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Formula Analysis

LP income from fees (AMM pools)

Pool model: constant-product (x·y = k). Marginal price and price impact follow from the invariant, as in Uniswap-v2-style pools.

Fee structure:

  • Base trading fee = 0.3%

  • Of this: 0.2% → LPs, 0.1% → protocol

Annual APR from pool fees (for the entire pool):

Individual LP share is proportional to the LP’s liquidity contribution:

(In practice, average daily volume and TVL, or rolling metrics, are used.)

Exact token output at swap (price impact) from x·y = k: If a trader deposits x, then:

→ Demonstrates why large trades cause stronger price impact.

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Farming (LP staking) — rewards

If a farm distributes rewards with intensity R tokens per unit of time, token price = P, and the total value of staked LP in the farm = TVL_farm, then the “gross” annual farming APR is:

Individual APR depends on the share of LP staked by the user:

(STON.fi provides SDKs/guides for staking and claiming, but the exact public formula for farm APR is not fixed in the documentation.)

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Conversion to APY (with n reinvestments per year):

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STON Staking → ARKENSTON and GEMSTON

Official staking mechanics:

  • On deposit of STON, the user receives an equal amount of soulbound-NFT ARKENSTON (grants DAO participation rights). At maturity, ARKENSTON is burned to return STON.

  • The user also receives an equal amount of GEMSTON (liquid engagement token), whose properties and applications are determined by DAO decisions.

  • 20M STON from the DAO Treasury are staked for 24 months (a protocol commitment).

Conditional “issuance formulas” during staking:

Understanding these formulas is critical for building optimal staking and farming strategies with STON.

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