Read a proof trail

What you’ll get

A cross-venue pair from the latest graph run, the ordered proof steps that relate its two contracts, and a decision: whether the lead priced on that pair could be filled at a profit when the books were read. On 2026-09-17 the only liquid cross-venue lead was a Brewers–Pirates total (Kalshi ↔ Polymarket, equivalent), proven in four steps and not executable at the prices on offer.

Prerequisites

An API key in ROUTEUR_API_KEY
Python 3 with requests

Find a cross-venue pair

Either start from the leads, which come with the depth check already done:

curl "https://api.routeur.app/v1/opportunities?cross_venue=true&limit=1" -H "X-API-Key: $ROUTEUR_API_KEY"

{
  "relation": "equivalent", "cross_venue": true,
  "left":  { "venue": "kalshi", "id": "KXMLBTOTAL-26SEP171235MILPIT-9", "title": "Over 8.5 runs scored",
             "quote": { "yes_ask_usd": "0.55", "no_ask_usd": "0.46" }, "volume_24h_usd": "16742.70", "liquidity": "tradeable" },
  "right": { "venue": "polymarket", "id": "mlb-mil-pit-2026-09-17-total-8pt5", "title": "Milwaukee Brewers vs. Pittsburgh Pirates: O/U 8.5",
             "quote": { "yes_ask_usd": "0.56", "no_ask_usd": "0.45" }, "volume_24h_usd": "1874.10", "liquidity": "tradeable" },
  "legs": [ { "side": "yes", "venue": "kalshi", "ask_usd": "0.54", "market_id": "KXMLBTOTAL-26SEP171235MILPIT-9" },
            { "side": "no", "venue": "polymarket", "ask_usd": "0.45", "market_id": "mlb-mil-pit-2026-09-17-total-8pt5" } ],
  "cost_usd": "0.99", "gross_edge_usd": "0.01", "estimated_fee_usd": "0.032375", "net_edge_usd": "-0.022375",
  "issues": [ "unverified: top-of-book depth is unknown; asks are discovery observations",
              "unverified: the covering payout assumes the event settles normally; postponement, cancellation and disputes settle differently across venues",
              "unverified: legs settle in USD and USDC; conversion and transfer costs are not priced" ],
  "depth": { "executable": false, "pairs": "0", "cost_usd": "0", "fees_usd": "0", "net_usd": "0",
             "limited_by": "price", "observed_at": "2026-09-17T12:10:12.831Z",
             "issues": [ "stale: leg books were read 23s apart" ] }
}

Or start from a market you already care about and ask for its relations to the other venue. Cross-venue relations come first:

curl "https://api.routeur.app/v1/markets/kalshi/KXMLBTOTAL-26SEP171235MILPIT-9/relations?cross_venue=true" \
  -H "X-API-Key: $ROUTEUR_API_KEY"

{ "relation": "equivalent", "cross_venue": true,
  "evidence": ["cross-venue: same mlb game scheduled 2026-09-17 ET, matched by team codes and team names; both settle on the game's final score; neither venue restricts periods; postponement and cancellation settle differently"],
  "market": { "venue": "polymarket", "id": "mlb-mil-pit-2026-09-17-total-8pt5", "liquidity": "tradeable", "quote": { "yes_ask_usd": "0.56", "no_ask_usd": "0.45" } } }
{ "relation": "implied_by", "cross_venue": true, "market": { "venue": "polymarket", "id": "mlb-mil-pit-2026-09-17-total-10pt5", "liquidity": "thin" } }
{ "relation": "implied_by", "cross_venue": true, "market": { "venue": "polymarket", "id": "mlb-mil-pit-2026-09-17-total-9pt5", "liquidity": "thin" } }

Fetch the proof

Either market may be given first; the trail is stated from the left one’s side.

curl "https://api.routeur.app/v1/relations/kalshi/KXMLBTOTAL-26SEP171235MILPIT-9/polymarket/mlb-mil-pit-2026-09-17-total-8pt5" \
  -H "X-API-Key: $ROUTEUR_API_KEY"

