AMM Mechanics

Bitrune implements a constant-product automated market maker on Bitcoin L1. Each pool holds a BTC reserve and a Rune reserve, bound by the invariant x × y = k.

Constant-Product Formula

reserve_btc × reserve_rune = k

Every swap preserves k (net of fees). The price of one asset in terms of the other is the ratio of reserves.

Quote Calculation

Given an input amount, the output is computed as follows:

fee_in        = amount_in × fee_bps / 10_000
amount_in_net = amount_in - fee_in
amount_out    = (amount_in_net × reserve_out) / (reserve_in + amount_in_net)

fee_bps: pool fee in basis points. Default is 30 (0.3%).
Fees remain in the pool reserves. They accrue to liquidity providers proportionally.

Price Impact

Price impact increases with trade size relative to pool depth. A swap that consumes a large fraction of reserve_out will receive a significantly worse rate than the spot price.

Slippage Protection

Every swap accepts a minimum output parameter. The transaction is not constructed if the computed output falls below this minimum. This protects the user from front-running and stale quotes.

LP Mechanics

Liquidity providers deposit both assets into a pool and receive LP shares representing their proportional ownership.

First Deposit

shares = sqrt(amount_a × amount_b)

The first depositor sets the initial price ratio.

Subsequent Deposits

shares = min(
    amount_a × total_shares / reserve_a,
    amount_b × total_shares / reserve_b
)

Depositing in a ratio that differs from the current reserves results in fewer shares (the excess is a donation to existing LPs).

Withdrawal (Burn)

amount_a = shares × reserve_a / total_shares
amount_b = shares × reserve_b / total_shares

Burning shares returns a proportional slice of both reserves.

LP-Rune

An on-chain Rune token represents LP shares for pools that have undergone LP-Rune etching. LP-Rune balances are tracked separately from the general balance ledger. LP-Rune tokens can be staked into mining pools to earn BITRUNE rewards.

Protocol Fee (kLast Accrual)

The protocol fee is accrued on every LP mint or burn event. It captures a fraction of the fee growth that occurred between LP events.

Calculation

root_k      = sqrt(reserve_a × reserve_b)       # current
root_k_last = sqrt(k_last)                       # snapshot from previous LP event

If root_k > root_k_last (the pool grew from swap fees):

treasury_shares = total_shares × (root_k - root_k_last) / (root_k × (phi - 1) + root_k_last)

Parameters

Parameter	Default	Meaning
`phi`	6	Fee split denominator
Protocol share	1/6	~16.67% of fee growth goes to treasury
LP share	5/6	~83.33% of fee growth stays with LPs

The k_last snapshot is updated after every mint or burn. Swap-only activity accumulates growth silently until the next LP event triggers accrual.

Getting Started

Guides

Protocol

Tools

Constant-Product Formula

Quote Calculation

Price Impact

Slippage Protection

LP Mechanics

First Deposit

Subsequent Deposits

Withdrawal (Burn)

LP-Rune

Protocol Fee (kLast Accrual)

Calculation

Parameters

​Constant-Product Formula

​Quote Calculation

​Price Impact

​Slippage Protection

​LP Mechanics

​First Deposit

​Subsequent Deposits

​Withdrawal (Burn)

​LP-Rune

​Protocol Fee (kLast Accrual)

​Calculation

​Parameters

Constant-Product Formula

Quote Calculation

Price Impact

Slippage Protection

LP Mechanics

First Deposit

Subsequent Deposits

Withdrawal (Burn)

LP-Rune

Protocol Fee (kLast Accrual)

Calculation

Parameters