Define MEΩ from first principles, show how we compute price, weights, returns, and risk in MEΩ units, with exact checks so anyone can audit the math.
This page is frozen to the bundled snapshot dated 2025-10-08. No live calls run in demo mode; all caps and weights below come from the checked-in JSON/CSV (M_world = 108.4T USD, kappa = 1e-6, P_USD^MEIc = 108.4M USD).
| Symbol | Meaning |
|---|---|
| j ∈ C(t) | One monetary species (USD/EUR/JPY/CHF M2, XAU, XAG, BTC, ETH, …) |
| PjUSD(t) | USD price of species j (FX, spot, or coin price) |
| Qj(t) | Quantity/stock: M2 for fiat, above-ground stock (oz/tonnes) for metals, free-float for crypto |
| MCjUSD(t) | = PjUSD(t) · Qj(t), USD "market cap" of species j |
| Mworld(t) | = Σj MCjUSD(t), Aggregated "world money" |
| κ | Scale constant (default 10-6) |
| PUSDMEΩ(t) | USD price of 1 MEΩ |
| wj(t) | Weight of species j in MEΩ (Σj wj = 1) |
Example: if Mworld = 174 trn USD, then PUSDMEΩ ≈ 174 million USD.
(always sums to 1)
This removes global money drift; you are measuring relative to the whole money universe.
r_i_MEΩ[t] = log(P_i_USD[t]/P_MEΩ_USD[t])
- log(P_i_USD[t-1]/P_MEΩ_USD[t-1])Why clip? To keep the update Lipschitz under jumps; avoids blow-ups.
r_clip[j] = clamp(r[j], -5*σ[j], +5*σ[j]) w[j] ← w[j] + w[j]*(r_clip[j] - Σ_k w[k]*r_clip[k]) normalize(w) # divide by Σ_j w[j]
Estimate tail with GPD on excesses above threshold; compute VaRα and CVaRα in MEΩ units.
Purpose: isolate skill, not currency or rate cycles.
Change of numéraire: With MEΩ as numéraire, discounted asset S̃t = St/PMEΩ is a martingale under QMEΩ.
Implementation usually uses Monte Carlo or local-vol; this is included for completeness.
Posts (Mworld, PUSDMEΩ, {wj}) from open feeds.
Merkle/zk proofs over inputs; MEΩ is a measurement unit, not a claim on reserves.
Daily recompute; no human overrides.
Stale data > 60 days or liquidity failure ⇒ set wj → 0 and renormalize.
Persist (date, symbol, weight, meo_usd, m_world_usd) daily.
abs(sum(w)-1) < 1e-9 P_meo_usd == kappa * sum(MC_usd) within 1 bp len(r_MEΩ) == len(P) and finite
-- Latest disclosed basket
SELECT date, symbol, ROUND(weight*100,2) AS pct,
meo_usd, m_world_usd
FROM benchmarks
WHERE date = (SELECT MAX(date) FROM benchmarks)
ORDER BY weight DESC
LIMIT 10;{
"date": "2025-10-08",
"meo_usd": 108400000,
"m_world_usd": 108400000000000,
"weights": [
{"symbol": "CNY", "w": 0.392, "mc_usd": 42492800000000},
{"symbol": "XAU", "w": 0.204, "mc_usd": 22113600000000},
{"symbol": "USD", "w": 0.198, "mc_usd": 21463200000000},
{"symbol": "EUR", "w": 0.155, "mc_usd": 16802000000000},
{"symbol": "BTC", "w": 0.021, "mc_usd": 2276400000000},
{"symbol": "JPY", "w": 0.016, "mc_usd": 1734400000000},
{"symbol": "XAG", "w": 0.01, "mc_usd": 1084000000000},
{"symbol": "ETH", "w": 0.004, "mc_usd": 433600000000}
]
}⇒ preserves Lipschitzness when composed with returns
Replicator update keeps wj ≥ 0 and Σj wj = 1 after renorm.
Foster–Lyapunov shows negative drift away from boundaries under clipped returns.
(Full proofs in the whitepaper; we keep the page practical.)