Abstract
The $tôkEx is an automated market mechanism for the continuous exchange of two fungible assets at a single fair price given in closed form — with no order book, no counterparty matching, and no liquidity pool.
Unlike a continuous double auction, a constant-function automated market maker (AMM), or a scoring-rule market maker, the $tôkEx elicits each participant's belief directly: they declare only an estimate of the two assets' relative value and a degree of confidence, from which a personal "trading robot" continuously buys low and sells high on their behalf. Every robot trades at velocities set by a shared trader function f(x) = x² − 1/x and a confidence weight w(θ) = (1/3)·tan(πθ/200%), where x is the ratio of the market price to the participant's estimate. The market price is the unique positive price that clears both assets simultaneously, and from an outsider's view the whole market is provably indistinguishable from a single aggregate participant. The market state advances exactly, event by event, with O(N log N) updates.
This defensive publication discloses the algorithm, its closed-form market price, the complete admissible family of trader functions, and machine-checked (Lean 4 / mathlib) proofs of its central results.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Tousignant, Maxime, "The $tôkEx Algorithm", Technical Disclosure Commons, ()
https://www.tdcommons.org/dpubs_series/12534