Horizon Contracts: Quoting Binary Claims by Strike

Prediction markets usually fix a question and let its price float, so one number becomes many thin markets, most of them priced far from 50¢. We describe the horizon contract, which inverts the quote: a binary contract on a number pays a fixed 2×, and the order book sets the strike, so every contract trades at 50/50. We give a formal definition and three results. The value of a forecast edge is greatest at the median, where a horizon contract always trades. With risk-neutral, budget-constrained traders, the clearing strike is the budget-weighted median of their medians. And a market maker's filled round trip cannot lose: it pays twice its size if the number finishes inside the spread. We report a one-day survey of 173 prices on Polymarket and Kalshi, of which 98 sat under 10¢ or over 90¢ and 5 sat between 40¢ and 60¢, and we set out the design's limits. No real-money evidence exists yet. Specification and reference code: github.com/PlathsOven/horizon-contracts. Guide: rizon.markets/horizon-contracts.