The steps and provenance, observed 2026-09-17 12:40 UTC (both contracts’ full terms are in left and right, left out here):

{
  "graph_run": 74,
  "data": {
    "relation": "equivalent", "graph_relation": "equivalent", "direction": "both_ways", "cross_venue": true,
    "left":  { "venue": "kalshi", "id": "KXMLBTOTAL-26SEP171235MILPIT-9", "rules_hash": "73562783085732ec…",
               "strike": { "type": "greater", "floor": "17/2" },
               "variable": "MLB total, Milwaukee vs Pittsburgh, 2026-09-17 ET", "interval": "(8.5, ∞)",
               "settlement": { "payout_currency": "USD", "scope": "the game's final score; neither venue restricts periods", "closes_at": "2026-09-20T16:35:00Z" } },
    "right": { "venue": "polymarket", "id": "mlb-mil-pit-2026-09-17-total-8pt5", "rules_hash": "0a6ca28b9b1edeea…",
               "strike": { "type": "greater", "floor": "17/2" },
               "variable": "MLB total, Milwaukee Brewers vs Pittsburgh Pirates, 2026-09-17 ET", "interval": "(8.5, ∞)",
               "settlement": { "payout_currency": "USDC", "scope": "the game's final score; neither venue restricts periods", "game_starts_at": "2026-09-17T16:35:00Z" } },
    "steps": [
      { "step": "game_quantity", "left": "MLB total, Milwaukee vs Pittsburgh, 2026-09-17 ET", "right": "MLB total, Milwaukee Brewers vs Pittsburgh Pirates, 2026-09-17 ET", "result": "same_kind" },
      { "step": "same_game", "detail": "cross-venue: same mlb game scheduled 2026-09-17 ET, matched by team codes and team names; both settle on the game's final score; neither venue restricts periods; postponement and cancellation settle differently", "result": "same" },
      { "step": "intervals", "left": "(8.5, ∞)", "right": "(8.5, ∞)", "result": "equivalent" },
      { "step": "conclusion", "relation": "equivalent" }
    ],
    "reproduced": true,
    "found_by":     { "id": 65, "graph_version": "contract-graph/v1", "finished_at": "2026-09-17T03:10:57.298293Z" },
    "confirmed_by": { "id": 74, "graph_version": "contract-graph/v1", "finished_at": "2026-09-17T12:10:36.937979Z" },
    "first_seen_at": "2026-09-17T03:10:57.298293Z", "last_confirmed_at": "2026-09-17T12:10:36.937979Z"
  }
}

Read the steps and decide

This script does all three: picks the first liquid cross-venue lead (or, when there is none, the first cross-venue relation of VENUE/MARKET_ID), prints the proof, and decides from depth.

Python

import os
import sys
import requests

API = "https://api.routeur.app"
session = requests.Session()
session.headers["X-API-Key"] = os.environ["ROUTEUR_API_KEY"]


def get(path, **params):
    res = session.get(f"{API}{path}", params=params, timeout=30)
    if res.status_code == 404:
        return None
    res.raise_for_status()
    return res.json()


# 1. Find a cross-venue pair. Prefer a lead, because it comes with the depth check.
lead = None
leads = get("/v1/opportunities", cross_venue="true", limit=10)["data"]      # booleans go as lowercase text
if leads:
    lead = leads[0]
    left, right = lead["left"], lead["right"]
else:
    # No liquid cross-venue lead right now: take the first cross-venue relation of a market you name.
    venue, market_id = os.environ["VENUE"], os.environ["MARKET_ID"]
    relations = get(f"/v1/markets/{venue}/{market_id}/relations", cross_venue="true", limit=1)["data"]
    if not relations:
        sys.exit("That market has no proven relation to the other venue.")
    left = {"venue": venue, "id": market_id}
    right = relations[0]["market"]

# 2. Fetch the proof.
proof = get(f"/v1/relations/{left['venue']}/{left['id']}/{right['venue']}/{right['id']}")
if proof is None:
    sys.exit("relation_not_found: the latest graph does not relate these contract versions any more.")
p, run = proof["data"], proof["graph_run"]

