network, cost to one member C_t(n) = 150 x (n - 1)
contract network, cost to one member C_c(T) = 250 x T
T = transactions per member per year
250 = per-transaction contracting cost: template, credit check,
purchase-order match, collections provision. On a 10,000
order that is 2.5% — well under the 21.5% enforcement tail,
because enforcement is the tail and not the mean.Set them equal:
150 (n - 1) = 250 T -> n = 1 + 1.667 T| transactions per member per year | trust network cheaper below |
|---|---|
| 12 | n = 21 |
| 30 | n = 51 |
| 60 | n = 101 |
| 90 | n = 151 |
| 150 | n = 251 |
Now look at what the two sides of that equation depend on. The trust network's cost is a function of membership. The contract network's is a function of transactions. They are not the same variable, and nothing in the sentimental treatment of social capital notices this.
The consequence is the Balenciaga cut of this chapter and it should be read twice: a high-trust community that does not trade with itself is the most expensive network topology in economics. Its cost is fixed by how many people belong; its benefit is earned only when they transact. A dense professional association of 300 people who meet, maintain, remember and refer — and who do eleven pieces of business a year with each other — is carrying 44,850 currency units of maintenance per member against 2,750 of contracting it could simply have paid. Trust is not free and it is not cheap. It is a fixed cost that becomes the bargain of your life at high volume and a luxury good at low volume.
Fourth, the capacity, with the interval the folklore drops.
Robin Dunbar's 1992 regression of primate group size on neocortex ratio predicts a human group size of 147.8 — and the paper states a 95 percent confidence interval of 100.2 to 231.1. The famous number was never a number. It was an interval about 131 people wide, and every architecture built on "150" was built on a point estimate its author did not claim. Patrik Lindenfors, Andreas Wartel and Johan Lind reran it in 2021 with updated primate data and modern phylogenetic methods and got intervals that, across specifications, run from fewer than five people to more than five hundred. The layered series — roughly 5, 15, 50, 150, 500, 1500, each about three times the last, from Zhou, Sornette, Hill and Dunbar — is more robust than the single figure, because a ratio is a weaker claim than a point.
Now put the capacity and the cost model together, because they turn out to be the same fact. Dunbar's own time-budget work puts human social interaction at around 20 percent of waking time; on a sixteen-hour waking day that is 3.2 hours, or 1,168 hours a year, for all relationships of every kind.
n dyads ties per member hours/yr share of 1,168 h cost/member
5 10 4 8.0 0.7 % 600
15 105 14 28.0 2.4 % 2,100
50 1,225 49 98.0 8.4 % 7,350
150 11,175 149 298.0 25.5 % 22,350
500 124,750 499 998.0 85.4 % 74,850
1500 1,124,250 1,499 2,998.0 256.7 % 224,850The layers fall out of a budget. At 150 you are spending a quarter of your entire social life on the network — feasible, and it is what a genuine professional community feels like from inside. At 500 you are spending 85.4 percent of it, which is why the fifth layer is acquaintance rather than relationship. At 1,500 the requirement is 256.7 percent of the hours that exist, which is not a cognitive limit at all. It is arithmetic.
Fifth, the honest negative that costs the most: closure, priced on both sides.
A high-trust closed network produces exclusion, and the exclusion is measurable. Marcel Fafchamps found that in Kenyan and Zimbabwean manufacturing, African-owned firms received systematically less supplier credit than Asian- and European-owned firms with the same observable characteristics — the network was doing its job beautifully and the job included keeping people out. Devah Pager, Bruce Western and Bonikowski's New York audit study found white testers receiving positive responses on about 31 percent of applications, Latino testers 25 percent, and identically credentialled Black testers 15 percent — a ratio of about 2.07 to one, in a labour market where most jobs travel along referral ties. Alejandro Portes named the general form in 1998: exclusion of outsiders, excess claims on members, restriction of individual freedom, downward levelling norms. Brian Uzzi found the dose-response curve — firm failure risk is U-shaped in the proportion of embedded ties, so a network can be over-embedded and the optimum is interior.
