fotoshi is a bonding curve on solana whose slope is computed from its own reserve instead of chosen by a person. entries move along the curve. exits that leave value behind move the curve itself, upward, permanently. the program holds three instructions, no owner, no fee, and no clock. every dotted line on this page is arithmetic, drawn from the formulas alone until the program is live, and from the chain alone after.
the supply line approaches K = 2 718 281, the first seven digits of e, and never arrives. the price line is the cost of the next token. entries move along the curve, exits move the curve.
the slope never falls.
every state change preserves s or raises it. proof in the paper.
a round trip cannot profit.
the exit pays at most your entry, and re entry meets a slope at least as steep.
the reserve is exactly sufficient.
r equals s times ln(K / (K − q)) at every moment, by construction, not by audit.
a deposit buys along p(q) = S / (K − q) and raises the reserve by exactly the integral it crossed. a mint never moves the slope. while people only enter, fotoshi is indistinguishable from a curve with a fixed slope, and every token is matched by sol in the reserve.
a burn is worth V = S · ln((K − q + b) / (K − q)) but pays min(V, basis). whatever remains stays in the reserve, and there is no address it could leave to. the payout rule follows each token through every transfer, because basis is a conserved quantity moved by the transfer hook.
S = R / ln(K / (K − q)), recomputed at every event. mints preserve it, exact exits preserve it, forfeits raise it. nothing in the instruction set lowers it. the staircase chart below is the history of everyone who left and what their leaving did to the price of coming back.
a chosen slope
a ratcheting slope
left: a curve whose slope was chosen once by a person. right: fotoshi, where every forfeit lifts the slope for everyone who comes later. shapes only, no measurements.
theory means computed from K = 2 718 281 and the genesis slope. measured means settled on chain. this page never blends the two without saying so.
tokens minted by each successive tranche of 500 sol at the genesis slope. the first tranche mints more fotoshi than any tranche ever will again. each one after mints less, without end. once the program is live these bars re draw from the live slope, and forfeits make them shrink faster.