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The presence of pseudo-differential Marcus noise necessitates new analytical tools, which we develop to control the delicate interaction between jump discontinuities and nonlocal operators.\n  We e"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"This application gives what appears to be the first positive answer to Shirikyan's open problem on the damped Euler equations on T^2 under genuinely mixed multiplicative noise. Furthermore, our framework goes beyond the original formulation of the problem: it resolves a substantially strengthened version in every dimension d≥2, on both T^d and R^d.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The pressure laws belong to a broad class (including piecewise Chaplygin-type laws and the white-dwarf equation of state) that permits a generalized Makino-type transformation while preserving the structure needed for classical solutions under the pseudo-differential noise.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Develops local classical solution theory for stochastic Euler equations with pseudo-differential Stratonovich/Itô and Marcus noise and establishes a criterion for invariant probability measures that resolves Shirikyan's open problem in the damped incompressible case across dimensions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Mixed continuous and discontinuous pseudo-differential noise yields local classical solutions to stochastic Euler equations and invariant measures for the damped incompressible case.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4757b482bcdf5b65e8bf5278d8fe696fd178747140fc9299d29c503f6f283595"},"source":{"id":"2605.16963","kind":"arxiv","version":1},"verdict":{"id":"be792bc9-42d3-475c-a84a-0001bd89e605","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:54:25.862400Z","strongest_claim":"This application gives what appears to be the first positive answer to Shirikyan's open problem on the damped Euler equations on T^2 under genuinely mixed multiplicative noise. Furthermore, our framework goes beyond the original formulation of the problem: it resolves a substantially strengthened version in every dimension d≥2, on both T^d and R^d.","one_line_summary":"Develops local classical solution theory for stochastic Euler equations with pseudo-differential Stratonovich/Itô and Marcus noise and establishes a criterion for invariant probability measures that resolves Shirikyan's open problem in the damped incompressible case across dimensions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The pressure laws belong to a broad class (including piecewise Chaplygin-type laws and the white-dwarf equation of state) that permits a generalized Makino-type transformation while preserving the structure needed for classical solutions under the pseudo-differential noise.","pith_extraction_headline":"Mixed continuous and discontinuous pseudo-differential noise yields local classical solutions to stochastic Euler equations and invariant measures for the damped incompressible case."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16963/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"cited_work_retraction","ran_at":"2026-05-19T19:51:57.937947Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T19:50:15.270050Z","status":"completed","version":"0.1.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.865393Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:01:00.464815Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.228955Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.314324Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ea3970d33a17c5a36e37236e965b724380001b629dca2dc7c1fa845a728209a9"},"references":{"count":101,"sample":[{"doi":"","year":2012,"title":"Abels.Pseudodifferential and singular integral operators: An Introduction with Applications","work_id":"aeef58cc-b7b6-4fb1-ac32-e60104609b56","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"S. 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