Opening a position

Three continuous knobs shape every corridor: how far you lean it, how far apart the rails sit, and how long you commit. Then you take a side, and its multiplier, the inverse of that outcome, is final the moment the entry locks.

The shape you draw

A line is a band on the live price with four parts: a centre, a half-width, a slope, and a start and end. The entry price fixes the centre when your position locks, and the rails track it as it leans.

centre(t) = entry * exp( angle * span * t )
rails     = centre(t) * exp( +/- width * span )

t runs from 0 at open to 1 at the end of the run.

Angle, width, duration

Angle tilts the corridor up or down and carries your read on the trend. Width sets how far the rails sit from the centre, measured in span, the asset's own volatility unit. Duration is how long it runs. Together they set one number, the probability the corridor holds to the end, and that number prices both sides. Tighter, steeper and longer are all harder to hold, so hold pays more and breach pays less.

Span, the volatility unit

Width and angle are measured in span, the typical size of a move for that asset over a run of that length. Span is what makes a 2x corridor the same difficulty on Bitcoin as on Tesla. A plain square-root-of-time estimate would make duration cosmetic, because the band and the price diffusion would grow at exactly the same rate, so the estimate is damped:

span = sigma_hour * duration^0.44

A 24h corridor at the same width is about 24% tighter in effective terms than a 10m one. Span only sizes your corridor at open, and freezes into your rails from there. It never decides who wins. The price against your rails does.

Your multiplier

The operator reads the asset's live volatility and the exact shape you drew, then computes P, the probability the corridor holds to the end. That is the chance a price path with drift never touches either rail, a double-barrier first-passage problem. The solution is the spectral expansion of the heat equation on the band with absorbing boundaries:

P = (2/L) * e^(-b*x0 - mu^2*T / 2*sigma^2)
    * SUM_n sin(n*pi*x0/L) * e^(-n^2*pi^2*sigma^2*T / 2*L^2)
            * k * [1 - (-1)^n * e^(b*L)] / (b^2 + k^2)

L  = the full band height in log space
x0 = the entry offset inside the band
mu = drift of the price relative to the corridor centre
k  = n*pi/L,   b = mu/sigma^2

Each side's multiplier is the inverse of its own outcome, less a published spread:

Hold:   M = (1 - d) / P
Breach: M = (1 - d) / (1 - P)

d is the published spread, 3.5%, identical on both sides.

A ceiling caps M so the backstop stays solvent. The spread sits beside the odds and never inside them, so anyone can recompute your multiplier from the signed inputs. The same P prices both sides of your corridor, which is why you can take either one. As a rough anchor, a 25% chance of holding pays about 3.9x on hold.

Your entry locks, you do not choose it

Opening is a request rather than an instant fill. Your deposit and signed quote go onchain, and the position activates only once it locks to a signed price report covering your timestamp. Neither you nor the operator picks the entry price: the report does. Your multiplier fixes at that moment and nothing about the deal changes afterward.

The open fee, the greater of 0.8% of your deposit and 0.5 $HOLD, comes out of the deposit at open whether you win or lose. What remains is your stake, the amount every payout formula multiplies.