Let each complete draw ask whether the stream still looks like itself.

Conformal surprise and betting capital

For every prefix, each draw receives the permutation-equivariant score

$a_i=1-\frac{1}{t-1}\sum_{j\ne i}\exp(-\gamma|S_i\triangle S_j|).$

The newest score is ranked among all scores in that prefix. Random tie-breaking turns the rank into a conformal p-value $p_t$. Under exchangeability these p-values are uniform, without specifying the draw distribution.

For a fixed $0<\epsilon<1$, $\epsilon p_t^{\epsilon-1}$ is a betting factor. Products of those factors form a test martingale. The watch averages three predeclared martingales, so Ville's inequality makes a 20× crossing an anytime-valid 5% alarm.

A monitor that does not need to name the fault first

Frequency tests look for frequency faults; drift windows look for a chosen kind of boundary. Conformal monitoring asks a broader question: does the newest complete object still exchange places naturally with those before it?

That makes it useful as a smoke alarm. It can justify investigation, but the same evidence cannot diagnose the fire. The construction follows research on conformal test martingales.