Unimodular Research

log(swap)

A risk-invariant liquidity primitive for institutional DeFi, built on the logarithmic invariant.

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usdc liquidity

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24h volume

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24h fees

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apy

devnet figures — mainnet is not live

Explore the concepts ↓

What follows from one invariant

Predictable market impact

The displayed liquidity L determines exact price impact, so what you see is what you get: log-price slippage is Δx = ΔQ / L.

Explicit liquidity

Liquidity L remains constant across prices above the floor. Risk is constant in the dimensions that matter: exposure — Δ — and the LVR risk — Γ — are both equal to L, making exposure hedgeable and P&L quantifiable.

Capital efficiency

For the same reserves, displayed liquidity is roughly four times that of the xy = k invariant — the same capital, four times the depth.

Simple liquidity workflows

Positions are fungible and liquidity is algebraic. Portfolios can be combined, split, rebalanced or resized without rebuilding fragmented ranges and positions.

Institutional infrastructure

At the core, the protocol provides the foundations for compliant liquidity infrastructure: protocol-owned liquidity, and private pools with controlled access. SLAs and KPIs are contract-enforced parameters, under the sponsor's full control.

Products

Permissionless Public markets Anyone trades, provides liquidity or opens a market. Each LP picks their own floor and cap, and resting orders fill in either direction. Read more → Controlled access Private pools A desk's own pool: gated minting and trading, lists of approved counterparties, an appointed operator, and a basket reshaped between generations. Read more → Treasuries Protocol-owned liquidity A permanent market for a treasury's token, open to every trader. The bid deepens from fees, and income comes out without selling the token. Read more → Token creators Launchpads A launch on a structural floor: the seed is burned at birth, only fee income ever leaves, and the token graduates in place — no migration. Read more →

Liquidity, Commoditized

Liquidity providers supply depth and earn fees. Arbitrageurs connect the pool to external markets, while organic traders consume liquidity. Follow the flow of trades, fees and realized variance below.

Illustrative market simulation40% annualized volatility · continuous

Solid: external priceYellow dashed: pool priceShading: ±1.67 bp fee bandMuted volume: organic flow

LP fees this hour $0.00Variance cost this hour $0.00Arb net this hour $0.00

Awaiting the first price divergence.

L = $1,000,000 · 40% annualized volatility (365-day year) · 1 animation second = 1 market minute · fresh random Gaussian increments · trade trigger ≈ 5 bps · assumed execution costs leave 10% of arbitrage-paid fees as arb net P&L. Organic orders average 2.4 per market minute, with 0.5–1.3 bp impact. Readouts reset each simulated hour; earned fees are not removed. Fees and variance are measured, not forced equal.

In log we trust

The whole synthesis is the whitepaper.

log(dex) log(docs) log(research) log(pad) soon log(earn) soon log(lend) soon

palette

h — square pixels