The thick-market effect has a formula.

Imagine twenty cities, and you want a direct flight between every pair of them. That is 190 routes. Most would fly half-empty, tickets would be expensive, and some routes would not survive at all.

Now build one hub. Every city flies to the hub and connects from there. Twenty cities need only nineteen routes. Each route is full, flights are frequent, and tickets are cheaper — even though most travelers now take two flights instead of one.

That is how much of the world's money already works. When a Brazilian company pays a supplier in Korea, the money usually does not go straight from reais to won. It goes reais to dollars, then dollars to won. The dollar is the hub. Economists call it a vehicle currency.

This is not a crypto idea

Economists have studied vehicle currencies for more than four decades. Paul Krugman published Vehicle Currencies and the Structure of International Exchange in 1980, twenty-eight years before his Nobel Prize. Hélène Rey extended the idea in 2001 in the Review of Economic Studies. In 2013, Michael Devereux and Shouyong Shi built a full dynamic general equilibrium model of a vehicle currency in the International Economic Review.

Their findings, in plain English:

• A hub collapses the number of markets that need to exist. Twenty currencies need 190 direct pairs or 19 hub pairs. The more currencies in the system, the bigger the saving. Devereux and Shi showed that the efficiency gain from a vehicle currency depends directly on the total number of currencies in existence.
• The saving feeds on itself. The more people trade through a hub, the cheaper the hub becomes to trade, which pulls in more trading. Rey called this a thick-market externality, and used it to explain how the dollar displaced the pound after the Second World War.

And one inference that follows from their models but is our own reading, not a finding the papers state: a thin hub makes things worse. A hub only pays when it is busy enough that two trades through it cost less than one direct trade. If the hub market is thinner than the markets it replaces, the detour costs more than the direct route it was supposed to save. That is the point most people miss, and it is the one this piece is about.

What the economists left out

All three papers agree that trading gets cheaper as a market gets busier. None of them says how much cheaper. The thick-market externality is a direction, not a number.

That is where this series comes in. Six parts and eighteen field notes have rested on one formula: the square-root law of market impact. It is part of a broader market-impact literature that runs from Barra's models in the 1990s through Almgren and Chriss's work on optimal execution to the large empirical studies of Bouchaud's group and Tóth and colleagues. The evidence for it is strongest in equities and futures, thinner for bonds and foreign exchange, and, as the series' source list records, independently confirmed on institutional crypto orders. In plain terms, the price move caused by a large trade depends on the trade's size relative to how much the market trades each day. Make the market four times busier, and the same trade moves the price about half as much.

The square-root law gives us a way to put numbers on the thick-market effect the economists described. The two ideas were developed separately, by different researchers in different fields. Connecting them is our own step, not something the original papers claimed. But once you connect them, you can do something the economics alone could not: estimate how deep a hub has to be before routing through it makes sense.

Putting the two together

The economists say a hub wins once it is busy enough that two trades through it cost less than one direct trade. The square-root law lets us estimate how busy "busy enough" is.

Part I sized the institutional case as a single $2 billion settlement, executed with no more than 10 basis points of slippage — one tenth of one percent — at an assumed daily volatility of 3%. Run that through the formula and XRP's market would need to trade roughly $1.8 trillion a day. At the series' central turnover assumption (1% of market value traded per day, across a tradeable float of roughly 61 billion XRP), that works out to about $2,950 per XRP. Stress every skeptic-friendly input at once — maximum netting of peak tickets and the high-efficiency 1.5% turnover case — and Part I's floor for the same scenario is roughly $1,300.

We call this a model-implied liquidity threshold, not a price floor. Nothing stops XRP from settling a $2 billion payment at $10. At $10, though, the market is not deep enough to absorb it without a price move far outside what an institution would accept.