Price it. Take a buyer choosing suppliers whose delivered prices are spread uniformly over a band of plus or minus 10 percent around the index. The expected best price from k independent candidates is 0.9 + 0.2/(k+1).
open to 40 qualified suppliers 0.9 + 0.2/41 = 0.904878 of index
closed to 8 network insiders 0.9 + 0.2/ 9 = 0.922222 of index
------------------------------------------------------------------
the price of closure 1.7344 % of purchase spend
on a purchase budget of 20,000,000 = 346,883 per yearAnd the cost to the excluded. Paul Resnick, Richard Zeckhauser, John Swanson and Kate Lockwood ran the cleanest available experiment: identical goods sold by an established reputation against the same goods sold under a fresh identity. The established identity earned 8.1 percent more. So a competent newcomer with 500,000 of annual revenue pays 40,500 a year for the crime of being new.
cost of closure to the closed network 1.7344 % of spend
cost of closure to the excluded firm 8.1000 % of revenue
ratio 4.67 xBoth sides pay, and the outsider pays about four and two-thirds times as much per unit of trade. That is the honest negative of this chapter, and it is not a footnote. It is the reason the diamond trade's centre of gravity moved: a closed network that will not price its own entry eventually meets another network that will, and India now cuts and polishes something close to 90 percent of the world's diamonds by piece.
(How shocks and failures propagate along these edges once they exist is Chapter II.05's arithmetic, not this one's. This chapter prices the edge; that one prices what runs down it.)
DREAM
What becomes ordinary
In the economy that has taken this seriously, a firm knows the topology of its own counterparty base the way it knows its ageing schedule.
Procurement carries two columns beside every supplier: what this relationship costs to maintain, and what it saves per transaction. Nobody argues about whether relationships matter, because the argument was settled by putting both figures in the same table and discovering that about a dozen suppliers repay their maintenance many times over and the rest are better served by a good template and prompt payment. The firm is not more trusting. It is trusting in the right places, on purpose, and it can say why.
Every closed network publishes its ladder. Not its membership — its ladder: the route in, the performance that earns each rung, the number of places opening each year. This is now ordinary, because the alternative was discovered to be expensive. A trade association that cannot say how a newcomer joins is understood to be carrying an unpriced liability, in the same register as an unfunded pension.
Hiring managers have a weak-tie budget. A fixed proportion of every intake arrives from outside the referral graph, not as a diversity gesture but as a search-quality instrument, because the arithmetic of best-of-k is taught in the first week and everybody can do it on the back of a page.
Credit is extended on ledgered performance rather than on acquaintance. A supplier who has delivered ninety consecutive orders on specification has an asset, and that asset is portable — it travels with the firm to a new buyer rather than evaporating at the network's edge. The 8.1 percent newcomer tax still exists, because reputation is genuinely informative, but it decays on a published schedule instead of a private one.
And the thing that is most changed is the smallest. When two people who have never met do business, they are able to find out enough about each other, fast and cheaply, that neither has to decide between the expensive contract and the uninsured handshake. The middle of the cost curve, which for most of economic history did not exist, is where most commerce now sits.
DESIGN
The structure that gets there
The design problem is not build trust. It is put each transaction on the cheaper of the two curves, and build the ramp that lets counterparties move between them.
One — measure both curves for your own book. For each counterparty: annual transaction count, average order value, current cost of contracting per order, and honest hours of relationship maintenance per year. That gives you T and n for your own firm. Most firms find, on first measurement, that they are maintaining relational overhead on suppliers they transact with four times a year and treating high-volume partners as strangers. Correcting that mismatch is free and usually pays for the rest of the programme.
Two — set the trust core by volume, not by sentiment. The core is the set of counterparties where 150 (n-1) < 250 T holds: high volume, high complexity, long-lived. Everyone else goes on the contract curve with a good template and prompt payment, which is not a demotion — it is the cheaper service for them too.
Three — build the ramp, and publish it. Three rungs works: a standard tier on templates; a preferred tier with faster payment and lighter inspection, earned on a stated number of clean deliveries; a core tier with shared planning and open books. The rungs must be earned on measured performance, not nomination, or you have rebuilt the closed network with a staircase painted on the wall. Reserve a fixed number of places per year for counterparties nobody in the firm has met. That reservation is the whole ethical content of the design and it pays for itself at 1.7344 percent of purchase spend.
