00 zero operators

fat0 is a bep20 token on bnb chain. lowercase name, a zero where the o should be. it is issued by a program that nobody administers, nobody can pause, and nobody can upgrade. there is no team allocation, no premine, no treasury, no roadmap. the program that is deployed is the program, forever. what follows is a description of a machine, not a promise.

01 issuance is gated twice

bitcoin meters its supply with time. blocks arrive, the subsidy decays, and no amount of money makes the next block come sooner. bonding curves meter supply with capital. each marginal token costs more than the last, and no amount of waiting makes it cheaper. fat0 does both at once. supply is released along a capital curve and a time curve, and at every moment the lower of the two is the law. you cannot buy the future faster than it arrives. you cannot wait your way into tokens without paying the curve.

02 the vault

every mint deposits bnb into a vault the program owns. every burn redeems bnb out of it along the inverse curve. those are the only two doors. the bytecode is immutable and contains no third instruction that touches the vault. bnb that enters at mint time is bnb available at burn time, plus the fees that fold inward, minus nothing.

03 curve math

supply at cumulative bnb e:
  q(e) = K * e / (e + S)          K = 16777216   S = 1024 bnb

marginal price at position e:
  p(e) = (e + S)^2 / (K * S)

position at supply q:
  e(q) = S * q / (K - q)

bnb redeemed burning b from supply q:
  delta e = S * K * b / ((K - q) * (K - q + b))

the curve is rational, not exponential. there is no e to the x anywhere in the program. every quote above is computed on chain in exact u128 integer arithmetic, which means the program spends almost nothing to price a mint and a human can check the math with a pen. half the asymptote sits at exactly 1024 bnb of cumulative inflow. the tail is heavy on purpose: the last quarter of supply costs more than everything before it combined.

04 the time gate

allowed supply at block t since genesis:
  A(t) = K * t / (t + H)          H = 78840000 blocks, about one year

effective ceiling at any moment:
  min( q(e), A(t) )

bnb chain's clock is not a timestamp somebody wrote down, it is block height, a verifiable counter the whole network agrees on. fat0 reads that clock and refuses to let supply outrun it. in the first year, no quantity of bnb can pull more than half the asymptote into existence. whichever gate is lower binds.

07 fees fold inward

twenty five basis points on each side of every mint and every burn, folded directly into the vault. the fee is not revenue. nobody can withdraw it, redirect it, or vote on it. it exists so that every trade, in either direction, permanently raises the bnb backing behind every token that remains. friction here is not a cost of the system, it is the system slowly reinforcing its own floor.

08 five checks

• minting is the curve contract alone
• there is no pauser
• there is no proxy and no owner
• metadata is fixed in the bytecode
• no vault exit but burn in the bytecode

trust here is not a narrative, it is five fields anyone can read out of an explorer in under a minute. if every person who shipped this vanished tonight, tomorrow the program would quote the same prices under the same rules to whoever showed up. that is the entire feature.

09 regimes

while the curve is young it is the only market, and every buyer advances the position. once secondary pools deepen on bnb chain's amms, the curve narrows into two roles: canonical issuer whenever secondary trades above the marginal mint price, and standing bid of last resort whenever secondary bids go quiet. the curve never runs out of inventory to buy back until the vault itself is empty. it always quotes. between the curve's quote and the secondary's quote, the better price wins, and the program does not care which door you use.