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Furthermore, we derive a simple"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under appropriate convexity and kernel assumptions, we establish the global existence of entropy weak solutions in L²(ℝ), together with two partial uniqueness results, in the L²-periodic setting and non-periodic setting with L¹(ℝ) kernel.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The convexity assumptions on the flux function and the specific regularity or positivity conditions imposed on the singular kernel (invoked in the abstract to obtain global existence and the Oleinik-type estimate).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Global existence of entropy weak solutions and partial uniqueness are established for scalar balance laws with singular nonlocal sources, plus an Oleinik-type estimate and a local smoothness/wave-breaking criterion.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Scalar nonlinear balance laws with singular nonlocal sources admit global entropy weak solutions in L2 under convexity and kernel conditions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c8083b1a8e2c2a08065420f07dd95897566c8856bff578b032bd1f78a849fc5b"},"source":{"id":"2605.17422","kind":"arxiv","version":1},"verdict":{"id":"5a54013e-ac93-4149-83e2-e597f0de09be","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:42:40.609351Z","strongest_claim":"Under appropriate convexity and kernel assumptions, we establish the global existence of entropy weak solutions in L²(ℝ), together with two partial uniqueness results, in the L²-periodic setting and non-periodic setting with L¹(ℝ) kernel.","one_line_summary":"Global existence of entropy weak solutions and partial uniqueness are established for scalar balance laws with singular nonlocal sources, plus an Oleinik-type estimate and a local smoothness/wave-breaking criterion.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The convexity assumptions on the flux function and the specific regularity or positivity conditions imposed on the singular kernel (invoked in the abstract to obtain global existence and the Oleinik-type estimate).","pith_extraction_headline":"Scalar nonlinear balance laws with singular nonlocal sources admit global entropy weak solutions in L2 under convexity and kernel conditions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17422/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.617525Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:52:12.461596Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.737083Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.683166Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c108489524d83b427cb14f8af4c42b90300d1830407d537b6bc7905e99fe948e"},"references":{"count":27,"sample":[{"doi":"","year":2012,"title":"F. 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