Four — build the bridges deliberately. Granovetter's finding is a design instruction: reach lives in ties that do not know each other. A cluster of fifteen people who all know each other returns nothing new for each additional tie inside it; one bridge to a different cluster of fifteen returns fourteen newly reachable people for the cost of one relationship. Fourteen against zero. Budget bridges the way you budget research: a named proportion of relational time spent outside the cluster, reviewed annually, defended when it is cut.
Five — make reputation portable. The asset a counterparty builds inside your network should be legible outside it: a delivery record they can show another buyer, a certificate that survives your relationship ending. This looks like generosity and is the opposite. A network whose reputational asset is non-portable has to be joined, which raises its entry price, which shrinks k, which costs you the 1.7344 percent. Portability is how you keep the selection pool wide while keeping the relationships deep.
Six — govern the failure mode directly. Uzzi's inverted U says the risk is over-embeddedness. Cap it: no core counterparty above a stated share of category spend, a standing second source for every critical input, and a review that asks not are these good relationships but how many of our alternatives have we let lapse.
DESTINY
How it holds when nobody is pushing
Three things make this self-sustaining, and they are the three that survive the person who built it leaving.
The ledger, not the relationship. A performance record, kept monthly, is the only part of a trust network that does not decay when people move roles. Roberts and Dunbar's work on relationship decay is unambiguous — an unmaintained tie falls in emotional closeness on a measurable schedule — and a firm that carries trust only in individuals' heads loses it on every departure. Carry it in a record that a successor can read on their first day.
The ramp has a number attached. "We are open to new suppliers" dies quietly. "Two core places open each January, earned on twelve clean deliveries" survives, because it is falsifiable and somebody will ask in January.
Somebody's compensation moves with supplier quality, not supplier comfort. An unpaid metric is a hobby.
Now the honest part, because this fails in four recognisable ways and each has a signature. It fails when the trust core is chosen by seniority rather than by transaction volume, and the tell is that the core list has not changed in three years. It fails when the ramp exists on paper and no one has walked up it, and the tell is that you cannot name the last counterparty who did. It fails when maintenance hours are counted as relationship-building but spent on dispute management, which is the same hours doing the opposite job — and the tell is that hours rise while transaction cost does not fall. And it fails, most often, when a network that was built on genuine mutual knowledge starts admitting people on the strength of who introduced them. That is the exact moment a trust network becomes a closed network, and the arithmetic changes sign.
DELIGHT
What it feels like
The pleasure here is specific, and it is the pleasure of the return call.
You send a message to somebody you have not spoken to in two years — not a strong tie, not really a friend, a person whose work you once liked — and they answer within the hour with something useful. That is a weak tie doing exactly what Granovetter said it does, and it feels, from inside, like luck. It is not luck. It is the return on two hours a year you spent without expecting anything, several years ago, and the fact that it arrives as delight rather than as interest income is the most agreeable feature of this entire asset class.
Then a second pleasure, quieter. You place an order with a supplier you have worked with for nine years and the order is four lines long, because everything else is understood. No specification appendix. No inspection clause. Four lines and a date. The absence of paperwork is not laziness; it is capitalised relationship, and you can feel exactly how much of it is standing behind the brevity.
A well-maintained network feels like competence and it is actually infrastructure. That is the whole of the joy: things are easy, and they are easy for reasons you could write down.
OPERATIONALIZE THIS
At the level of finance
The instrument: an open trusted-counterparty facility, with a published entry ladder and a working-capital leg.
This is a supplier-terms instrument, not a philosophy. It converts measured counterparty performance into extended payment terms and reduced inspection — both of which are real money — and prices the whole thing against the firm's own cost of capital.
The structure. Three tiers. Standard: template terms, standard payment, full goods-inward inspection. Preferred: fifteen additional days of payment terms, reduced inspection, earned on twelve consecutive conforming deliveries. Core: shared forecasting, open-book costing, joint improvement targets, entered by invitation from the Preferred tier on measured performance. Two Core places are reserved each year for counterparties with no prior relationship to the firm — the ramp is contractual, published, and auditable.
