dPUMP/dt

$PUMP is the asset everyone on this platform is already long, whether they hold it or not. The promised distribution is a future event with unknown timing, unknown size, and unknown eligibility. dPUMP/dt does not wait for it. It builds the position mechanically, in the open market, out of the only revenue a token reliably produces: its own creator fee.

Supply is fixed at exactly 1,000,000,000. Nothing is emitted, nothing inflates, there is no schedule. Every trade against the dPUMP/dt pool earns a creator fee, that fee is used to market-buy $PUMP, and the acquired PUMP is credited to holders in proportion to what they hold. You are not farming an allocation — you are accumulating the underlying, trade by trade.

Let V be cumulative fee volume, in SOL, routed through the protocol. Cumulative PUMP acquired is not linear in V, because market-buying moves the price against you — each marginal SOL fills at a worse price than the last. Modeling fill price with the standard square-root market-impact form gives a sub-linear acquisition curve: acquired(V) = A · V^(1−γ), with γ the impact exponent.

Differentiate it and you get the protocol's name. dPUMP/dt = A(1−γ) · V^(−γ) — the instantaneous PUMP accrued per unit of fee flow. It is a power-law decay, not a cliff and not a cutoff. Early fee flow buys PUMP cheaply. Later flow pays up. The rate falls forever and never reaches zero, so accumulation never stops while the pool sees volume.

This is the honest version of the mechanism, and it is why both curves are on the chart. The solid curve is what you own. The dashed curve is what the next SOL of fees will buy you. They are the same equation, read at different orders.

The creator fee never lands in a wallet the team can spend. It accrues into a buy buffer, and when that buffer clears the execution threshold it is swept into an open-market PUMP buy in a single transaction. The acquired PUMP is written to a distribution accumulator keyed to dPUMP balances.

Because the sweep triggers on buffer size rather than on a clock, the distribution cadence is a function of volume. Quiet markets distribute slowly. Active markets distribute constantly. There is no epoch to game and no snapshot to front-run — your claim is a continuous function of your balance and the fee flow that occurred while you held it.

Nothing about this changes the dPUMP supply. The billion is the billion. What grows is the PUMP standing behind it — a real, on-chain, market-bought position that can be verified block by block and claimed at any time, with no lockup and no counterparty.

The result is a token whose backing is monotonically increasing in the one variable it actually controls: how much it is traded. Every trade is a buy order for $PUMP that you did not have to place.