pat0contracttoken
market
price
market cap
fully diluted
liquidity
volume 24h
trades 24h
holders
change 24h
docs4 of 14
pat0the machine
pressure

pressure is a congestion multiplier kept in the contract as a fixed point number with eighteen decimals. it changes once per block and only in response to how many tokens that block issued.

budget and target

headroom = K − totalSupply
budget   = headroom >> 7
target   = budget >> 1

the budget is the most a block may issue. it is one part in 128 of the headroom, so the opening block may issue 262 144 tokens, which is almost exactly what a full two eth pat issues at position zero, and the budget shrinks as the curve fills. target is half the budget, and one eth at the opening issues just under target.

settlement

at the start of every mint the contract settles pressure up to the current block. the block that last saw a mint applies its own multiplier: one plus the excess of its issuance over target, divided by eight targets. if that block had issued under target the multiplier is below one, and the result is floored at zero. if pressure was zero and the block crossed target, pressure is seeded at one sixty fourth first. every block since then was idle and multiplies pressure by seven eighths, computed as a power in fixed point with rounding down at each squaring. after five hundred and twelve idle blocks pressure is set to exactly zero without computing the power.

pressure
under target every blockunder target, pressure has nowhere to go but zero.full every block12341.0 at block 36full then idle12340.0001690816243240485664
how pressure moves block to block for three patterns of use. drawn from the settlement rule, not from a feed.
idle decay ladder
idle blocksfactorfactor fp18time at 100 ms10.875000875 000 000 000 000 0000.1 s20.765625765 625 000 000 000 0000.2 s40.586182586 181 640 625 000 0000.4 s80.343609343 608 915 805 816 6500.8 s160.118067118 067 087 021 248 7951.6 s320.01394013 939 837 037 683 1353.2 s640.000194194 319 056 637 1626.4 s1280.00000037 759 895 77212.8 s2560.0000001 42525.6 s5120 treated as zero051.2 s
the idle decay factor at nine idle spans, computed the way the contract computes it.

the split

c = v × 1e18 / (1e18 + pressure)
r = v − c

v is the eth sent. c walks the curve. r is surcharge. both enter the cistern. only c changes position and only c issues tokens. pressure one means half. pressure three means a quarter. pressure has no ceiling.

the split
π = 0c 100.0%r 0.0%π = 1c 50.0%r 50.0%π = 3c 25.0%r 75.0%live
one mint of v split by pressure into curve entry and surcharge.