Bonding curve

Each token uses a shifted constant-product curve with 18-decimal integer arithmetic.

Constants

Parameter	Value
Total supply	1,000,000,000 tokens
Curve allocation	800,000,000 tokens
Graduation LP allocation	200,000,000 tokens
Virtual token reserve	`1,066,666,666.666666666666666667` tokens
Virtual ETH reserve	1 ETH
Net graduation reserve	3 ETH
Trading fee	1% of accepted buy gross or gross sell output
Initial reported price	`937,500,000` wei per whole token
Terminal reported price	`15,000,000,000` wei per whole token

Invariant

Let:

s be sold curve tokens in base units;
r be active ETH principal in wei;
Vt be the virtual token reserve;
Ve be the virtual ETH reserve;
K = Vt × Ve.

The virtual coordinates are:

x = Vt - s
y = Ve + r
x × y ≈ K

The contract uses Solidity integer arithmetic. Outputs round down, while the post-trade virtual ETH coordinate uses ceiling division. Those rounding rules are part of the implementation. For a nonterminal buy with net curve input Δr, the contract computes:

postVirtualTokens = ceil(K / (Ve + r + Δr))
tokensOut = (Vt - s) - postVirtualTokens

For a sell of Δs tokens:

postSold = s - Δs
postVirtualETH = ceil(K / (Vt - postSold))
grossETHOut = (Ve + r) - postVirtualETH
netSellerOutput = grossETHOut - fee

The reported spot price is ceil((Ve + reserveCoordinate) × 1e18 / (Vt - s)) wei per whole token. Price rises as buys reduce virtual token inventory and add net reserve; sells reverse that movement before graduation.

The curve formula does not guarantee value, liquidity at a desired price, or graduation. Transaction ordering and slippage can materially change execution.

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Invariant

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Constants

Invariant