Now the comparison the number needs. The Bank for International Settlements measured global foreign-exchange turnover at $9.6 trillion a day in April 2025, with spot trading roughly a third of that, near $3 trillion, and the dollar on one side of 89% of all trades. The institutional scenario therefore asks XRP's market to trade on the order of 60% of all global FX spot, every day, before the hub clears a single $2 billion ticket at 10 basis points. At 1% turnover, that volume implies a tradeable float worth about $180 trillion, larger than every listed equity market on earth combined, which stood between roughly $150 and $160 trillion at the end of 2025. And XRP's reported 24-hour spot volume on 30 September 2026 was between about $2 billion and $4 billion depending on the tracker (CoinDesk showed $1.99 billion; CoinGecko about $3.4 billion): somewhere between 450 and 900 times short of the scenario. A reader who is not given that comparison will treat $2,950 as a destination. A reader who is given it will read it the way the model intends: as the model saying the bar is extraordinary.

One input deserves its own sentence, because it swings the answer by orders of magnitude. The formula divides required volume by turnover, so a hub that trades $1.8 trillion a day against 1% turnover needs a float worth $180 trillion, while the same hub at 10% turnover needs a tenth of that. A bridge asset is defined by throughput, which seems to argue for high turnover and a lower price. Part I argues the opposite happens as institutions arrive: inventory buffers, treasury allocations, and pre-positioned corridors pull turnover down, and today's 2% to 2.5% ratio is driven by speculation rather than settlement. Observatory No. 1 models that inversion in detail. Readers who reject it should divide every dollar figure in this piece accordingly. The crossover logic survives; the price attached to it does not.

Below the threshold, XRP cannot win on liquidity cost alone; speed, counterparty exposure, capital treatment, or the absence of a direct pair might still justify it, but the economics of the hub do not. Above it, each new user makes XRP cheaper for everyone else, and the thick-market feedback loop the economists described can begin working in XRP's favor.

The two-trade cost is how a hub gets chosen

Back to the airport. A connecting flight means two takeoffs and two landings, so there are two chances for delay. Bridging money works the same way. Routing reais to won through XRP means two trades: reais into XRP, then XRP into won. Each trade nudges the price, so each one has a cost.

Here is the logic in one illustrative example. Say trading Currency A directly into Currency B costs 4 cents per $100. Going through XRP means two trades, and while XRP's market is thin, each leg also costs 4 cents. That is 8 cents in total, so nobody takes the detour.

As XRP's market gets busier, each leg gets cheaper: 3 cents, then 2, then 1.5. At some point the two legs together cost less than the direct route. From then on, routing through XRP wins on price alone.

Every trade that switches routes adds volume to XRP's market. That makes XRP cheaper for the next pair of currencies, which may then switch too. That is the feedback loop the economists described, and the square-root law tells us roughly where the crossover sits.

How the two-trade cost changes the math

We want to be upfront about one assumption, because it moves the number a long way.

Part I's $2,950 threshold applies the 10 basis point tolerance to each trade on its own. Part II makes the convention explicit: the slippage tolerance governs what the pool has to absorb per transaction. If an institution instead wants the whole journey — both legs combined — to stay under 10 basis points, each leg only gets half the allowance.

Because of how the square-root law works, cutting the allowance in half does not double the required market size. It quadruples it. The required daily volume moves from roughly $1.8 trillion to roughly $7.2 trillion, and the implied price moves from about $2,950 to about $11,800 under the same turnover and float assumptions. Part I's stress-tested floor would move from roughly $1,300 to roughly $5,200.

We are not claiming the higher figure. The answer depends on how institutions define their tolerance, and they have not said. Under this framework, the liquidity threshold sits somewhere in that range, depending on a convention that has not been made public.

Three things soften the upper bound without removing it. First, the two legs of a bridge trade happen in two different markets — the reais-to-XRP market and the XRP-to-won market — and the series uses XRP's aggregate daily volume as a proxy for both. Second, a liquidity provider who handles both legs can net them, so the market only has to absorb the imbalance. Third, and most important: the square-root law is an empirical regularity for large orders worked through continuous public order books. It is not a theorem about settlement bridges. Inventory-based market makers, OTC netting, and prefunded corridors do not pay the full public-book impact on every leg. In this piece the law is a proxy for how deep the market has to be, not a measurement of how a bridge desk would actually quote. None of this changes the direction of the adjustment. An end-to-end standard raises the threshold. It does not lower it.

