> ## Documentation Index
> Fetch the complete documentation index at: https://inflexion.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# What is Inflexion

> The first market to price Uniswap v3 in-range impermanent-loss risk on-chain — a collateralized, capped, bilateral convexity hedge with a pooled cvAMM floor and competing-MM ceiling.

**Inflexion is the first market for Uniswap v3 impermanent-loss risk — and the first to price that risk on-chain.**

A Uniswap v3 LP brings a specific position (its NFT), picks a duration, and pays a fixed upfront **premium**. At expiry the protocol pays the LP their realized impermanent loss — **capped at MaxIL** — trustlessly, from collateral that an underwriter locked up front. The product is precisely an [**in-range convexity hedge**](/concepts/in-range-convexity-hedge), not "IL insurance": the cap is load-bearing, not cosmetic.

<Note>
  The payoff is $\min(\text{realized\_IL},\ \text{MaxIL})$. Entry requires the position to be in range — $P_a \le P_0 \le P_b$ is [enforced at creation](/concepts/in-range-convexity-hedge) — and the cap is what makes full collateralization (and therefore the [no-bad-debt guarantee](/concepts/no-bad-debt)) possible.
</Note>

## In one paragraph

> If you've ever provided liquidity on Uniswap and ended up with less than if you'd just held — that's impermanent loss. It costs LPs over a billion dollars a year and there's no trustless way to hedge it. Inflexion is the first market that prices that risk on-chain: a pooled underwriter always quotes you a fair, code-capped price, market makers compete to beat it, and if your position suffers impermanent loss within its range you're paid back — from pre-locked collateral, with no middleman who can run off with the money.

## What it is, in one line

> Inflexion is the first market for Uniswap LP convexity priced on-chain — **MaxIL is the capital unit.** A pooled cvAMM always quotes a code-capped fair price with dual-tranche structure (junior vol-seller, senior savings account), and competing market makers undercut it. The resulting flow is a structural DeFi volatility-risk-premium surface for Uniswap LPs — the first on-chain dataset of this market's microstructure.

## Why this market didn't exist before

Uniswap v3 LPs carry a **structural short-gamma exposure** — their position value is a concave function of price, so they lose on both up and down moves relative to holding. Impermanent loss is the realization of that exposure, estimated at **>\$1B/year of realized losses across DeFi**, with no trustless, non-inflationary way to hedge it.

Three things blocked a clean on-chain hedge until now:

<CardGroup cols={3}>
  <Card title="No trustless instrument" icon="ban">
    Prior "IL protection" (Bancor v2.1) relied on **token inflation** to cover losses — a death-spiral mechanism, not a collateralized hedge. Inflexion mints nothing and pays from pre-locked USDC.
  </Card>

  <Card title="Beyond-range IL is unbounded" icon="arrows-left-right-to-line">
    Past the range edge, IL grows without bound, so a product covering it could never be fully collateralized — and therefore never trustless. **In-range** IL is convex and bounded.
  </Card>

  <Card title="Two-sided cold start" icon="snowflake">
    A purely LP-vs-MM market has no liquidity until market makers arrive — a classic chicken-and-egg. The pooled cvAMM solves it by always quoting.
  </Card>
</CardGroup>

## How it works, in five parts

<Steps>
  <Step title="Capped in-range IL transfer">
    Coverage pays $\min(\text{realized\_IL},\ \text{MaxIL})$. [**MaxIL**](/concepts/maxil) is the maximum in-range IL of the *specific* position — pure geometry computable at creation from $(P_a, P_b, L, P_0)$, **frozen at creation**, and **identical across all three durations.**
  </Step>

  <Step title="On-chain fair pricing">
    The protocol computes and publishes $\text{FairPremium} = \text{fairRate} \cdot \text{MaxIL}$ on-chain via the [`FairValueOracle`](/concepts/fair-value) — an exact closed-form [$\Phi$-sum](/math/fair-value-phi-sum), never a fitted surface.
  </Step>

  <Step title="Two rails, one settlement core">
    [Path A](/protocol/path-a-cvamm) is the always-on pooled cvAMM (signature-free, on-chain). [Path B](/protocol/path-b-mm) is competing market makers (EIP-712 signed quotes). [`createSwapRouted`](/protocol/routing) gives the LP the **cheaper of `{pool, best MM quote}`.**
  </Step>

