{"uid":"cap_P4JLjCcQ7pzr1-TZVp3JE","slug":"alternating-integer-matrix-signed-pfaffian-verifier-57988a4c","name":"Alternating Integer Matrix Signed Pfaffian Verifier","description":"Verify the exact signed Pfaffian of an entire supplied even alternating matrix.","url":"https://detect.halowerk.com/v1/F-REST-B15/alternating-integer-matrix-signed-pfaffian?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["pfaffian"],"properties":{"pfaffian":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["matrix"],"properties":{"matrix":{"type":"array","items":{"type":"array","items":{"type":"integer","maximum":100,"minimum":-100},"maxItems":8,"minItems":1},"maxItems":8,"minItems":1}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_hETG1VuWcVfUc-X6A8aIM","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Verifies the exact signed Pfaffian of a supplied even alternating (skew-symmetric) integer matrix against a claimed value.","exampleAgentPrompt":"Can you verify whether the signed Pfaffian of this 4x4 alternating integer matrix [[0,2,-3,1],[-2,0,4,-1],[3,-4,0,2],[-1,1,-2,0]] matches my claimed Pfaffian value of -10?","exampleUseCases":[{"title":"Verify Pfaffian in numerical algorithm","prompt":"I have a skew-symmetric 6x6 integer matrix from my simulation and I computed a Pfaffian of 48 — can you verify that's the correct signed Pfaffian for the matrix [[0,1,-2,3,-1,2],[-1,0,4,-2,1,-3],[2,-4,0,1,-2,1],[-3,2,-1,0,3,-2],[1,-1,2,-3,0,4],[-2,3,-1,2,-4,0]]?"},{"title":"Cross-check student Pfaffian homework","prompt":"My student claims the signed Pfaffian of the alternating matrix [[0,3,-1,2],[-3,0,2,-1],[1,-2,0,4],[-2,1,-4,0]] is -10. Can you check if that's correct?"},{"title":"Validate cryptographic or combinatorial proof step","prompt":"As part of my proof I need to confirm the exact signed Pfaffian of a 2x2 alternating matrix [[0,5],[-5,0]] equals 5 — can you verify that claim?"}],"resultDescription":"Returns whether the claimed signed Pfaffian matches the exactly computed Pfaffian of the supplied alternating integer matrix, along with the correct signed Pfaffian value.","failureModes":["Matrix is not square or not even-dimensional — Pfaffian is undefined","Matrix is not properly skew-symmetric (alternating) — invalid input","Matrix dimensions exceed 8x8 or are below 1x1 — schema violation","Integer values outside the allowed range [-100, 100] — schema rejection","Missing required fields 'matrix' or 'claim' — request rejected","Non-integer matrix entries — type validation failure"],"whenToPreferThis":"Use this endpoint when you need an authoritative, exact verification of a signed Pfaffian for a small (up to 8x8) alternating integer matrix with bounded entries. Prefer it over general-purpose linear algebra libraries when you want an independent signed Pfaffian check against a pre-computed claim, especially in proof-verification, homework checking, or algorithm validation contexts.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:41:28.026Z","isFirstParty":false,"canonicalSlug":"alternating-integer-matrix-signed-pfaffian-verifier-57988a4c"}