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Finite Matroid Independence Family Axioms Verifier
x402
Finite Matroid Independence Family Axioms Verifier is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).
Validates whether a fully-specified finite independent family satisfies all three matroid axioms (empty set, hereditary, augmentation), reporting any violations.
Price / call$0.003
Success—
StatusUnknown
How this service works
Prüft eine vollständig gelieferte endliche Unabhängigkeitsfamilie gegen die drei Matroidaxiome, einschließlich Austauschfehlern, Schleifen und leerer Grundmenge; bestätigt keine bloße Stichprobe und berechnet keinen greedy Lösungsweg.
Output
Returns a structured validation report confirming or refuting each of the three matroid axioms (empty set, hereditary closure, augmentation/exchange), cross-checked against the caller's claims about ground element count, independent set count, maximum cardinality, and overall matroid status. Violations are flagged with specifics (e.g. exchange errors, missing empty set, non-hereditary subsets).
Example use cases
Catching augmentation axiom failure
“I have a ground set ['x','y','z'] and independent sets [[], [0], [1], [0,1], [0,2]] — my claims say augmentation is true and it's a matroid, but can you verify all three matroid axioms and tell me if the augmentation property actually holds?”
Verifying student-submitted matroid homework
“My student submitted a matroid with ground set ['e1','e2','e3','e4'] and independent families [[], [0], [1], [2], [0,1], [1,2], [0,1,2]], claiming 4 ground elements, 7 independent sets, maximum cardinality 3, hereditary true, augmentation true, empty set present, and is_matroid true — please validate all three matroid axioms and confirm or refute their claims.”
Detecting loops in combinatorial structure
“I built a set system over ground set ['p','q','r'] with independent sets [[], [1], [2], [1,2]] and I claim hereditary=true, augmentation=false, empty_set_present=true, is_matroid=false, 3 ground elements, 4 independent sets, max cardinality 2 — run the full matroid axiom check and tell me if there are any loops or hereditary violations.”
Technical details
Endpoint
POSThttps://detect.halowerk.com/v1/F-B-NIGHT-MATROID_INDEPENDENCE_AXIOMS/finite-matroid-independent-family-axioms?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need to definitively verify whether a fully enumerated finite independent family satisfies all three matroid axioms, especially when you want to detect subtle violations like missing empty set, non-hereditary subsets, or augmentation failures. It is not suitable for sampling-based checks, greedy algorithm computation, or matroid optimization — it only validates axiom compliance on a complete, explicitly provided independent family up to 16 elements and 256 sets.
Side effects
- Input ground_set has duplicate elements (schema requires uniqueItems)
- Independent set references index out of range for ground_set size (index >= ground_set.length)
- ground_set exceeds 16 elements or independent_sets exceeds 256 entries
- claims counts do not match actual sizes (ground_elements or independent_sets mismatch)
- Malformed or missing required fields in artifact or claims objects
- Payment failure or x402 protocol error resulting in 402 response
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| artifact | object |
Tags
x402
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