the maths
the exact bonding-curve math, pump.fun vs the protected curve. same game — buys push price up a curve. the entire difference is what a sell does.
protected vs pump-style launchpads (unprotected curves)
both are bonding curves. the difference is where the risk lives.
| pump / unprotected curve | protected curve | |
|---|---|---|
| how you exit | sell back down the same curve — your own exit moves price against you | redeem from an ETH vault at NAV — zero price impact, sells don't touch the curve |
| worst case | unbounded — bought a pump top, you can be down −90%+ | capped on-chain — ~18% at β=0.9; the contract reverts any NAV drop |
| price direction | fully reversible — dumps print red candles all the way down | monotone up on the curve — the floor only rises, can't print red |
| rug surface | dev/whale dumps the curve · snipers · LP pulled after graduation | spray LP is protocol-owned and cannot be pulled; the protected curve remains the canonical floor venue |
| where fees go | pure extraction — skimmed out to platform/creator | 2% of buys + 5% of sells STAY in the vault → they raise everyone's floor |
| graduation | migrates to a DEX — a brand-new dump surface + LP risk | none — the curve is perpetual, nothing to migrate |
| premine / team bags | possible — allocations, presales, insider supply | none — genesis = your seed × 1e6, minted against your own ETH |
| network flywheel | none, or opaque | ¼ of every buy fee buys-&-burns the network token, forever |
| the guarantee | trust the marketing thread | an invariant coded into the hook — it reverts rather than lie |
the one-sentence difference: pump's sell formula is its buy formula run backwards through the same curve; the protected curve's sell doesn't contain the curve at all — it's a vault redemption, so there's nothing to dump down.
Canonical curve vs distribution pools
The protected Uniswap v4-hook curve is the source of truth for NAV, floor, and protected redemptions. It is perpetual and always taxed: 3% on buys and 6% on sells.
Additional hookless v4 and v3 pools distribute token-only inventory across RH quotes. Their prices can diverge from NAV and do not carry the curve loss bound. Their principal is protocol-owned; harvested fees split 70% to the creator and 30% to the protocol, with permissionless claims.
pump.fun — constant product
invariant x·y = k (virtual SOL × virtual tokens) price p = x / y = x² / k BUY Δtokens = y − k/(x+Δsol) SELL Δsol = x − k/(y+Δtok)
Sells run the same k backwards — every exit rides the identical curve down. Price is fully reversible.
protected power curve
invariant S = k·V^β, β = 0.9 (supply vs vault) price p = V / (β·S) · floor NAV = V/S = β·p BUY S₁ = S₀·((V₀+0.97x)/V₀)^β, V₁ = V₀+0.99x SELL eth = 0.94·T·V/S → V₁ = V−0.95·T·V/S
Sells never touch the curve — they redeem from the vault at NAV. 5% of every exit stays, so the floor rises as people leave.
Identical scenario, both machines: 25 buys… then everyone sells
quoted price, indexed to 100 at launch
pump priceprotected priceprotected floor
worst case: you bought the exact top
−97%+
loss = 1 − p_after/p_entry · (1−fees)² dump → x returns to x₀ → p_after ≈ p₀. bought 7× above p₀ ⇒ ≈ −86%; deeper ⇒ −97%+. unbounded.
worst case: you bought the exact top
−17.94%, hard cap
recover = 0.97 · β · 0.94 = 0.9118·β loss = 1 − 0.9118·0.9 = 0.1794 floor is monotone: contract reverts any NAV drop.
fees: pump 1%/1% (pure extraction) · protected 3% buy / 6% sell — but 2%+5% of those stay in the vault: the fees are what makes the floor rise. cap applies to curve round-trips at β=0.9; a β=0.825 launch caps at −24.8%. Buying in a secondary spray pool isn't capped relative to what you overpaid there — the protected curve is the canonical protected path.