> ## Documentation Index
> Fetch the complete documentation index at: https://docs.routeur.app/llms.txt
> Use this file to discover all available pages before exploring further.

# Relations

> What it means for two markets to be proven related.

A relation says how two markets' outcomes constrain each other. Routeur only states one when it follows from both contracts' structured terms and exact arithmetic; wording is never enough, and ambiguous or conflicting evidence is withheld.

## Kinds

Read from the market you asked about:

| Relation      | Meaning                                                           |
| ------------- | ----------------------------------------------------------------- |
| `implies`     | If this market resolves Yes, the other one does too.              |
| `implied_by`  | If the other market resolves Yes, this one does.                  |
| `equivalent`  | Both resolve the same way in every outcome.                       |
| `contradicts` | Both cannot resolve Yes.                                          |
| `overlaps`    | Their outcome sets intersect without either containing the other. |

Lists of opportunities state relations from the left market's side, as `equivalent`, `subset`, `superset`, `contradicts` or `overlaps`.

## How a relation is proven

<Steps>
  <Step title="Same variable">
    Both markets must measure the same real-world quantity with the same settlement scope: the same game and team, the same data series, the same event.
  </Step>

  <Step title="Outcome sets">
    Each market's Yes is turned into a set of outcomes, such as "the 49ers score more than 10.5 points", which is the interval (10.5, ∞).
  </Step>

  <Step title="Compare exactly">
    The sets are compared with exact rationals. (10.5, ∞) sits inside (3.5, ∞), so "over 10.5" implies "over 3.5".
  </Step>
</Steps>

One-winner events add exclusions between their outcomes, and matched games across venues add equivalences.

## Reading relations

```bash theme={null}
curl "https://api.routeur.app/v1/markets/$VENUE/$MARKET_ID/relations?relation=implies&cross_venue=true" \
  -H "X-API-Key: $ROUTEUR_API_KEY"
```

<Tip>
  A relation is a constraint on prices. If a market implies another, its Yes should never cost more than the other's Yes. When it does, there is a [lead](/concepts/leads).
</Tip>