The bonding curve

Constant product with virtual reserves

The curve behaves like a Uniswap-style constant-product market maker, but it is seeded with virtual reserves instead of real deposits. That means the pool starts with a sensible price and reasonable depth even though nobody has put in a single ETH yet. Buying adds ETH and removes tokens; selling does the reverse. The product of the two reserves stays constant.

k = virtualEth × virtualTokens
  = 1.45 ETH × 1,085,000,000 tokens

ethReserve   = virtualEth   + realEth        (real ETH raised so far)
tokenReserve = virtualTokens − sold          (tokens still on the curve)

The starting reserves

Because tokenReserve starts at the full 1,085,000,000 virtual amount and only 800,000,000 of it is ever sold, the curve never runs dry — the last token on the curve still has a finite price. When all 800,000,000 have been sold, the token graduates.

Buy and sell math

The exact amounts are computed from the invariant. A 1% fee is charged on the ETH side of every trade before the swap is priced (see Fees). The published formulas are:

buy  (you send ethIn):
  fee = ethIn × 1%
  out = tokenReserve − k / (ethReserve + ethIn − fee)

sell (you send tokensIn):
  gross  = ethReserve − ⌈ k / (tokenReserve + tokensIn) ⌉
  payout = gross − gross × 1%

• Buy: your ETH (minus the fee) is added to ethReserve; the number of tokens the invariant releases from tokenReserve is what you receive.
• Sell: your tokens are added back to tokenReserve; the ETH the invariant frees from ethReserve is your gross, and the 1% fee is taken from that before payout. The ceiling rounds in the pool's favour by at most one wei.

Price discovery

Price is simply ethReserve / tokenReserve. Early buys move it a lot because the reserves are small; as more ETH enters, each additional token costs more and the curve steepens. This front-loads risk and reward: the earliest buyers get the lowest average price, and the market cap climbs smoothly from ~1.34 ETH at launch toward the graduation cap.

Tokenomics at a glance