The exact arithmetic behind the U index, the chain of mechanisms that turns a number into a redemption right, and a data answer to the obvious question: wouldn't gold, bitcoin, real estate or food make it even more stable?
Companion to the U design spec · every figure below recomputed from public data (FRED, OECD, BIS, IMF, S&P, Yahoo)
Research archive. This document records the original multi-currency research design. The shipped Base is the Ethereum-native composition — USDC 50 / gold 25 / S&P tokens 15 / ETH 10, every leg bought on-chain at mint — described on the home page and in the mechanism.
"Purchasing power" is only a guaranteeable object if you define the basket, the geography, and the tolerance. U's promise is narrow enough to be honest and broad enough to matter:
Any holder can always redeem 1 U for collateral worth the current cost of the reference world consumption basket — the consumption-weighted composite of the US, euro-area, Japanese, UK and Swiss CPI baskets — within a disclosed tracking band (target: ±50 bp), enforced by open mint/redeem arbitrage against a collateral portfolio whose own value is contractually indexed to the same basket.
Three deliberate boundaries. (1) It is the reference basket, not your personal one — a Berlin techno promoter and a Tokyo pensioner consume different baskets; U tracks the weighted world average. (2) The five blocs cover roughly 55–60% of world household consumption at market rates — the part with trustworthy statistics and investable inflation-linked bonds; §M5 covers expansion. (3) The band is a tolerance, not an escape hatch: it is the sum of measurable error sources, each budgeted below.
Five national/supranational CPIs — BLS CPI-U, Eurostat HICP, Japan's e-Stat CPI, ONS CPI, Swiss FSO CPI — each read onchain as the median of N independent oracle operators reporting the same public release. No private data vendor can move the anchor.
Each region's basket cost is expressed in dollars: Cᵢ(t) = CPIᵢ(t) · Sᵢ(t), with FX from median-of-feeds daily fixes. The dollar is only the display unit — the math is symmetric in any numeraire, which is the point.
W(t) = Π Cᵢ(t)^vᵢ with consumption weights v = 40/30/15/10/5. Geometric (log-additive) mean, so no rebalancing drift, no arithmetic-mean bias when currencies diverge, and each region contributes exactly its weight in log space.
CPIs arrive monthly with a lag, so the published target follows the TIPS convention: a reference index with a ~2–3 month indexation lag, interpolated day-weighted between prints (USDi already runs this in production). The target path for the next ~30 days is therefore known in advance — the peg never ambushes a market maker. Prints are used first-print-final; revisions never restate history.
A source that hasn't printed (Swiss CPI runs ~6 months behind on OECD's feed) is extrapolated at its own trailing-12-month rate, and the dashboard's audit table shows every source's last official print. Statistical honesty is a UI feature.
Every ratio is relative to January 1999 (= 1.0000). Multiply each region's basket-cost ratio raised to its weight; the product is the world price level.
| Region | Weight vᵢ | CPI ratio | FX ratio (USD) | Cᵢ = CPI·FX | Cᵢ^vᵢ |
|---|---|---|---|---|---|
| United States | 0.40 | 1.9795 | 1.0000 | 1.9795 | 1.3141 |
| Euro area | 0.30 | 1.7631 | 1.0103 | 1.7813 | 1.1891 |
| Japan | 0.15 | 1.1519 | 0.7266 | 0.8370 | 0.9737 |
| United Kingdom | 0.10 | 1.9485 | 0.8115 | 1.5811 | 1.0469 |
| Switzerland | 0.05 | 1.1735 | 1.7387 | 2.0403 | 1.0363 |
| W(2025-12) = product of the last column | 1.6506 | ||||
Reading it: the world's consumption basket cost 65.06% more dollars in December 2025 than in January 1999 — so a dollar kept 1/1.6506 ≈ 61% of its purchasing power. Rebasing to the token epoch (2026-01 = $1.0000) gives today's published price, $1.0123 as of August 2026 — the number the live index shows. The US prices-doubled story (CPI ratio 1.98) and the yen's collapse story (FX ratio 0.73 despite only 15% domestic inflation) are both visible in one table — that is why both CPI and FX legs are required.
Arithmetic baskets overweight whichever currency just appreciated; geometric contributions stay exactly vᵢ regardless of level, and monthly log-returns add cleanly — the whole backtest math stays linear.
The min-variance optimizer, run on 27 years of data, lands within ~2pp of the consumption weights on every window tested. The structure, not the fitting, carries the stability — so weights can be public, simple, and revised at most ±2pp/year.
