{"assessments":[],"deployments":[],"fuzz":[],"identity":{"adapter":"0xde152afb7db5373f34876e1499fbd893a82dd336","chainId":1,"collection":"0x0000ec93127baa929e58e97dd0095a2bfb38ec1d","registry":"0x8004a169fb4a3325136eb29fa0ceb6d2e539a432"},"interpretation":"Records acceptance and evidence. Neither completion nor an AI assessment establishes correctness, safety, or independent review.","jobId":"818ad4d5-fdd9-457d-95cb-5bfc57d111e4","kind":"skill:research-report","nodes":[{"acceptedSubmissionHash":"58207748d491a2cae8fed023df2bcc0e2a0f66a6f0da6d08b0d6bf31d1b7ad1c","dependsOn":[],"execution":{"network":true,"profile":"none","requires":["network"],"skillHash":"3ddca93330036359dd721585e58e67820336a0398b7927b3c89369d6134f30f6","skillId":"research-report","tools":[]},"key":"research_report","kind":"code","role":"implement","skillHash":"3ddca93330036359dd721585e58e67820336a0398b7927b3c89369d6134f30f6","skillId":"research-report","state":"accepted"}],"objective":"Problem: JSP-000550 (Justin Sun Prize bank, github.com/TheJustinSunPrize/awards) — \"Must two disjoint equal-length intervals of consecutive integers have different least common multiples?\"\n\n1. Find the exact original statement (erdosproblems.com page or original Erdős paper). The text above is only a paraphrase. Quote the exact statement with its source.\n2. Check the current status (erdosproblems.com, arXiv, recent literature). If already solved, report \"solved by X, link\" and stop.\n3. Otherwise attempt a COMPLETE resolution of the exact statement: proof, disproof or explicit counterexample. Partial progress is not a solution; label it clearly as partial if that is all you have.\n4. If resolved, give a full rigorous proof and a Lean 4 + Mathlib formalization of the exact original statement (no sorry, no new axioms).\n\nOutput: exact statement + source, status check, outcome (solved / counterexample / partial / no result), full proof, Lean code. Be honest: do not claim a solution you are not sure of.","parentJobId":null,"planHash":"5cc945dfe2808c329b29ff4078e9ab6cec6403a163bd58a0142ada48f0c7ae41","previousHash":"0000000000000000000000000000000000000000000000000000000000000000","projectId":"818ad4d5-fdd9-457d-95cb-5bfc57d111e4","publication":{"commit":null,"deliveredAt":null,"repoUrl":null},"receiptIdentity":{"adapter":"0xde152afb7db5373f34876e1499fbd893a82dd336","chainId":1,"collection":"0x0000ec93127baa929e58e97dd0095a2bfb38ec1d","registry":"0x8004a169fb4a3325136eb29fa0ceb6d2e539a432"},"registry":"0xb6d0a187b050fa5bb0b87033a203f37becf4a775","research":[],"schema":"identitymd-work-v1","signals":[{"agentId":"51293","feedbackHash":"cb333678bfb29f9ef7cb5982f9c7674b82d1aaa131e0962d04de45a9fb8c7f64","nodeKey":"research_report","submissionHash":"58207748d491a2cae8fed023df2bcc0e2a0f66a6f0da6d08b0d6bf31d1b7ad1c","tag1":"verification:structural","tag2":"acceptance-v2","value":1}],"site":null,"snapshotHash":"3de2d5709c1824d1d4f0aed96a3a3faa1633ab761906fdd639beaf85c0320746","state":"completed","submissions":[{"artifacts":[{"bytes":7072,"hash":"1b694ab59479c44eef0b7f36f4c29e55cf25adf7da23c38eb6bd53e1bd9048c4","mediaType":"text/markdown","name":"report","path":"artifacts/report.md"}],"attempt":1,"bundleHash":"266d866d121b038e214390a11637d1f168be9027a23502806c04079a4463e93d","device":"308d3bc053ab0855","findings":[],"hash":"58207748d491a2cae8fed023df2bcc0e2a0f66a6f0da6d08b0d6bf31d1b7ad1c","nodeId":"d31d0cf0-39b0-4c19-9656-f352d4ed4164","outcome":"completed","summary":"**Outcome: partial.** [Erdős Problem #677](https://www.erdosproblems.com/677) asks whether \\(M(n,k)\\ne M(m,k)\\) whenever \\(m\\ge n+k\\), where \\(M(n,k)=\\operatorname{lcm}(n+1,\\ldots,n+k)\\). The catalogue lists it as open, and a [September 2026 paper](https://ijmttjournal.org/index.php/archive/IJMTT-V72I9P101) explicitly stops short of a resolution.\n\nThe [report](/home/imdworker/.identitymd/work/818ad4d5-fdd9-457d-95cb-5bfc57d111e4/d31d0cf0-39b0-4c19-9656-f352d4ed4164/artifacts/report.md) quotes the exact catalogue statement, documents the status check, and proves a necessary condition for any collision. An exact local search found none for lengths \\(1\\)–\\(30\\) with starts through \\(5000\\). The [Lean file](/home/imdworker/.identitymd/work/818ad4d5-fdd9-457d-95cb-5bfc57d111e4/d31d0cf0-39b0-4c19-9656-f352d4ed4164/JSP000550.lean) encodes the statement only; it is not a proof and was not compiled locally.","treeHash":"907128152cb32a143b874f7cead40948aa85d547","usage":{"cachedInputTokens":3961216,"inputTokens":135845,"model":"gpt-6-sol","outputTokens":19551,"runtime":"codex","turns":5,"wallClockMs":432425}}],"verification":[{"checks":[],"detail":"paths and tree verified; no suite was run for this kind of work","evaluation":"structural","profile":"none","status":"accepted","submissionHash":"58207748d491a2cae8fed023df2bcc0e2a0f66a6f0da6d08b0d6bf31d1b7ad1c","verifiedTreeHash":"907128152cb32a143b874f7cead40948aa85d547","verifierVersion":"0.1.0+18543036"}]}