The exact arithmetic behind the GLU 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 GLU design spec · every figure below recomputed from public data (FRED, OECD, BIS, IMF, S&P, Yahoo)
"Purchasing power" is only a guaranteeable object if you define the basket, the geography, and the tolerance. GLU's promise is narrow enough to be honest and broad enough to matter:
Any holder can always redeem 1 GLU 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; GLU 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 GLU 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 GLU for W(t) of collateral, in kind or via the liquidity sleeve, fee 10–25 bp (widens under stress, hard-capped, never gated). 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 NAV 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 GLU'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 GLU 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 GLU 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.