  <Step title="Full collateralization (FULL mode, the default)">
    The underwriter locks exactly $\text{MaxIL}$. Since $\text{covered\_payoff} \le \text{MaxIL} = \text{collateral}$ by construction, FULL mode **cannot produce bad debt under any price path** — invariant [I1](/security/invariants), provable by Foundry invariant tests.
  </Step>

  <Step title="Non-custodial on-chain settlement">
    At expiry, `settle()` reads the Chainlink round pinned at $T$, computes realized IL using the $L$ stored at creation, pays the LP $\min(\text{realized\_IL},\ \text{MaxIL})$ from the underwriter's locked collateral, returns the residual, and returns the NFT.
  </Step>
</Steps>

## The three pillars

The protocol stands on [three pillars](/concepts/three-pillars) — read these before anything else.

<CardGroup cols={3}>
  <Card title="On-chain published FairValue" icon="square-root-variable" href="/concepts/fair-value">
    An exact closed-form $\Phi$-sum, evaluated live per quote by the production **Stylus** `FairValueOracle` — **never reimplemented off-chain.** $\text{fairRate}$ carries all the vol/time dependence; MaxIL carries none.
  </Card>

  <Card title="The cvAMM — floor of liquidity" icon="layer-group" href="/protocol/path-a-cvamm">
    An always-on, signature-free pooled underwriter quoting off `FairPremium`, **capped in code at** $\text{FairPremium}\cdot(1+\text{maxLoad})$ by invariant I10. It removes cold-start: there is always a price.
  </Card>

  <Card title="MM competition — ceiling of price" icon="gavel" href="/protocol/path-b-mm">
    Sophisticated MMs stream firm EIP-712 signed quotes (no last-look) and win only by beating the capped pool. Hedged MMs **export** short-gamma risk out of the system.
  </Card>
</CardGroup>

<Tip>
  **Floor + ceiling in one line:** the cvAMM is the floor of liquidity (always quotes a code-capped price); the MMs are the ceiling of price (win only by beating it). `createSwapRouted` routes to the cheaper rail and never reverts on a bad MM quote — it falls back to the pool, and only the executed rail mutates nonce, capacity, and lock.
</Tip>

## MaxIL — the cap and the unit of risk

MaxIL is two things at once, and both are load-bearing:

* **The cap.** $\text{IL}(P)$ is convex on $[P_a, P_b]$, so its in-range maximum is at a boundary: $\text{MaxIL} = \max\!\big(\text{IL}(P_a),\, \text{IL}(P_b)\big)$. Because $\text{collateral} = \text{MaxIL} \ge \text{payout}$, no bad debt in FULL is a *construction*, not a hope.
* **The unit.** MaxIL is pure geometry, frozen at creation, L-independent in the fair-rate sense — which makes positions **fungible to an underwriter within a market.** An MM quote is therefore [**per-market**](/protocol/markets) (a load + a MaxIL-ratio band + capacity), **never per-NFT** — the signed quote carries no `tokenId`.

See [MaxIL — the cap and the unit of risk](/concepts/maxil) for the full doctrine, and [the worked example](/math/worked-example) for one position priced across three durations on a single, constant MaxIL.

## Who it's for — the four doors

<CardGroup cols={2}>
  <Card title="Protect my LP position" icon="shield-halved" href="/app/protect">
    Uniswap v3 LPs who want to hedge in-range IL — pay one number, get certainty. The prize customer is **DAO / treasury protocol-owned liquidity** that needs predictable, reportable P\&L.
  </Card>

  <Card title="Earn in the cvAMM" icon="piggy-bank" href="/app/earn">
    Capital providers who want to earn the volatility-risk premium across [two tranches](/concepts/tranches): senior (a convexity savings account) or junior (a pure vol-selling, first-loss tranche).
  </Card>

  <Card title="Underwrite & compete" icon="gavel" href="/app/underwrite">
    Sophisticated market makers who run their own vol models, stream firm signed quotes below the pool, and hedge short gamma off-system (Deribit / Panoptic / perps). Optional and additive.
  </Card>

