Cairn
The law $CAIRN Robinhood Chain (4663) Uniswap v4
The rule of $CAIRN, written out. Every figure of the protocol below reads set at deploy: a constant of the deployment, printed here and on the explorer, with no setter for any of it. The ridge on the front page runs the same rule on its own numbers and says so wherever it shows one, and so do the two tables on this page that are worked through it.
Robinhood Chain is at block 00 000 000, read from the chain a moment ago.
Article 01 · the level of a tick
level = floor( tick ÷ level width )
A level is a fixed number of ticks wide, set at deployment. Levels tile the whole range of the pool's price and never move: a level is an address, not a window. The level of a tick is the tick divided by the width, rounded down, so that the ticks below nought are cut into levels of exactly the same width as the ticks above it.
level = floor( tick ÷ level width )
After every swap the hook reads the pool's tick, finds the level it landed in, and lays one stone on that level's cairn. One swap, one stone. The size of the swap, its side and its price impact change nothing at all. The table below is five swaps on one level, worked through the rule on this site's own numbers: each lays one stone, and only the toll grows with the size.
| Swap | Size | Stones laid | The cairn after it | Its toll |
|---|
This runs the rule on its own numbers; the real ones are set at deploy.
A cairn is finished at a published number of stones. The number is the same for every level: no level is easier than another, and none is kept for anybody.
The swap that lays the last stone puts the capstone on: the whole reserve buys $CAIRN on the pool and sends it to the dead address, inside that transaction. The cairn is written to the ridge with its level, the block it was started, the block it was finished and the amount burned. If the buy cannot be made, the swap still goes through: the cairn is marked as capped and owed, and the burn is tried again on the next swap.
The table below is seven swaps worked through the rule itself, on this site's own numbers, from a cairn of 20 stones and a reserve of 30.00. The price wanders off a level and back; the swap that lays the 24th stone burns the whole reserve; the next swap there pays its toll and lays nothing.
| Swap | Side and size | Level | What the rule does | Its cairn | Reserve after |
|---|
This runs the rule on its own numbers; the real ones are set at deploy.
A level that has been capped never takes another stone. Swaps that land there afterwards pay the toll like all the others and lay nothing. There is no way to reopen a level, and there is no setter that could. A level can therefore be finished by somebody else's swap at any moment, and it is then closed for ever.
A swap lays at most one stone and can finish at most one cairn. There is no cascade anywhere in this design: a capstone does not lay a stone anywhere else, and a burn does not move any count.
A cairn that is never finished is never cleared either. Half-built cairns stay at their height for ever and are drawn at their true height, because they are the honest record of a level the market visited and left.
The address whose swap finishes a cairn pays the same toll as everybody and receives nothing. There is no prize, so there is no race, so there is nothing for whoever orders the transactions of a block to sell. The hook reads no address and credits no address: every figure it keeps is a total, or a count for a level that belongs to nobody.
The team's share of the toll, of the reserve and of anything else this protocol touches is none.
The reserve has no owner: no withdrawal, no destination that can be set, no pause, and no setter on the level width, on the height or on the toll.
Every swap pays a toll, a fixed share of its size, set at deployment and rounded up. It is the only income of this protocol and it goes into one reserve, which leaves only as $CAIRN bought on the pool and burned, whole, when a capstone goes on. The reserve's buy rounds down, and the dust burns with the next capstone.
Size buys nothing here, and the toll still grows with size, so a large trade pays far more for the same stone as a small one. That is simply what the rule does; it is not offered as fairness. A market that never comes back to a level never finishes a cairn, and the reserve waits, in full view, with the tallest cairn not finished named beside it.
The ridge records block numbers: the block a cairn was started and the block it was finished. On Robinhood Chain a contract can read two of them, and the rule has to say which it means.
block.number15 sa step
Ethereum's block, as the chain's sequencer last read it. It moves a step every 15 seconds, sometimes by two, and about 148 of the chain's own blocks share each value.
ArbSys(0x64).arbBlockNumber()about0.1 sa block
The chain's own block, about one every tenth of a second.
Cairn only records these numbers; nothing in the rule counts them, so the choice changes what the ridge says about time and nothing about what burns. It is made at gate 1 of the sheet, with the level width, the height and the toll, and published here. The ridge on the front page keeps a block of its own, one a second, and its block numbers are its own.
$CAIRN, and only when a capstone goes on.| Parameter | What it does |
|---|---|
| Set at deploy | |
| The level width | Ticks in one level; the levels tile the range and never move |
| The height | Stones that finish a cairn, the same for every level |
| The toll | The share of every swap that goes to the reserve |
| The clock | Which block number the ridge records, article 11 |
| Quote asset | If it is USDG, its 6 decimals are carried into the toll; levels are in ticks and are unaffected |
| Supply | Published before deployment, with the rest of this table |
| Fixed | |
| The stone | One per swap, on the level of the tick after it, whatever the size or the side |
| The capstone | The whole reserve buys $CAIRN and burns, inside the swap that lays the last stone |
| A finished level | Takes no stone again; swaps there pay the toll and lay nothing |
| Rounding | Levels round down, tolls up, the reserve's buy down |
| None | |
| Paid for a capstone | To the swap that lays it, or to anyone |
| The team's share | Of the toll, of the reserve, of anything |
| Where it runs | |
| Chain | 4663Robinhood Chain |
| Venue | own poolUniswap v4, a hook of ours on its own pool, in the PoolManager 0x8366a39CC670B4001A1121B8F6A443A643e40951 |
| Liquidity | lockedProtocol liquidity locked with no withdraw; outside liquidity refused, because the reserve buys on this pool |
Gas on Robinhood Chain runs around 0.02 gwei. The explorer is robinhoodchain.blockscout.com. Addresses are published here and on X at launch, nowhere else.
Cairn has no call of its own: the rule runs inside every swap. The app reads the figures from the hook by the view names below, the first name that answers for each, and the two views that take a level are called with the level as their argument. Each four byte selector is worked out in the browser by js/keccak.js, and the routine is checked against the known selector of transfer(address,uint256), which is 0xa9059cbb.
| What is read | Signature | Selector | Also tried |
|---|
No. Every swap lays one stone on the level its tick lands in, whatever its size and whatever its side. Only the toll grows with the size. Article 02.
Nothing. You pay the same toll as everybody, the whole reserve burns inside your swap, and the burn belongs to every holder.
Yes, at any moment, with any swap that lands on that level. The level is then closed for ever, whoever arrives next. It is said here in advance because it is the sharpest edge of the design.
No. There is no way to reopen a level and no setter that could. The market has to build somewhere else.
It pays its toll into the reserve, like every swap, and lays nothing.
Yes, by swapping on the same level again and again, paying every toll and every lot of gas. What it buys is a burn that belongs to everybody.
Its cairn stays where the crowd left it, at its true height, for ever. That is the scree, article 07.
Either Ethereum's block as the sequencer last read it, a step every 15 seconds, or the chain's own block, about a tenth of a second. The choice is made at gate 1 and published here. The ridge on the front page keeps its own block, one a second. Article 11.
It is real arithmetic on made up trades. It runs this law in full, on this site's own numbers, one block a second, so that a capstone can be watched. There is no contract yet.
The level width, the height and the toll, together, simulated on the chain's real swaps so that an ordinary month finishes a cairn or two and dust costs more than it is worth; and which clock the ridge records. All of it is published before anything is deployed.
published at launch
Explorer
Contract address published here and on X at launch, nowhere else. Anything claiming to be it anywhere else is not it.