The mechanics, worked on a real book.
annual purchase spend 20,000,000
suppliers 40
current procurement transaction cost, 2.5% 500,000
move the top 12 suppliers, 60% of spend = 12,000,000, to relational
terms; transaction cost on that spend falls 2.5% -> 0.8%
saving 12,000,000 x 1.7% 204,000
costs of the facility
relationship maintenance 12 x 40 h x 75 36,000
15 days terms on 12,000,000 = 493,151 at 9% 44,384
expected credit loss 0.5% x 493,151 2,466
-----------------------------------------------------------
total cost 82,849
NET ANNUAL BENEFIT 121,151
return on the incremental working capital 24.6 %The balance-sheet treatment. The working-capital leg is exactly that: an increase in trade payables' duration financed at the firm's cost of capital, and it belongs in the cash-conversion-cycle discussion where treasury already lives. The transaction-cost saving lands in operating expense, not in a sustainability appendix. Where the facility funds joint improvement work with a Core supplier that creates a tooling or process asset, capitalise on the usual test and disclose the counterparty concentration, because concentration is the risk this instrument creates and the auditors will ask.
The counterparty. Internal first — procurement and treasury, documented in a fortnight, no external party. The external version of the same structure is supply-chain finance, and you will get a materially better rate on it once you can show a bank two years of ledgered supplier performance, because that ledger is the credit file.
The first ninety days.
| Day | Action | Artifact |
|---|---|---|
| 1–15 | Count T and cost per order for every counterparty | The two-curve table |
| 16–30 | Compute the crossover; name the trust core by volume | Core list, with arithmetic |
| 31–45 | Draft the three tiers and the reserved places | Tier schedule |
| 46–60 | Agree terms cost with treasury; sign the baseline | Signed baseline |
| 61–75 | Publish the ladder to all counterparties | The published ramp |
| 76–90 | First measurement; open the reserved places | Quarterly ledger |
The number that decides it. One inequality, on the front page:
transaction-cost saving - relationship maintenance
---------------------------------------------------------- > WACC
incremental working capital + verification costOn the book above: (204,000 - 36,000) / 493,151 = 34.1% against a 9 percent WACC, before the credit-loss provision and 24.6 percent after it. If that inequality holds, this is not a supplier-relations initiative. It is the cheapest working capital on the firm's balance sheet, and the reserved places are worth a further 346,883 a year in supplier-selection option value, which means the open door is the profitable half of the design rather than the charitable one.
APPRECIATIVE QUESTIONS
Twelve, for a room
Discovery — what is already working
- Name a counterparty relationship in this business that saves us real money every month. Who built it, what did they do, and has anyone ever thanked them for it in a form that appears in the accounts?
- Think of a time something difficult got done here on a phone call rather than a contract. What made that call possible, and how long had it been in the making?
- Which of us got our job, or our best supplier, or our best idea through someone we barely knew? What does that tell us about where to spend the next hour?
Dream — what becomes possible
- If we knew the maintenance cost and the transaction saving for every counterparty we have, what would we stop doing by Friday?
- Imagine a newcomer with no connection to anyone here becoming one of our best suppliers within two years. What would have had to be true in year one?
- If reputation earned with us travelled with a supplier when they left, what would that do to who wants to work with us?
Design — what we build
- What is the ladder into this network, stated so precisely that a stranger could follow it without asking us?
- Where are we carrying relationship cost on a counterparty we transact with four times a year — and where are we treating a high-volume partner as a stranger?
- What proportion of our relational time is spent outside our own cluster, and who would defend that budget if it were cut?
Destiny — how it holds
- If the three people who hold our key relationships left in the same month, what would a successor be able to read on their first morning?
- What is the first sign that our network has started admitting people on introduction rather than on performance, and who would see it first?
- How many of our alternatives have we let lapse, and what would it take to keep two live in every critical category?
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Note on figures. Growth slopes, compounding, the two cost curves, the dyad and time-budget table, the order-statistic price of closure and the facility arithmetic are all computed in lib/verify/II_08.py and reproducible there. Where a published effect size is contested, the contest is named in the text rather than resolved in our favour.