# Polymarket's Up-or-Down Crypto Markets: 60% of Its Trades, Priced About Right, 1.6% Fee

Publication scope revised on 28 October 2026; body SHA-256: `20ee3c171df607429d2c6ec6da32b7dcac5db1a22ff35915bbda57d3fc11649f`.

The original selected arithmetic or conditional formulas are retained for the remaining Polymarket analysis. No new source observations or new formal-verification run are claimed.

- The asset-level displayed shares account for the stated 59.6% of all observed trades. (`polymarket_bitcoin_up_or_down_5_minute_markets_1`; arithmetic).
- The duration-level displayed shares total 59.54%, retaining their own rounding precision. (`polymarket_bitcoin_up_or_down_5_minute_markets_2`; arithmetic).
- Displayed Share of trades values lie between 0 and 100 in share-by-interval-chart. (`polymarket_bitcoin_up_or_down_5_minute_markets_3`; displayed-value-domain).
- Displayed Share of notional values lie between 0 and 100 in share-by-interval-chart. (`polymarket_bitcoin_up_or_down_5_minute_markets_4`; displayed-value-domain).
- Displayed Share of all trades values lie between 0 and 100 in bitcoin-chart. (`polymarket_bitcoin_up_or_down_5_minute_markets_5`; displayed-value-domain).
- Displayed Up-or-down share of trades values lie between 0 and 100 in when-chart. (`polymarket_bitcoin_up_or_down_5_minute_markets_6`; displayed-value-domain).
- Displayed How often Up won values lie between 0 and 100 in calibration-chart. (`polymarket_bitcoin_up_or_down_5_minute_markets_7`; displayed-value-domain).
- Displayed Average price of Up values lie between 0 and 100 in calibration-chart. (`polymarket_bitcoin_up_or_down_5_minute_markets_8`; displayed-value-domain).

Outside the proof:

- Authenticity, completeness and accuracy of source observations.
- Data collection, sampling, classification, bootstrap intervals and causal inference.
- Current prices, policy, legal status, allegations, product claims and future outcomes.
- Production code correctness, execution, available liquidity and profitability.

[Selected Lean calculations](../LibraryChecks.lean). [Mathematical definitions](../ResearchModels.lean). [About this public subset](../README.md).