A region enters the index only if its statistics are independent and its government issues investable inflation-linked debt — the index must remain hedgeable (§M2). That is what excludes, for now, blocs with capital controls or thin linker markets.
Real-time private feeds (Truflation-class) were hacked in 2024 and moved 1.56pp by one internal model change in 2026. They may nowcast between prints, capped to basis points; the anchor is always the slow, boring, canonical release.
An index guarantees nothing by itself. The guarantee is a chain of four links, each independently attackable, each with a disclosed failure mode — and the purchasing-power promise is exactly as strong as the weakest link.
The redemption value of 1 U is W(t), published daily with a 30-day forward path. Error source: oracle/nowcast noise between official prints. Budget: ±10–20 bp, converging to zero at each release.
The reserve holds what the liability promises: a ladder of inflation-linked sovereigns in index weights — TIPS (40%), euro linkers (30%), JGBi (15%), UK linkers (10%), CHF bills + gold insurance sleeve (5%) — plus a ~5% T-bill liquidity overlay. Their principal is contractually indexed to the same CPIs that define W(t): asset–liability matching, not yield-chasing. Error source: ladder tracking (indexation lags, hedge slippage). Budget: ±30–50 bp/yr, absorbed by the buffer before holders ever see it.
Hard, always-on primary market: mint by depositing W(t) of eligible collateral, redeem 1 U for W(t) of collateral, in kind or via the liquidity sleeve, with a small conversion fee (hard-capped, never gated; terms published separately). This is the link every failed flatcoin skipped — SPOT "targets" its index and trades 84% away from it.
With a known forward path and hard redemption, any deviation beyond fee+gas is riskless arbitrage. The peg isn't defended; it is farmed by whoever shows up. Secondary venues (AMM ranges recentred along the drip) are conveniences, not load-bearing.
| Layer | Funded by | Absorbs | If exhausted |
|---|---|---|---|
| 1 · Real-yield income | Ladder real yield (~1–2%/yr above the index) | Routine tracking error, operations | flows to layer 2 |
| 2 · Equity buffer | Retained surplus, target 2–4% of supply | ILB liquidity gaps, negative-real-rate stretches | layer 3 |
| 3 · Issuer capital | Own funds (MiCA-style requirement) | Tail events | layer 4 |
| 4 · Disclosed U rate discount | — | Whatever remains | Published haircut, pro-rata, never a hidden gate |
A guarantee is not the absence of failure modes. It is the enumeration of them, with a named payer for each.
The intuition is respectable: real assets for a real-value coin. So we ran the same purchasing-power machinery over gold (2001→), bitcoin (2015→), US housing (Case-Shiller), and the IMF global food-price index — everything measured in the world basket W(t), exactly like the currencies. The intuition does not survive contact with the data.
| Asset | PP volatility /yr 2001–2025 | PP volatility /yr 2015–2025 | Real drift /yr | Max real drawdown |
|---|---|---|---|---|
| US dollar (reference) | 3.82% | 3.09% | −2.2% | −45% |
| US housing (Case-Shiller) | 4.64%* | 3.87%* | +2.2% | −40% |
| Food commodities (IMF index) | 9.63% | 9.48% | +0.9% | −35% |
| Gold | 15.48% | 12.81% | +9.4% | −34% |
| Bitcoin | — | 67.08% | +69.6% | −76% |
| Min-variance fiat basket | 0.87% | 0.85% | −1.9%† | — |
* Appraisal-smoothed and ~2-months lagged — true transactable volatility is meaningfully higher. † The fiat basket's drift is world inflation itself, removed by U's indexation, not by asset selection.
The practical question isn't "are they volatile" but "does a small sleeve help." So: take the min-variance fiat basket, carve out a sleeve, measure the portfolio's purchasing-power volatility again.
| Portfolio | PP volatility /yr | vs fiat-only |
|---|---|---|
| Fiat basket only (2001–2025) | 0.872% | — |
| + 5% housing | 0.874% | +0.2% |
| + 5% food | 0.929% | +7% |
| + 5% gold | 1.181% | +35% |
| + 10% gold | 1.794% | +106% |
| + 2% bitcoin (2015–2025 vs 0.851%) | 1.639% | +93% |
| + 5% bitcoin (2015–2025) | 3.517% | +313% |
And when the long-only min-variance optimizer is simply offered the new assets, it answers directly: gold gets 0.0% weight (the optimum is unchanged to four decimals), bitcoin gets 0.0%, food gets 1.4%, and housing gets 6.7% — the last two shaving the volatility from 0.872% to 0.841%, a three-basis-point improvement that sits inside estimation noise and leans entirely on appraisal-smoothed housing data. Gold is genuinely uncorrelated with every fiat's purchasing power (ρ ≈ 0.03–0.08) — but diversification cannot rescue an asset whose own volatility is 18× the portfolio's.
