Bonding curve

Each launch uses a virtual constant-product curve. State: vT (virtual token reserves), vS (virtual SOL reserves), rT (real tokens left for sale), rS (real SOL held). The invariant is vT · vS ≥ k₀. All math is u128 integer arithmetic with explicit rounding; the web app uses an exact BigInt port of the same code and both are tested against shared vectors.

Buy

fee = ceil(g · f / 10 000)          g = gross SOL in, f = fee bps
net = g − fee
out = floor(vT · net / (vS + net))

if out ≥ rT (the buy would empty the curve):
  out = rT
  net = ceil(vS · out / (vT − out))
  g   = ceil(net · 10 000 / (10 000 − f))
  fee = g − net                     only g is charged; the curve completes

Sell

gross = min(floor(vS · t / (vT + t)), rS)
fee   = ceil(gross · f / 10 000)
out   = gross − fee

Fee split

sweep    = floor(fee · s / 10 000)
creator  = floor(fee · c / 10 000)
protocol = fee − sweep − creator      (s + c + p = 10 000)

Display values

• Spot price (lamports per base unit) = vS / vT; market cap = vS · totalSupply / vT.
• Price impact = 1 − (out / net) / (vT / vS), computed in bps.
• Slippage: minOut = floor(quoteOut · (10 000 − slippageBps) / 10 000). The program rejects the trade if the actual output is below minOut.

Rounding always favours the curve and the vaults, never the trader: fees round up, outputs round down, required inputs round up.