The instrument reads pool reserve accounts. It does not read a price feed, an oracle, an indexer, or a third party endpoint that reports what a price was. It requests the raw account data, decodes the two reserve amounts, and forms the mid price itself from their ratio.
This is slower and it fails more often than reading a feed would. It is done this way because a feed is a claim about the state of the chain, and a reserve account is the state of the chain. When the two disagree the instrument would have no way to know, so it declines to hold the second one.
Every quantity on this site is computed over a window of two hundred and fifty six slots, which is somewhere near two minutes depending on how the network is behaving. The window slides forward on every read and nothing outside it contributes to anything.
The length was chosen once, before deployment, and it will not be tuned. A shorter window would make the drive twitch on single trades. A longer one would smooth away the thing the instrument exists to observe. Two hundred and fifty six sits between those failures rather than avoiding either, and the honest description of it is a compromise that was fixed early so that it could not later be fitted to whatever produced the nicest looking output.
Two quantities are formed from the window. The first is the realised variance of the log price, being the sum of squared log returns over the window divided by one less than the number of samples in it.
The second is the turnover, being the quote volume that crossed the pool during the window divided by the quote reserve standing at its close.
Neither carries a unit. Both are bounded below by zero. Neither is informative on its own: a pool can be violently variable on almost no volume, and it can turn over its entire reserve without the price moving at all. The product is what has meaning, because it describes movement that was paid for.
The drive is that product under a square root, passed through a bounded map.
The constant κ was fixed before deployment and there is no instruction anywhere in the program that edits it. The map is monotone, so a larger product always produces a larger c and never the reverse. The range is closed at both ends. c cannot fall below two nor rise above five point seven, whatever the market does, which means no read however extreme can push the parameter somewhere the system was not examined.
The parameter is fed to a system of three equations written down by Otto Rössler in 1976. Two of them are linear. The third contains one product of two variables and that product is the entire source of the behaviour.
With a and b held at two tenths, c decides how far the orbit is allowed to widen before the nonlinear term catches it and throws it back toward the centre. At low c the orbit closes after one turn. Raised, it needs two, then four, then eight. The intervals between those doublings shrink by very nearly a constant factor, so they accumulate at a finite value rather than continuing forever.
These boundaries are computed from the system. They were not chosen, they cannot be moved, and they would be the same numbers if this instrument had never been built.
What the instrument reports is the band, which is the number of distinct turns the orbit currently requires before it returns to where it started, and the position within it, which is which of those turns has just closed.
A band of one means the market is settling into a single repeating state. A band of two means it is alternating between two. A band of four means four. The number is a count, not a magnitude, and a higher count is not a worse condition or a better one.
Past the accumulation point no finite count is correct. The instrument reports a dash there. It does not report a large number, it does not report zero, and it does not report the last count that happened to be valid.
Reads fail. The endpoint drops them, the account is unavailable, the response arrives malformed, or it arrives too late to belong to the window it was requested for. When that happens the cycle is skipped and recorded as a gap.
A gap is never retried and the missing slot is never filled in afterwards. A read performed later is a different measurement to the one that was missed, and treating the two as interchangeable would make every figure on this site slightly untrue in a way that could not be detected from the outside. The gaps stay.
When a read fails the figure does not clear. It holds the last trajectory it drew, the affected values render as dashes, and nothing on the page announces an error. A stalled instrument and a still market look almost the same here, which is a real limitation and is stated rather than designed around.
There is no instruction that edits the window, the constant, the band boundaries, or the parameters a and b. There is no pause. There is no upgrade authority; it was burned at deployment. There is no operator with discretion over any figure that appears on this site.
The cycle is permissionless and anyone may crank it. If nobody does, the record simply stops advancing. That is a pause and not a loss, and the state it pauses in is the last one that was actually measured.
Nothing here reverses.
In 1976 Otto Rössler wrote down a system of three equations with a single nonlinear term in it. He was not modelling anything. He was asking how little structure a system needs before it stops repeating itself, and the answer turned out to be one product of two variables. Everything else in the system is a straight line. The whole of the behaviour comes from that one term switching on when the orbit gets far enough out.
The shape it produces is a flat spiral that widens until it reaches a threshold, at which point it is lifted, folded over, and dropped back near the centre. The lifting is the nonlinear term. The dropping back is why the orbit never leaves. A trajectory can wander for a long time and still be bounded, which is the property that makes the system worth borrowing.
There is one parameter that matters. Call it c. It sets how far the spiral is allowed to widen before the fold catches it. At low c the orbit closes after a single turn and repeats forever. Raise it and the orbit needs two turns to close, then four, then eight. The doublings come faster and faster and accumulate at a finite value, past which the orbit never closes at all. This is not a metaphor for anything. It is a property of the equations that can be computed to as many digits as anyone cares to.
whorl measures c from a market and reports where on that route the market currently sits. It reads pool reserves directly, over a window of two hundred and fifty six slots, and forms two quantities: how much the log price moved, and how much of the reserve turned over while it moved. Those combine into a single bounded drive, and the drive maps onto c. Nothing is fitted. There are no free parameters after genesis and no model is being trained.
What the instrument then says is narrow and it is worth stating what it excludes. It does not say the price will rise or fall. It does not say a move is coming. It says how many distinct turns the system currently requires before it returns to where it started, and it says how far the drive sits from the next doubling. A band of two means the market is currently alternating between two states rather than settling into one. A band of four means it is alternating between four. Past the accumulation point it means the count has failed and the instrument says so.
The count fails often. This is the honest part. Real reserves are noisy, reads drop, and the window is short enough that a single large trade can move the drive more than a day of ordinary activity. When a read fails the cycle is logged as a gap and skipped. It is never retried and the missing slot is never filled in afterwards, because a backfilled read is not the same measurement as the one that was missed and pretending otherwise would make the log worth less than nothing.
The figure to the left is redrawn every cycle at the measured c. The three faint traces behind it are the three cycles before, holding their shape as they fade. When the market is still they lie on top of one another and the figure looks like a single clean line. When the drive is moving they separate, and the separation is the only thing on this page that constitutes a signal.
The program is immutable and the upgrade authority is burned. The cycle is permissionless and anyone may crank it. If nobody does, the log simply stops advancing, which is a pause rather than a failure. Nothing here reverses.