15% purchasing-power volatility and a +9.4%/yr real drift: gold is a bent ruler that also happens to be getting longer. Every sleeve size tested makes U less stable. But its zero correlation with all five fiats is exactly the profile of tail insurance against the one scenario the index cannot see — coordinated debasement where all five CPIs are politically suppressed at once. The design keeps the 5% hard-buffer sleeve and prices it honestly: roughly +30 bp of volatility as a knowable insurance premium, governance-capped at 10%.
67% volatility and a −76% real drawdown during its best decade ever. A 2% sleeve doubles the coin's instability; 5% quadruples it. The honest role for crypto is not inside the reserve but beside it: an optional, overcollateralized ETH/BTC minting vault (RAI-style, 150%+ collateral, its own liquidation engine) for users who need censorship-resistant entry — a separate product lane whose risk never touches the main reserve.
The optimizer's small housing allocation is a statistical mirage: Case-Shiller is appraisal-smoothed, two months lagged, and not a tradable instrument — real transaction volatility is far higher, and 2008 (−40% real, on the smoothed series) shows the tail. Tokenized RE in 2026 is still fractionalized single buildings with venue-level liquidity — nowhere near redemption-grade. And here is the deeper point: housing is already in the index — shelter is ~33% of US CPI, ~a fifth of the others — so the liability side already breathes with rents, and the ILB ladder already hedges it. Revisit if a deep, investable, transaction-based tokenized RE index emerges.
Right instinct, wrong slot. Food is already inside W(t) with real weight — roughly 13% of US CPI, ~20% of the euro area's, ~26% of Japan's — so U holders are food-hedged through the index by construction; holding futures on top would add 9.6% volatility, negative roll yield, and no real coupon. Where raw food prices earn a place is the oracle layer: the IMF/FAO food index is fast, global, and hard to fake — the design adds it as a manipulation tripwire, flagging any national CPI print that diverges from observed food inflation beyond a disclosed band. Food doesn't back the guarantee; it audits it.
Every asset that feels like an inflation hedge is a growth asset with good marketing. The only instrument whose contract tracks the basket is the inflation-linked bond — which is why it, and not the vibes, backs the guarantee.
| Sleeve | Weight | Status | Role |
|---|---|---|---|
| Inflation-linked ladder (TIPS / euro linkers / JGBi / UK linkers) | ~90% | unchanged | The guarantee — asset–liability matching in index weights |
| CHF bills | ~2–3% | unchanged | CHF leg (no Swiss linkers exist) |
| Gold | 2–5% | reframed | Tail insurance vs coordinated debasement — priced as premium (~+30 bp vol), cap 10%, never a "stability" claim |
| T-bill / money-fund liquidity overlay | ~5% | unchanged | Same-day redemptions |
| Bitcoin / crypto | 0% | decided | Excluded from reserve; optional overcollateralized mint vault as a separate lane |
| Tokenized real estate | 0% | watchlist | Re-test when a transaction-based, investable tokenized index exists |
| Food commodities | 0% | new role | Oracle tripwire: IMF/FAO food index audits CPI prints for manipulation |
The five blocs are where trustworthy statistics and investable linkers overlap today. A candidate bloc joins the index when it clears four gates, in order: (1) statistical independence — a national CPI with credible methodology and revision discipline; (2) open capital account — the currency leg must be hedgeable offshore; (3) an investable inflation-linked market — the guarantee requires matching assets, not just a number (India and Brazil have linkers; China effectively doesn't); (4) oracle redundancy — at least two independent paths to the print. Weights move at most ±2pp per annual revision, so entries are gradual and announced.
Sequencing under study: a CNY bloc fails gate 2 today; INR and BRL clear gates 1–3 with thinner linker markets — likely first additions at small weights; an EM composite sleeve (hedged via a basket of local linkers) could lift world-consumption coverage toward ~75–80% without breaking hedgeability. Every addition is a trade: more "world" in the numerator, more oracle and hedge risk in the guarantee. The rule stays: the index never outruns the collateral that makes it redeemable.