the price of the next token is the reciprocal of the slope of the supply function:
p(e) = (S + e)³ / ( 2 × K × S² )
at position zero this is 7 629 394 531 250 wei per token. at position S it is eight times that. at 3S it is sixty four times. the price grows with the cube of depth, so the second half of supply is far more expensive than the first, and the last sixteenth is more expensive than everything before it combined.
the contract does not evaluate p. it evaluates q twice, before and after the curve entry, and issues the difference. the difference is exact to the base unit because the two evaluations each round down once. the view function state returns a curve price for display, computed as the cube of S plus position over twice 33 554 432 times S squared, in wei per whole token.