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coprocesseur-deterministe — Great-Circle Distance (Haversine)
x402
coprocesseur-deterministe — Great-Circle Distance (Haversine) is a paid API for AI agents from x402.laboiteatubes.media, paid per call via x402, $0.001/call, status unknown (last checked 2026-10-13).
Computes the great-circle (orthodromic) distance between two geographic coordinates using the Haversine formula on a spherical Earth model, returning distance in km, m, and nautical miles, initial bearing, central angle, and a verifiable SHA-256 proof.
Price / call$0.001
Success—
StatusUnknown
How this service works
Trois calculs déterministes destinés aux agents IA : amortissement de prêt, distance orthodromique, conversion d'unités. Chaque réponse porte son résultat, la formule appliquée, ses limites, et une empreinte SHA-256 recalculable — la chaîne exacte qui a été hachée est renvoyée avec, et `POST /verifier` permet de la contrôler gratuitement. Un même appel rend toujours la même empreinte : l'horodatage est exclu du hachage. Le paiement suit le protocole x402 (version 2), en USDC sur Base.
Output
A JSON object containing: distance in metres, kilometres, and nautical miles; the central angle in radians; the initial azimuth/bearing in degrees; the applied Haversine formula expression with variable definitions; a SHA-256 proof block with the exact canonical string that was hashed (recursively sorted JSON keys, no spaces) and the fields covered — allowing independent verification that the result has not changed.
Example use cases
Flight planning distance check
“What's the great-circle distance from London Heathrow (51.4775°N, 0.4614°W) to New York JFK (40.6413°N, 73.7781°W)? Give me the result in kilometres, nautical miles, and the initial bearing, with a verifiable fingerprint.”
Delivery radius eligibility
“Can you calculate the surface distance between our warehouse at 48.8566°N, 2.3522°E and a customer at 48.6921°N, 6.1844°E so I can check whether they fall within our 300 km delivery zone? I want the result in metres and kilometres.”
Maritime route estimation
“I need the orthodromic distance and initial compass bearing from Cape Town (33.9249°S, 18.4241°E) to Buenos Aires (34.6037°S, 58.3816°W) in kilometres and nautical miles, plus a SHA-256 proof hash so I can confirm the calculation is deterministic.”
Technical details
Endpoint
GEThttps://x402.laboiteatubes.media/distance?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need a deterministic, auditable great-circle distance computation whose result can be independently verified via the included SHA-256 proof. It is ideal for AI agents and automated pipelines that require reproducible, provenance-tracked geographic calculations at low cost ($0.001 USDC). Use it when accuracy within ~0.3–0.5% (spherical vs ellipsoidal) is acceptable. Prefer an ellipsoidal (Vincenty/WGS84) service instead when sub-millimetre geodetic precision is required. Sibling endpoints on the same service cover loan amortisation and unit conversion under the same verifiable proof pattern.
Side effects
- Missing required query parameter (lat1, lon1, lat2, or lon2) — returns 400 Bad Request
- Latitude out of range [-90, 90] or longitude out of range [-180, 180] — returns 400 validation error
- Payment not included or insufficient (x402 protocol) — returns 402 Payment Required
- Identical input points return distance 0 and undefined azimuth
- Antipodal or near-antipodal points may have numerically unstable azimuth values
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Output
Schema · Response
{
"type": "json",
"example": {
"notes": [
"Modèle SPHÉRIQUE : l'écart avec un calcul ellipsoïdal (Vincenty / WGS84) atteint typiquement 0,3 à 0,5 %. Pour du géodésique de précision, ce service n'est pas le bon outil.",
"L'altitude n'est pas prise en compte : c'est une distance au niveau de la sphère de référence.",
"L'azimut renvoyé est le cap INITIAL ; il varie le long d'un grand cercle."
],
"preuve": {
"note": "L'horodatage `calcule_le` est volontairement exclu de l'empreinte.",
"empreinte": "7052442400f9fd1c636e78e5d88ab34ccb7cf9ada9406209a860bf33096aa8e2",
"algorithme": "SHA-256",
"chaine_hachee": "{\"entrees\":{\"lat1\":48.8566,\"lat2\":45.764,\"lon1\":2.3522,\"lon2\":4.8357,\"rayon_terre_m\":6371008.8},\"formule_expression\":\"a = sin²(Δφ/2) + cos φ₁ · cos φ₂ · sin²(Δλ/2) ; c = 2·atan2(√a, √(1−a)) ; d = R·c\",\"operation\":\"distance\",\"resultat\":{\"angle_central_rad\":0.061450154085,\"azimut_initial_deg\":150.5125,\"distance_km\":391.499472,\"distance_m\":391499.472,\"distance_mille_nautique\":211.392804},\"version_formule\":\"haversine@1.0.0\"}",
"champs_couverts": [
"operation",
"version_formule",
"entrees",
"resultat",
"formule_expression"
],
"canonicalisation": "JSON à clés triées récursivement, sans espace, encodé en UTF-8"
},
"entrees": {
"lat1": 48.8566,
"lat2": 45.764,
"lon1": 2.3522,
"lon2": 4.8357,
"rayon_terre_m": 6371008.8
},
"formule": {
"reference": "R. W. Sinnott, « Virtues of the Haversine », Sky & Telescope, 1984.",
"variables": {
"R": "rayon terrestre moyen, 6371008.8 m",
"d": "distance orthodromique en mètres",
"Δφ, Δλ": "différences de latitude et de longitude, en radians",
"φ₁, φ₂": "latitudes des deux points, en radians"
},
"expression": "a = sin²(Δφ/2) + cos φ₁ · cos φ₂ · sin²(Δλ/2) ; c = 2·atan2(√a, √(1−a)) ; d = R·c",
"description": "Formule de haversine : distance sur un modèle sphérique de la Terre, le long du grand cercle."
},
"service": "coprocesseur-deterministe",
"resultat": {
"distance_m": 391499.472,
"distance_km": 391.499472,
"angle_central_rad": 0.061450154085,
"azimut_initial_deg": 150.5125,
"distance_mille_nautique": 211.392804
},
"operation": "distance",
"calcule_le": "2026-08-16T08:29:39.318Z",
"version_formule": "haversine@1.0.0",
"version_service": "1.0.0"
}
}Tags
x402
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