What on-chain prices actually do
Three measurements of machinery that decides money, each carried out against the chain itself rather than against a description of it.
Every number printed in these papers is produced by the same run that checks it, and the input hashes are stamped into the output, so a reader can tell whether their copy of the data is the one the tables came from. Where a claim did not survive the measurement, the paper says so and keeps the measurement.
Making simulation affordable on chain
Every on-chain option protocol prices with a closed form, because simulation costs too much to run inside a call. That choice is paid for twice: a payoff with no closed form cannot be quoted at all, and the volatility a closed form needs has to be imported from off chain or agreed by a vote. This measures where a simulated quote spends its gas and removes most of it.
The term a Monte Carlo engine drops
A simulated price walks in steps of one fixed size. Real steps are not one fixed size. Fitting every statistic per ticker on nine equities, the direction of a move carries nothing and its size carries a great deal, and pricing the same contracts over a process that has that property moves them.
The Reynolds number of an on-chain price
An oracle holds still until the price has travelled a fixed distance. In a calm market nobody notices. Comparing what the chain was saying against the tape, minute by minute, the departures concentrate where the market is moving faster than the oracle can follow.