  <Card title="Integrate & build on the data" icon="code" href="/integrate/architecture">
    Quants, vol-arb desks, and risk teams reading [the data moat](/concepts/data-moat) — the first on-chain view into the microstructure of the DeFi LP volatility-risk premium, exposed as free public [SDK](/sdk/overview), [subgraph](/integrate/subgraph), and [REST API](/integrate/api-overview).
  </Card>
</CardGroup>

## It's live

Inflexion is deployed on **Arbitrum Sepolia** (chainId 421614), with a full create→settle lifecycle run on both rails on the 2026-06-05 stack — Path A paid an LP from the `ConvexityVault`, and Path B routed to a market maker whose **own collateral** was locked and paid out. Live addresses:

<AddressTable />

See [the deployments reference](/reference/deployments) for the full registry and [the live status](/status) for the status of every component.

<Note>
  **Structures ship from day one; the full DYNAMICS (pool-vs-MM spread as a forward-vol signal) mature with multiple competing MMs and volume. The dataset begins at the single redeploy; the off-chain telemetry halves begin at the first interaction logged.**

  What Inflexion offers today is the **architecture and the first public view** into the microstructure of the DeFi LP volatility-risk premium — not yet a mature dataset:

  * **Structures are present day-one.** All five non-circular behavioral signals are defined and queryable from launch.
  * **Dynamics mature with volume.** The richer signal — the pool-vs-MM spread read as a forward-vol indicator — only sharpens once multiple market makers compete and real flow accumulates.
  * **The dataset begins at the single redeploy**, and the off-chain telemetry halves begin at the first interaction logged. History is served live from the subgraph via the API; if a backing (subgraph URL / RPC / telemetry) is absent, surfaces degrade to a typed `pending` state — never an error.
</Note>

## The honest line

Two claims, always separate, never merged:

1. **LPs are always paid** — no bad debt in FULL, code-enforced by invariant [I1](/security/invariants).
2. **Depositors and MMs can lose principal** — the pool is a volatility seller, and capital is **not** guaranteed for either tranche (junior is first-loss; senior is protected from *underwriting* loss only, never from the systemic tail).

<Warning>
  **LPs are always paid with no bad debt in FULL mode — qualified: capped payoff + solvent USDC + oracle/settlement liveness.**

  The no-bad-debt guarantee is **exact only** under the full clause:

  * **FULL collateralization** — the underwriter has posted exactly `MaxIL` per swap, locked for the life of the position.
  * **Capped payoff** — the payout is `min(realized_IL, MaxIL)`. The cap is load-bearing: it is what makes `payout ≤ collateral` hold by construction.
  * **Solvent USDC** — the collateral numeraire (`dUSDC`) holds its peg and remains redeemable.
  * **Oracle / settlement liveness** — the price oracle stays live and `settle()` runs within the protocol's settlement window.
  * **No rehypothecation breach** — locked collateral stays instantly liquid; it is never routed to utilization-gated venues.

  Stated without these qualifiers, the guarantee is **not** correct.
</Warning>

It is **not** Bancor (no token inflation), **not** GammaSwap (no active management), **not** Panoptic (the LP pays one number), and **not** "insurance" (it is a collateralized derivative). See [what this is not](/what-this-is-not) for the full set of differentiators.

## Where to go next

<CardGroup cols={3}>
  <Card title="Quickstart" icon="rocket" href="/quickstart">
    Cover a position, deposit, or pull data in a few lines.
  </Card>

  <Card title="Why Inflexion" icon="lightbulb" href="/why-inflexion">
    The problem, the surplus, and the differentiators.
  </Card>

  <Card title="Why now" icon="clock" href="/why-now">
    The 2025 theory (LVR, Lipton–Lucic–Sepp) and the Arbitrum + Stylus stack.
  </Card>

  <Card title="The math" icon="square-root-variable" href="/math/overview">
    The IL formula, the MaxIL derivation, and the $\Phi$-sum.
  </Card>

  <Card title="The protocol" icon="diagram-project" href="/protocol/overview">
    Pricing stack, lifecycle, vaults, oracles, routing.
  </Card>

  <Card title="The data moat" icon="database" href="/concepts/data-moat">
    Five behavioral signals into the DeFi LP vol-risk premium.
  </Card>
</CardGroup>


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