{"uid":"cap_qz2ORLwYnncIEpJup8fzF","slug":"modular-phase-intersection-validator-f73d500f","name":"Modular Phase Intersection Validator","description":"An agent that joins independently phased integer tick schedules needs its claimed first common tick and repeating period checked with noncoprime moduli.","url":"https://detect.halowerk.com/v1/workflow/workflow-modular-phase-intersection?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["congruences","claimed_first","claimed_period"],"properties":{"congruences":{"type":"array","items":{"type":"object","required":["residue","modulus"],"properties":{"modulus":{"type":"integer","maximum":1000000,"minimum":1},"residue":{"type":"integer","maximum":999999,"minimum":0}},"additionalProperties":false},"maxItems":32,"minItems":1},"claimed_first":{"type":"integer","maximum":1000000000000,"minimum":-1},"claimed_period":{"type":"integer","maximum":1000000000000,"minimum":0}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.002","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":"$0.002/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.002","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.002","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm__msWw_pYOw6UV7wcGF4Nt","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.002","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Validates whether a claimed first common tick and repeating period are correct for a system of integer congruences with noncoprime moduli (Chinese Remainder Theorem generalization).","exampleAgentPrompt":"I have three independent tick schedules: one fires at residue 3 mod 10, one at residue 5 mod 14, and one at residue 7 mod 21. Someone claims the first common tick is 143 and the period repeats every 210 steps — can you verify that?","exampleUseCases":[{"title":"Multi-agent schedule synchronization check","prompt":"We have two agents: agent A fires every 12 ticks starting at offset 4, and agent B fires every 15 ticks starting at offset 7. A colleague claims their first joint tick is at step 19 and they repeat every 60 ticks — please verify that claim."},{"title":"Noncoprime moduli CRT validation","prompt":"I need to verify a generalized CRT solution: I have congruences x ≡ 2 mod 6, x ≡ 3 mod 9, and x ≡ 5 mod 12. The claimed first solution is x=20 with period 36. Is that correct?"},{"title":"Periodic event co-occurrence audit","prompt":"Three sensors send pings on independent schedules: residue 1 mod 4, residue 3 mod 6, residue 5 mod 10. Someone says the first simultaneous ping is at tick 25 and they sync every 60 ticks after that — can you check if that's right?"}],"resultDescription":"Returns whether the claimed first common tick and claimed period are correct for the given set of congruences with potentially noncoprime moduli, along with the true first intersection tick and true repeating period (or a counterexample witness if the claim is wrong).","failureModes":["Residue exceeds modulus (residue must be < modulus)","No common intersection exists (system of congruences is inconsistent — no solution)","Claimed first tick is outside valid range","More than 32 congruence pairs provided","Modulus or residue out of allowed bounds (modulus 1–1000000, residue 0–999999)","claimed_period of 0 when a nonzero period exists"],"whenToPreferThis":"Use this endpoint when you need to verify or audit a claimed solution to a system of integer congruences where the moduli may share common factors (noncoprime), making standard CRT inapplicable. Ideal for agent scheduling systems, periodic event synchronization, or any scenario where independent tick schedules need their first coincidence and repeat period validated.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:40:17.161Z","isFirstParty":false,"canonicalSlug":"modular-phase-intersection-validator-f73d500f"}