How Geometric Brownian Motion Makes Catapult the Fairest Market in Crypto

There is a famous quote attributed to various mathematicians: ‘God does not play dice.’ Whether or not that is true of the universe, Catapult.trade plays dice — and it is transparent about every roll.

Geometric Brownian Motion (GBM) is the stochastic process that Catapult uses to generate every chart on the platform. To understand why GBM makes markets fair, you need to understand three things about it: what it is, why it cannot be rigged, and why it produces 0% house edge.

GBM is defined by two parameters: drift (mu) and volatility (sigma). In mathematical notation: dS = muSdt + sigmaSdW, where dW is a Wiener process (Brownian motion). Drift is the deterministic trend component. Volatility is the random component. The Wiener process is what makes it genuinely random — it draws from a standard normal distribution at each infinitesimally small time step.

On Catapult, the parameters for each chart are set at creation and visible to all traders. The drift and volatility values are public. What is not known — and cannot be known before the session starts — is the specific path the Wiener process will trace. That path is determined by the random seed, which is cryptographically committed before session start and revealed afterward.

Why can GBM not be rigged Because the random seed is committed to the blockchain before the chart is visible to any participant, including the Catapult team. No one can see the seed, predict the path, or front-run the chart. The commitment scheme uses a standard hash function — you can verify the pre-commitment yourself by checking the on-chain transaction timestamp against the session start time.

Why does GBM produce 0% house edge A GBM process with zero drift is a martingale. By definition, the expected value of a martingale at any future time, given all current information, is equal to its current value. This means: if you have to bet on whether a zero-drift GBM will be higher or lower in 5 minutes, the fair price for both bets is exactly 50 cents on the dollar. No structural advantage for either side.

Catapult charts typically use small non-zero drift values (the drift parameters are disclosed per chart). Even with drift, the edge on direction is negligible compared to a standard casino or a traditional crypto exchange where market makers have millisecond advantages.

The comparison to pump.fun is instructive. On pump.fun, token launches have insiders who can purchase before the token is publicly visible. On AMM platforms, sandwich bots extract value on every significant trade. On centralized exchanges, market makers have co-located servers with microsecond latency advantages. On Catapult, none of these advantages exist — because the price path is not known to anyone until it is generated live in your browser.

This is why the CEO says: ‘Brother this is GBM. Look it up.’ It is not a meme. It is a mathematical guarantee.