Why a neutral hub matters

Devereux and Shi found two things about who wins when a vehicle currency emerges. The welfare gains are real, but they tilt heavily toward the residents of the country that issues the hub currency. And the hub's survival places natural limits on that country's monetary policy: a hub that inflates too freely stops being a hub. Today the dollar is the hub, so the United States collects the advantage and lives with the constraint.

XRP has no issuing country. No nation's citizens automatically collect the hub advantage, and no central bank can expand XRP's supply through monetary policy: the maximum supply was fixed at 100 billion when the ledger launched, and transaction fees are destroyed rather than paid to anyone. That does not mean nobody profits from a bridge role. Market makers, liquidity providers, exchanges, and holders all could. It means the sovereign advantage the economists identified does not apply.

"A hub no one controls" needs one caveat, because critics will raise it. Ripple still holds about 32 billion XRP in time-locked escrow, which releases up to 1 billion a month with most of it re-locked, plus several billion more in operational wallets: together more than a third of total supply. That is not monetary policy; the ledger cannot create new XRP. But it is a concentration no vehicle currency has had, and whether institutions and central banks value a hub with no sovereign — or distrust a hub with one dominant holder — is still an open question.

The incumbent is already on-chain

The thick-market logic cuts both ways, and the piece would be dishonest if it only pointed it at XRP's advantage. The incumbent on-chain bridge is not a thin market waiting to be displaced. It is the dollar, in stablecoin form, and by the same externality Rey described, incumbency is the largest advantage a hub can have. Dollar stablecoins already carry most of the volume that moves between tokens and across chains, and every trade through them deepens them further.

Rey's own historical example is sobering here. The dollar displaced sterling as the vehicle currency only after a hegemonic shift: two world wars, the collapse of Britain's creditor position, and decades of trade re-routing through American markets. Thick-market externalities explain why the shift, once started, was self-reinforcing. They do not explain why it started. For XRP to displace a dollar stablecoin as the on-chain hub, something has to overcome the incumbent's head start: a cost advantage large enough to beat two legs against one, a regulatory or neutrality reason that stablecoins cannot satisfy, or corridors where no deep dollar pair exists. The watch table below treats stablecoin depth as a first-order test for that reason, not a footnote.

What this piece adds to the series

Until now, the series has rested on market mechanics: how big trades move prices, how settlement timing works, how much money moves through the system. This piece puts an economic foundation underneath it.

The economics tells us why liquidity tends to gather around a hub. The open question is which asset, or small group of assets, captures that liquidity, and whether XRP becomes one of them.

Economists modeled why vehicle currencies emerge. Market researchers measured how liquidity changes trading costs. XRP gives us a real bridge asset to test both ideas against, on a public ledger, every quarter.

What would prove this wrong

The XRP Ledger has had a built-in feature called auto-bridging since 2014. When an offer on the ledger's decentralized exchange would swap one issued token for another, the ledger automatically checks whether routing through XRP — token to XRP, then XRP to token — gives a better rate than the direct order book, and fills the offer with whichever combination is best. Cross-currency payments work differently: they do not use auto-bridging by default, but the ledger's pathfinding can produce the same XRP-intermediated route when it is the cheapest path, and since the 2024 AMM amendment those paths can draw on both order-book offers and automated market maker pools. Either way, the behavior the economists described is not hypothetical here. It is written into the ledger's code.

That makes the test unusually clean, with one limit stated up front. The share of token-to-token trades that actually route through XRP is measurable on-ledger. But token-to-token volume on the ledger's own exchange is a small fraction of XRP's global trading, most of which happens on centralized venues. So the auto-bridged share tests whether the hub mechanism works where it is hard-coded, not whether global settlement flow has arrived. Within that limit: if XRP is becoming a hub, that share should rise over time. If it stays flat while volume grows, the hub is forming somewhere else.

The question, then, is not whether markets prefer hubs. They already do. Nor is it whether XRP can technically sit between two assets. It already can. The unanswered question is whether XRP can become liquid enough that routing through it is cheaper than routing around it, against an incumbent that is already deep. If that crossover happens, liquidity begins attracting liquidity, and the economics changes from adoption chasing depth to depth attracting adoption. If it never happens, the tests above will say so.

XRP is not being valued. It is being sized.