The law of the box.

01The box

A box is two numbers: an anchor and a half width, both in ticks. The anchor is the tick at which the last box opened. The half width is fixed at deployment and is the same for every box, for the whole life of the pool.

The price is inside its box while it is strictly between the two rules. A price on a rule has left: touching counts.

The box is drawn by a rule around a past price. It is not a signal, it does not predict anything, and this site never calls an opening a breakout.

02The crank

The crank counts the blocks since the box was drawn. Nothing runs and nothing is stored while it counts: the turns are computed from the block the box was drawn at, so a box that nobody touches for a day costs no gas for that day.

One block inside the box is one turn. A block in which the price leaves is not a turn: it is an opening.

03The stop

The crank stops counting at a fixed maximum, set at deployment. Past it the turns stay where they are, however long the quiet lasts, and the share stops growing with them.

The stop exists so that the largest possible burn is knowable in advance, from the cap of the curve, rather than from how long a market can sit still.

04The toll and the reserve

Every swap pays a toll, a fixed share of its size, the same for a buy and for a sell, set at deployment. The toll is the only income of this protocol.

It goes into the reserve. The reserve has one way in, the tolls, and one way out, the dead address, when a box opens. No owner, no withdrawal, no setter, no destination that can be changed.

05The share

The share of the reserve a box burns is a concave function of its turns, published as an exact integer formula. Zero at zero turns, exactly the cap at the maximum, and never the whole reserve.

share = cap × turns × (max + bend) ÷ ((turns + bend) × max), rounded down

Concave, so the second hour of quiet adds less than the first. The reserve and the share grow together during a long quiet stretch, which is why the burn at the end of one is large twice over. That is the product, and it is the reason the crank is worth watching.

The curve below is the toy's own, on this page's numbers: a cap of 50 %, a bend of 50 turns and a maximum of 100. The deployed ones are printed here at launch.

06The opening

At the end of every swap the hook compares the pool's tick with the box. If the tick is outside, the box opens in that transaction: the share buys $COIL on the pool and sends it to the dead address, the box counter goes up by one, and a new box is drawn around the tick at which the swap ended.

Not queued, not claimable, not announced. Done, in the block that left the box.

07The order inside it

The order of operations inside an opening matters, so it is written here:

1. The toll of the swap goes into the reserve.
2. The tick the swap ended on is read, before anything of ours moves the price.
3. That tick is compared with the box.
4. If it is outside, the turns are counted, the share of the reserve is bought and burned.
5. The new box is drawn around that same tick, not around where our own buy left the price.

Otherwise the protocol's buy would move its own anchor, and a burn could open the next box by itself.

08Up and down are the same

A box that opens upward and a box that opens downward burn the same share for the same turns. The direction is recorded and changes nothing.

This site never colours the two differently, and the toy leaves each way out to a coin toss.

09Nobody is paid

The swap that leaves the box pays the same toll as any other and receives nothing. No finder's fee, no rebate, no share of the reserve, no rank in a table.

It is not a prize, so it is not a race, so there is nothing for a sequencer to sell. The team's share of the toll, of the reserve and of anything else this protocol touches is none.

10No owner, no setter

There is no withdrawal from the reserve, no destination that can be set, no pause, and no setter on the half width, the maximum turns, the curve or its cap.

What the contract cannot do is the point. A reserve that has been filling for a week is only worth watching if nobody, including us, can reach into it.

11Rounding

• Tolls round up. A toll is never short by a fraction of the smallest denomination.
• The share rounds down. A box never burns more than the curve says.
• Dust burns. What rounding leaves in the reserve stays in the reserve, for the next box.

12What the contracts enforce

13What can go wrong

1. Somebody opens the box on purpose. They can, at the cost of the toll and of the price impact of moving the pool by half a box, and what they get is a burn that belongs to everybody. After a long quiet stretch it is even likely.
   Half a box, for the toll and the price impact
2. A wick outside, and the arbitrage that brings it back. The box opened; that is the rule. The new box is drawn where the swap ended, and the price coming back leaves that new box too if the wick was long enough, with a crank of a few blocks and a share near zero. It is stated rather than papered over with a confirmation delay that would make the rule harder to say.
3. The half width is wrong. Too wide and the lid never opens; too narrow and it never stays shut long enough to matter. It is the one number that decides whether there is a product, and it is simulated on real traces before it is set.
4. A dead market. The crank reaches its maximum and stops, the reserve sits full, nothing burns. It is the honest failure state, which is why this site shows the turns and the reserve and not only the total burned.
   Stopped at its maximum · nothing burns
5. Somebody reads the box as a signal. It is not one. The box counts how long nothing happened.
   It counts how long nothing happened

14Parameters and venue