# 3. Read the steps.
print(f"{p['left']['title']!r} on {p['left']['venue']}  is {p['relation']}  {p['right']['title']!r} on {p['right']['venue']}")
print(f"direction {p['direction']} · found by run {p['found_by']['id']} · confirmed by run {p['confirmed_by']['id']} · reproduced: {p['reproduced']}")
print(f"  left  reads {p['left'].get('variable')} in {p['left'].get('interval')}, pays in {p['left']['settlement'].get('payout_currency')}")
print(f"  right reads {p['right'].get('variable')} in {p['right'].get('interval')}, pays in {p['right']['settlement'].get('payout_currency')}")
for i, step in enumerate(p["steps"], 1):
    parts = [f"{i}. {step['step']}"]
    if step.get("left"):
        parts.append(f"left={step['left']}")
    if step.get("right"):
        parts.append(f"right={step['right']}")
    if step.get("result"):
        parts.append(f"→ {step['result']}")
    if step.get("relation"):
        parts.append(f"→ {step['relation']}")
    print("  " + "  ".join(parts))
    if step.get("detail"):
        print(f"       {step['detail']}")

# 4. Decide whether it is executable.
if lead is None:
    print("\nNo lead is priced on this pair right now, so there is nothing to size.")
else:
    depth = lead.get("depth")
    print(f"\nLead: buy {lead['legs'][0]['side']} on {lead['legs'][0]['venue']} at {float(lead['legs'][0]['ask_usd']) * 100:.1f}¢ "
          f"+ {lead['legs'][1]['side']} on {lead['legs'][1]['venue']} at {float(lead['legs'][1]['ask_usd']) * 100:.1f}¢ "
          f"= {float(lead['cost_usd']) * 100:.1f}¢ for $1, net {float(lead['net_edge_usd']) * 100:+.1f}¢ after estimated fees (top of book)")
    if depth is None:
        print("Not sized against the books this run: treat as not executable.")
    elif depth["limited_by"] == "informational":
        print("Informational only: the venues could settle this differently, so it is never offered as executable.")
    elif depth["executable"]:
        print(f"Executable when the books were read at {depth['observed_at']}: {depth['pairs']} pairs for ${depth['cost_usd']}, "
              f"${depth['net_usd']} net after ${depth['fees_usd']} fees; growth stopped by {depth['limited_by']}.")
    else:
        print(f"Not executable at {depth['observed_at']}: {depth['pairs']} pairs would fill, net ${depth['net_usd']}; stopped by {depth['limited_by']}.")
    if not p["reproduced"]:
        print("Warning: the proof no longer reproduces from the stored contracts. Do not trade on it.")
    for issue in lead.get("issues") or []:
        print(f"  caveat: {issue}")

Output observed 2026-09-17 12:52 UTC:

'Over 8.5 runs scored' on kalshi  is equivalent  'Milwaukee Brewers vs. Pittsburgh Pirates: O/U 8.5' on polymarket
direction both_ways · found by run 65 · confirmed by run 74 · reproduced: True
  left  reads MLB total, Milwaukee vs Pittsburgh, 2026-09-17 ET in (8.5, ∞), pays in USD
  right reads MLB total, Milwaukee Brewers vs Pittsburgh Pirates, 2026-09-17 ET in (8.5, ∞), pays in USDC
  1. game_quantity  left=MLB total, Milwaukee vs Pittsburgh, 2026-09-17 ET  right=MLB total, Milwaukee Brewers vs Pittsburgh Pirates, 2026-09-17 ET  → same_kind
  2. same_game  → same
       cross-venue: same mlb game scheduled 2026-09-17 ET, matched by team codes and team names; both settle on the game's final score; neither venue restricts periods; postponement and cancellation settle differently
  3. intervals  left=(8.5, ∞)  right=(8.5, ∞)  → equivalent
  4. conclusion  → equivalent

Lead: buy yes on kalshi at 54.0¢ + no on polymarket at 45.0¢ = 99.0¢ for $1, net -2.2¢ after estimated fees (top of book)
Not executable at 2026-09-17T12:10:12.831Z: 0 pairs would fill, net $0; stopped by price.
  caveat: unverified: top-of-book depth is unknown; asks are discovery observations
  caveat: estimated: Kalshi standard 0.07 taker fee for one contract; series fee multipliers and rounding across quantities are not applied
  caveat: estimated: Polymarket taker fee rate * p * (1 - p) for one share, before rounding
  caveat: unverified: the covering payout assumes the event settles normally; postponement, cancellation and disputes settle differently across venues
  caveat: unverified: legs settle in USD and USDC; conversion and transfer costs are not priced

The proof holds; the prices do not pay. Yes at 54¢ plus No at 45¢ is 99¢ for a guaranteed $1, and 3.2¢ of estimated fees turn a 1¢ gross edge into a 2.2¢ loss.

Read the result

Field	Meaning
`relation`	From the left market’s side: `equivalent`, `implies`, `implied_by`, `contradicts` or `overlaps`. `graph_relation` is the same fact in the graph’s own terms (`subset`, `superset`).
`direction`	Which way the implication runs: `both_ways` for equivalent, `left_implies_right`, `right_implies_left`, `mutually_exclusive`, or `neither`.
`left.variable`, `left.interval`	What the proof read the contract as: the quantity it pays on, and the Yes range on it in interval notation over exact decimals. `(8.5, ∞)` is “more than 8.5”.
`left.settlement`	What settlement reads and what it pays in. `USD` on Kalshi, `USDC` on Polymarket.
`left.rules_hash`	The contract version the proof holds for. A rules change is a new version, and the proof must be found again.
`steps[]`	The proof, in order. `game_quantity` and `econ_quantity` establish both contracts pay on the same kind of thing; `same_game`, `same_event` and `same_variable` that it is the same instance; `orient_margin` flips a margin stated from the other team’s side; `intervals` compares the ranges; `mutually_exclusive` uses an event’s one-winner rule; `conclusion` states the result.
`reproduced`	Rebuilding the graph from the stored contract versions still yields this relation. When `false`, the steps end with `not_reproduced` and the recorded conclusion.
`found_by`, `confirmed_by`	The run that first proved it and the latest run that still lists both contract versions. Runs finish hourly.
`depth` (on the lead)	The lead sized against live books at `observed_at`: `executable` means at least one whole pair could be bought for less than it pays after fees and minimum sizes; `limited_by` names what stopped the fill growing: `price`, `depth`, `minimum`, `fees`, `unavailable` or `informational`.
`issues`	Caveats on the estimate. `unverified` ones are things the API cannot check; `estimated` ones are fee models; `stale` ones are timing.

Pitfalls

limited_by: informational is never executable, however good the numbers look. It means the relation rests on a settlement the venues could resolve differently: economic releases that get delayed or cancelled. Treat it as a note about prices, not a trade.
A proof is per contract version. When either venue edits its rules, the pair’s rules_hash changes and the next run must prove it again. Until then GET /v1/relations/… returns 404 relation_not_found: “the latest graph does not relate their current contract versions”. A relation that was there an hour ago and is gone now is worth reading as a warning, not a bug. See Rule-change watch.
depth.observed_at is the graph run’s time, not now. On 2026-09-17 it was 12:10 UTC for a request at 12:52. Books move; size again before you act, with Slippage at size.
Postponement settles differently. Every cross-venue evidence line says so. An equivalent pair is equivalent when the game is played; a rain-out can pay one leg and void the other.
cross_venue=True is a 400. Send cross_venue=true; requests encodes Python booleans with a capital letter.

Relations: the three steps behind every proof, and what each relation bounds.
Leads: how a two-leg purchase pays $1 in every outcome, and how fees are estimated.
Liquid opportunities: every lead, gap and strategy match, ranked by edge × volume.
Rule-change watch: know when a contract version changes under a proof.

​What you’ll get

​Prerequisites

​Read the result

​Pitfalls

​Related

What you’ll get

Prerequisites

Read the result

Pitfalls

Related